FIN531 201090 SG

FIN531Investment AnalysisFACULTY OF BUSINESS

Study Guide 201090

*FIN531*

Investments Analysis

FIN531 Study Guide

Faculty of Business

Written byRuhina Karim

Educational DesignerPauline Graf

Produced by Division of Learning and Teaching Services, Charles Sturt University, Albury - Bathurst - Wagga Wagga, New South Wales, Australia.

Revised June 1994Reprinted June 2001Revised July 2002, July 2003, July 2004, July 2005, July 2006, July 2007, July 2008Reprinted July 2009Revised September 2010

Printed at Charles Sturt University

© Charles Sturt University

Previously published material in this book is copied on behalf of Charles Sturt University pursuant to Part VB of the Commonwealth Copyright Act 1968.

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Contents

Page

Topic 1 Overview to investments 1

Topic 2 Securities-Markets and mechanics 10

Topic 3 Risk and return 16

Topic 4 Portfolio selection 30

Topic 5 Asset pricing models 38

Topic 6 Market efficiency 49

Topic 7 Fixed income securities 55

Topic 8 Security analysis 68

Topic 9 International diversification 75

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Topic 1 Overview to Investments

Topic 1 Overview to investments

Objectives

After completing this topic, you should be able to:

1. explain why people invest;

2. in broad terms, describe the significance of 'Risk-Return Trade-off';

3. describe the differences between Real and Financial Assets;

4. describe the participants who form the Financial System;

5. describe how the environment responds to clientele demands;

6. describe Markets and the Market Structure;

7. describe recent trends that have been occurring in the investment environment;

8. describe the relationship between the Household and Business Sectors;

9. describe the characteristics of Shares;

10. interpret share price data published in the financial press;

11. describe the various methods for calculating Stock Market Indices and be able to apply them.

Prescribed reading

Text: Chapter 1 The investment environmentChapter 2 Asset classes and financial instruments (pp. 42-56 inclusive)

Reading 1: S & P Understanding Indices

Reference websites

http://www.asx.com.au The Australian Stock Exchange (ASX)

Note: The purpose of these Study Guide notes is to direct, expand and illuminate the material covered in the text. The notes do not specifically refer to all sections of the text. If a section of the text is included in the Prescribed Reading, but not specifically mentioned in more detail in these notes, that section should still be covered. Furthermore, the Study Guide and Readings in many instances enhance materials covered in text.

Therefore, you must read all prescribed Readings as well as this Study Guide.

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http://www.asx.com.au/


Review questions

Text: Chapter 1 Problems 1-5, 7, 8Chapter 2 Problems 3, 4, 7-9, 11, 14, 15

Comments

This subject is called 'Investment Analysis', so we start with the question,

Why people invest?

Why would you invest if you can think of many ways to spend every dollar you earn or will ever earn?

The simple answer is,

Because almost always one's current income does not equal current consumption.

Hence, at any one point of time one has either a deficit or a surplus of funds. What would you do if there were a deficit? You may go without or you may try to borrow. What would you do if there were a surplus? You can do many things, but essentially a surplus should lead us to invest these funds.

Investment can be defined as:

The current commitment of funds for a period of time in order to derive a future flow of funds that will compensate the investor for:

The time the funds are committed The expected rate of inflation The uncertainty involved in the future flow of funds

Now consider, why do you think investors want to be compensated for each of these?

It is also then relevant to ask why one would study investments? In the twenty first century most of us have financial wealth of some nature or other, and must make investment decisions sometimes in our lives. It is our choice if we want to make an informed decision or a blind one. Choosing the first would require knowledge of investments, to what degree again is up to you. Interestingly, those who are at the forefront of developments in types of securities have not been accountants, lawyers or financiers BUT those who have an education based upon mathematics, the so-called rocket scientists.

The first two topics provide an overview of the broad area of investments and security analysis, and as such are fairly descriptive. For many students, depending upon your work and educational background, this will be old hat and you can skim through it if you wish.

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In the first topic you would gain an overview about securities markets and the various types of securities that are traded in those markets. Some of these specifics differ from country to country. The text provides an American perspective, but Reading 1 in this topic presents an Australian point of view. Students who are studying in other countries and / or are interested in the specifics of securities markets in other countries may find it helpful to contact their local security exchanges for more information.

Chapter 1 The Investment Environment

In Corporate Finance you have examined investment decisions involving Real Assets, such as, land, buildings and equipments that are used to produce goods and services. In Investment Analysis, we are concerned with examining investment decisions involving Financial Assets, which are claims to income generated by Real Assets.

So, what are the roles of financial assets and markets?

Firstly, financial assets and markets allow an individual or a firm to adjust consumption to achieve the highest level of satisfaction or utility. Secondly, they allow participants to shift risk to the parties that are most willing to bear that risk. Financial markets also allow the separation of ownership from management and increase the utilization of the assets of the economy.

In Australia, the Household Sector usually has a surplus - the only sector to do so. Thus it becomes a major source of funds for corporations, government and financial institutions. Although not mentioned in the Chapter, the Rest of the World has been a major supplier of funds to Australia leading to Australia's foreign debt problem.

In reviewing Financial Intermediation you should look at why financial intermediaries exist. Financial intermediaries meet the needs of investors by pooling small amounts of investment funds and investing those funds in an efficient fashion. They play a major role in moving funds from lenders to borrowers.

Financial intermediaries include banks, credit unions, mutual funds and insurance companies and have emerged in response to the need for a 'go between' to help both borrowers and lenders meet their needs. For example, if a firm wants to borrow $5m for 10 years, two alternative methods by which it can do this are:

1. Borrow money from a bank2. Knock on individual householders' doors asking if the occupant is willing to

lend some money to the firm

Alternative 'b' is obviously not practical, time consuming and an expensive exercise. Even if the borrower did raise enough funds, there is little chance that all the lenders would be willing to lend the money for the desired 10 years. This alternative is not likely to be successful.

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However, it does clearly demonstrate the advantages of financial intermediaries. Those with excess funds are able to deposit them with the financial intermediaries and those with insufficient funds can borrow from the financial intermediaries. It does not matter that the amounts and maturities of the deposits and loans do not match - it is the business of the financial intermediaries to manage that flow of funds (this is covered in later Finance subjects).

A sophisticated financial sector is essential for an economy to grow. Without it, as we have seen with the simple example above, the business sector cannot raise the funds that are necessary to finance production and expand the productive capacity of the economy.

One of the underlying concepts in Finance is that investors are risk averse. That is, investors will only take on more risk if they expect to be adequately compensated for it, in the form of a higher expected return. The Australian Reserve Bank produces many statistics in their Bulletin. Tables F.1 to F.3 give various interest rates ranging from the official cash rate to credit card rates. If you examined these Tables you would notice that the official cash rate has the lowest yield, whereas credit cards have the highest rates. Which do you think has more risk associated with it? Which do you think would therefore have higher rates? (If you said 'credit cards' in each case, then you are correct and can go to the top of the class.)

Significant innovation has taken place in the last few decades with the development of derivative securities. Derivative securities make is possible for firms to secure capital at the lowest possible cost and make it more efficient for firms to manage risk.

The financial system constantly innovates to minimize the costs associated with taxes and regulation. Examples of such innovation include the zero coupon bond and development of the Eurodollar market.

The chapter concludes with key trends in financial markets, globalisation, securitisation, financial engineering and communication networks.

Chapter 2 Asset classes and financial instruments

This chapter describes the financial instruments traded in the primary and secondary markets. At this stage some of these securities (such as, shares and bonds) will be revision from previous subjects, others however may be new to you (such as, options and futures). Do not worry at this stage if you do not completely follow the 'new' ones, as we will be returning to them at various stages throughout the subject.

It contains an overview discussion of money market, capital market instruments and derivative securities. The various market indexes that are used as indicators of 'the market' are also described. The chapter concludes with a discussion of options and futures.

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The Australian Financial Review and other financial press publishes large amounts of data on listed companies regularly, and of course vast amount of financial data is accessible via Internet.

Stock market indicators

Major market indices are designed to serve as a benchmark.

In Australia, The All Ordinaries Share Price Index (AOI or XAO) is based on 500 highest capitalised and most liquid companies listed on Australian stock exchange. There are also many sub-indices including the All Ordinaries Accumulation Index, Resource sectors, Industrial sectors, ASX20, ASX50, ASX100, ASX200, ASX300, small ordinaries. In Australia, unlike any other country, there are also 'Accumulation Indices'. These assume that any dividends are reinvested back into the company. Thus, these are an indication of total return. The current indices commenced in 31/12/70 with a base of 500.0 (Share Price Index) and 1000.0 (Accumulation Index).

Undoubtedly the most widely known Stock Market Indicator in the world is the Dow Jones. While this is a U.S. indicator you should still be conversant with it because of its significance. The Dow is based on share prices, whereas indices in Australia are calculated on a market value-weighted basis, as are the various S&P indices.

Reading 1, 'Understanding indices' provides a broad overview of how ASX indices are calculated and the regulations that determine whether or not a stock is included. This supplements your text giving an Australian point of view. It will also be a good idea to explore The Australian Stock Exchange (ASX) and The Sydney Futures Exchange (SFE) websites. It is an old resource but provides clear background knowledge. You should access more up to date information in ASX website.

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Answers to Review problems

Note: For qualitative questions you should use this as guidelines to develop your own answers incorporating examples, formulas, graphs (if applicable) and opinions.

Chapter 1

1. a. Cash is a financial asset because it is the liability of the federal government.

b. No. The cash does not directly add to the productive capacity of the economy.

c. Yes.

d. If the economy is already operating at full capacity, and you now command the additional purchasing power provided by the $10 billion, then your increased ability to purchase goods must be offset by a decrease in the ability of others to purchase goods. Thus, the other individuals in the economy can be made worse off by your discovery.

2. a. The bank loan is a financial liability for Lanni. (Lanni’s IOU is the bank’s financial asset). The cash Lanni receives is a financial asset. The new financial asset created is Lanni's promissory note (that is, Lanni’s IOU to the bank).

b. Lanni transfers financial assets (cash) to the software developers. In return, Lanni gets a real asset, the completed software. No financial assets are created or destroyed; cash is simply transferred from one party to another.

c. Lanni gives the real asset (the software) to Microsoft in exchange for a financial asset, 1,500 shares of stock in Microsoft. If Microsoft issues new shares in order to pay Lanni, then this would represent the creation of new financial assets.

d. Lanni exchanges one financial asset (1,500 shares of stock) for another ($120,000). Lanni gives a financial asset ($50,000 cash) to the bank and gets back another financial asset (its IOU). The loan is “destroyed” in the transaction, since it is retired when paid off and no longer exists.

3. a.Assets Liabilities &

Shareholders’ equity

Cash $ 70,000 Bank loan $ 50,000

Computers 30,000 Shareholders’ equity 50,000

Total $100,000 Total $100,000

Ratio of real to total assets = $30,000/$100,000 = 0.30

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b.Assets Liabilities &


Software product* $ 70,000 Bank loan $ 50,000


Total $100,000 Total $100,000

*Valued at cost

Ratio of real to total assets = $100,000/$100,000 = 1.0

c.Assets Liabilities &


Microsoft shares $120,000 Bank loan $ 50,000


Total $150,000 Total $150,000

Ratio of real to total assets = $30,000/$150,000 = 0.20Conclusion: when the firm starts up and raises working capital, it will be characterized by a low ratio of real to total assets. When it is in full production, it will have a high ratio of real assets. When the project “shuts down” and the firm sells it off for cash, financial assets once again replace real assets.

4. a. A fixed salary means that compensation is (at least in the short run) independent of the firm’s success. This salary structure does not tie the manager’s immediate compensation to the success of the firm. However, the manager might view this as the safest compensation structure and therefore value it more highly.

b. A salary that is paid in the form of stock in the firm means that the manager earns the most when the shareholders’ wealth is maximized. This structure is therefore most likely to align the interests of managers and shareholders. If stock compensation is overdone, however, the manager might view it as overly risky since the manager’s career is already linked to the firm, and this undiversified exposure would be exacerbated with a large stock position in the firm.

c. Call options on shares of the firm create great incentives for managers to contribute to the firm’s success. In some cases, however, stock options can lead to other agency problems. For example, a manager with numerous call options might be tempted to take on a very risky investment project, reasoning that if the project succeeds the payoff will be huge, while if it fails, the losses are limited to the lost value of the options. Shareholders, in contrast, bear the losses as well as the gains on the project, and might be less willing to assume that risk

5. Even if an individual shareholder could monitor and improve managers’ performance, and thereby increase the value of the firm, the payoff would be small, since the ownership share in a large corporation would be very

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small. For example, if you own $10,000 of GM stock and can increase the value of the firm by 5%, a very ambitious goal, you benefit by only (0.05 $10,000) = $500.

In contrast, a bank that has a multimillion-dollar loan outstanding to the firm has a big stake in making sure that the firm can repay the loan. It is clearly worthwhile for the bank to spend considerable resources to monitor the firm.

7. a. No. Diversification calls for investing your savings in assets that do well when GM is doing poorly.

b. No. Although Toyota is a competitor of GM, both are subject to fluctuations in the automobile market.

8. Unlike fixed salary contracts, bonuses create better incentives for executives to enhance the performance of the firm.

Chapter 2

3. a. You would have to pay the asked price of:112:05 = 112.15625% of par = $1,121.5625

b. The coupon rate is 5.625% implying coupon payments of $56.25 annually or, more precisely, $28.125 semiannually.

c. Current yield = (Annual coupon income/price)= $56.25/$1,121.5625 = 0.0502 = 5.02%

4. Preferred stock is like long-term debt in that it typically promises a fixed payment each year. In this way, it is a perpetuity. Preferred stock is also like long-term debt in that it does not give the holder voting rights in the firm.

Preferred stock is like equity in that the firm is under no contractual obligation to make the preferred stock dividend payments. Failure to make payments does not set off corporate bankruptcy. With respect to the priority of claims to the assets of the firm in the event of corporate bankruptcy, preferred stock has a higher priority than common equity but a lower priority than bonds.

7. The total before-tax income is $4. After the 70% exclusion for preferred stock dividends, the taxable income is: 0.30 x $4 = $1.20

Therefore, taxes are: 0.30 x $1.20 = $0.36After-tax income is: $4.00 – $0.36 = $3.64Rate of return is: $3.64/$40.00 = 9.1%

8. a. At t = 0, the value of the index is: (90 + 50 + 100)/3 = 80At t = 1, the value of the index is: (95 + 45 + 110)/3 = 83.333The rate of return is: (83.333/80)/ 1 = 4.17%

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b. In the absence of a split, Stock C would sell for 110, so the value of the index would be: 250/3 = 83.333

After the split, Stock C sells for 55. Therefore, we need to find the divisor (d) such that:83.333 = (95 + 45 + 55)/d d = 2.340

c. The return is zero. The index remains unchanged because the return for each stock separately equals zero.

9. a. Total market value at t = 0 is: ($9,000 + $10,000 + $20,000) = $39,000

Total market value at t = 1 is: ($9,500 + $9,000 + $22,000) = $40,500

Rate of return = ($40,500/$39,000) – 1 = 3.85%

b. The return on each stock is as follows:

rA = (95/90) – 1 = 0.0556rB = (45/50) – 1 = –0.10rC = (110/100) – 1 = 0.10

The equally-weighted average is: [0.0556 + (-0.10) + 0.10]/3 = 0.0185 = 1.85%

11. a. The higher coupon bond.

b. The call with the lower exercise price.

c. The put on the lower priced stock.

14. A put option conveys the right to sell the underlying asset at the exercise price. A short position in a futures contract carries an obligation to sell the underlying asset at the futures price.

15. A call option conveys the right to buy the underlying asset at the exercise price. A long position in a futures contract carries an obligation to buy the underlying asset at the futures price.

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Topic 2 Securities - Markets and mechanics

Topic 2 Securities-Markets and mechanics

Objectives


1. describe the primary and the secondary markets

2. describe the Options and Futures Derivative Markets

3. describe how securities are traded in the primary market;

4. what is the difference between direct and indirect investment?

5. discuss the importance of managed funds

Prescribed reading

Reading 2: Jones How securities are traded

Reading 3: Valentine Managed Funds

Reference websites

1. http://www.asx.com.au The Australian Stock Exchange (ASX)

Review problems

Text: Chapter 3 Problems 1-4, 8

Comments

Generally, there are two types of markets where financial assets can be traded, the primary and the secondary market.

Primary markets

The market in which assets are traded for the first time is known as the primary market. Typically in Australia, there is a lead underwriter, most likely a stockbroker. There will be a number of sub-underwriters, who could be other stockbrokers, merchant banks, life offices etc.

A relatively inexpensive and quick method of raising funds is Private Placements, which do not require a prospectus and is showing a rising trend in Australia.

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Secondary markets

Secondary markets are the markets in which securities are traded subsequent to their initial issue. The Australian Stock Exchange (ASX), Sydney Futures Exchange (SFE) and Over-the-counter (OTC) markets provide secondary markets in Australia.

The main products listed on the ASX include ordinary shares, preference shares, contributing shares, bonus issues, rights issues, company options, convertible notes, listed equity trusts, listed property trusts, bonds, debentures, exchange traded options and ASX warrants. Newspapers such as the Australian Financial Review and the Sydney Morning Herald report daily the trading details of all listed securities.

If you wish to obtain more information on the Australian securities and derivatives markets, I highly recommend the Australian Stock Exchange (ASX) publications. The ASX provides many excellent resources on the specifics of the stock market in Australia including its history, how it operates today, and an examination of the different financial instruments that are traded. These resources are available from the ASX in various formats including print based and also on a web site at http://www.asx.com.au.

Reading 2, 'How securities are traded' by Jones examines the Australian stock market and as such is a substitute for the chapter 3 of your text (You can of course also read chapter 3 of your text if you wish).

It is important to understand first the major aspects of brokerage transactions: what brokers do, what are the types of brokerage operations (full-service vs. discount vs. deep discount), how brokers are compensated, and how much they make annually.

In this context you also need to know the types of brokerage accounts, commissions, investing without a broker, how orders work, the types of orders, clearing procedures, using the Internet, and so forth. You may supplement your knowledge by any current relevant discussions in the popular press, where there are usually numerous interesting illustrations that can be given of brokerage costs, how orders work on the exchanges and in the OTC, market orders versus limit orders and margin lending.

In essence you can buy share by the following process:

1. Buyer instructs own adviser (broker) to buy shares.

2. Operator enters the buy order on SEATS.

3. SEATS matches buy and sell orders and executes trade.

4. Stockbroking firm sends contract note to buyer.

5. Buyer pays stockbroking firm within 3 business days after the transaction (T+3 rule).

6. Funds are transferred between stockbroking firms via CHESS.

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7. CHESS transfers shares electronically from selling stockbroker to buying stockbroker and notifies share registry.

8. Share registry issues new share certificate or holding statement to buyer.

9. CHESS transfers shares electronically from selling stockbroker to buying stockbroker and notifies share registry.

10. Share registry issues new share certificate or holding statement to buyer.

It is imperative to know and understand how investors can be protected in the markets. This covers not only federal legislation and the ASIC but also self-regulation by the stock exchanges, including the ASX's trading halts and the important role of the APRA in regulating brokers and dealers. In p.119, 'Industry Experience' details the trial of a former Macquarie Bank high-flyer for insider trading. You would have also read about the trial and conviction of Mr Rene Rivkin for insider trading.

Short sales

Short selling is the process of selling stocks that you do not already own.

Securities that may be short sold are called Approved Securities. It is permitted in Australia in specified blue-chip companies. However, a limit of 10% of the issued capital only can be short at any time. The uptick rule applies in Australia; that is, a share can only be sold short if the last change in the share price was an increase. A rule known as the 'T+3' settlement rule applies - it requires that the share scrip must be delivered within 3 days of any trade, or fail fees may be enforced. Some institutions 'lend' share scrip to investors to short sell. A short seller of a security, therefore, hopes the price will fall within these three days. There is also the margin cover, usually 20% of the value of trade, which must be obtained before placing the short sell order.

Also check ASX website at: http://www.asx.com.au

Now do relevant problems from your text, chapter 3.

Reading 3, 'Managed Funds' by Valentine examines the Australian managed funds market and as such is a substitute for the chapter 4 of your text (You can of course also read chapter 4 of your text if you wish).

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Chapter 3

1. a. In addition to the explicit fees of $70,000, FBN appears to have paid an implicit price in underpricing of the IPO. The underpricing is $3 per share, or a total of $300,000, implying total costs of $370,000.

b. No. The underwriters do not capture the part of the costs corresponding to the underpricing. The underpricing may be a rational marketing strategy. Without it, the underwriters would need to spend more resources in order to place the issue with the public. The underwriters would then need to charge higher explicit fees to the issuing firm. The issuing firm may be just as well off paying the implicit issuance cost represented by the underpricing.

2. a. In principle, potential losses are unbounded, growing directly with increases in the price of IBX.

b. If the stop-buy order can be filled at $78, the maximum possible loss per share is $8. If the price of IBX shares goes above $78, then the stop-buy order would be executed, limiting the losses from the short sale.

3. a. The stock is purchased for: (300 $40) = $12,000The amount borrowed is $4,000. Therefore, the investor put up equity, or margin, of $8,000.

b. If the share price falls to $30, then the value of the stock falls to $9,000. By the end of the year, the amount of the loan owed to the broker grows to:

($4,000 1.08) = $4,320.

Therefore, the remaining margin in the investor’s account is: ($9,000 $4,320) = $4,680.

The percentage margin is now: ($4,680/$9,000) = 0.52 = 52%.

Therefore, the investor will not receive a margin call.

c. The rate of return on the investment over the year is:(Ending equity in the account Initial equity)/Initial equity = ($4,680 $8,000)/$8,000 = 0.415 = 41.5%

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4. a. The initial margin was: (0.50 1,000 $40) = $20,000

As a result of the increase in the stock price, Old Economy Traders loses:($10 1,000) = $10,000. Therefore, margin decreases by $10,000. Moreover, Old Economy Traders must pay the dividend of $2 per share to the lender of the shares, so that the margin in the account decreases by an additional $2,000. Therefore, the remaining margin is: ($20,000 $10,000 $2,000) = $8,000

b. The percentage margin is: ($8,000/$50,000) = 0.16 = 16%Therefore, there will be a margin call.

c. The rate of return on the investment is:(Ending equity in the account Initial equity)/Initial equity = ($8,000 $20,000)/$20,000 = 0.60 = 60.0%

8. The total cost of the purchase is ($40 500) = $20,000. You borrow $5,000 from your broker, and invest $15,000 of your own funds. Your margin account starts out with net worth of $15,000.

a. (i) Net worth increases to: ($44 500) – $5,000 = $17,000Percentage gain = $2,000/$15,000 = 0.1333 = 13.33%

(ii) With price unchanged, net worth is unchanged.Percentage gain = zero

(iii) Net worth falls to ($36 500) – $5,000 = $13,000Percentage gain = –$2,000/$15,000 = –0.1333 = –13.33%

The relationship between the percentage change in the price of the stock and the investor’s percentage gain is given by:

% gain = % change in price

= % change in price 1.333

For example, when the stock price rises from $40 to $44, the percentage change in price is 10%, while the percentage gain for the investor is:

% gain = 10% = 13.33%

b. The value of the 500 shares is: 500PEquity is: (500P – $5,000)You will receive a margin call when:

= 0.25 when P = $13.33 or lower

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c. The value of the 500 shares is 500P. But now you have borrowed $10,000 instead of $5,000. Therefore, equity is: (500P – $10,000)You will receive a margin call when:

= 0.25 when P = $26.67

With less equity in the account, you are far more vulnerable to a margin call.

d. By the end of the year, the amount of the loan owed to the broker grows to:($5,000 1.08) = $5,400

The equity in your account is: (500P – $5,400)

Initial equity was $15,000. Therefore, your rate of return after one year is as follows:

(i) = 0.1067 = 10.67%

(ii) = –0.0267 = –2.67%

(iii) = –0.1600 = –16.00%

The relationship between the percentage change in the price of Rio Tinto and the investor’s percentage gain is given by:% gain =

For example, when the stock price rises from $40 to $44, the percentage change in price is 10%, while the percentage gain for the investor is:

=10.67%

e. The value of the 500 shares is: 500P

Equity is: (500P – $5,400)

You will receive a margin call when:

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= 0.25 when P = $14.40 or lower

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Topic 3 Risk and return


Objectives


1. describe the factors that determine interest rates

2. distinguish Real and Nominal Rates and calculate each

3. calculate Risk and Return of different instruments

4. interpret the historical rates and return over the twentieth century

5. discuss the significance of Risk and Utility and be able to calculate the Utility function

6. describe the effect of Asset Risk on Portfolio Risk and be able to calculate Portfolio Risk

7. describe the basic statistical measurements and properties that are used to develop portfolio theory

8. describe the effect of the introduction of the Risk Free Asset on Portfolio Risk and calculate the associated mathematics

9. describe Passive Investment Strategies based upon the Capital Market Line.

Prescribed reading

Text: Chapter 5 History of interest rate and risk premium Chapter 6Chapter 7

Risk and risk aversion Capital allocation between risky assets and the risk free asset

Portfolio Mathematics – Included at the end of this topic in your study guide.

Review problems

Text: Chapter 5 Problems 1, 3-5, 8, 11-17Chapter 6Chapter 7

Problems 1-5, 7-9, 10, 13-15Problems 1-4, 11-13, 18-23

Comments

This topic builds on your previous knowledge of Corporate Finance, and you should refresh your memory if required. The concepts covered in this topic and the next are very important for the rest of the subject and you should attempt to acquire clear understanding of them.

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Chapter 5 History of interest rate and risk premium

In making any investment decision, one needs to consider future interest rates. If these are perceived to be increasing, then one will require an increasing rate of return to compensate for this.

The first section of the chapter describes the major factors influencing the level of interest rates and discusses the Fisher Effect, examining real and nominal rates of return.

The second part of the chapter investigates holding period returns for different holding periods and presents information on historical risk/return data on different types of financial assets.

Chapter 6 Risk and risk aversion

This chapter presents statistical calculations of risk and returns measures, both ex post and ex ante. Note how one calculates 'Risk' and 'Return'. These calculations should be revision from Corporate Finance (FIN516) for you. In the literature there is some debate as to whether or not variance/standard deviation is an appropriate measure of risk. However, as it is almost universally used, we shall stay with it. Although your text does not examine the factors that determine risk premium, perhaps you should take a few moments to ponder what they may be. For example:

Business risk: uncertainty of income flows due to the nature of the firm's business. Such as, oil exploration vs. food retailer.

Financial risk: uncertainty caused by the method of financing the investment. Example, equity vs. debt.

Liquidity risk: how quickly can the investment by sold and at what price. Example, government securities vs. an antique.

Exchange rate risk: if investment is overseas, then movements in the exchange rate will affect the investment's return.

This chapter introduces the concepts of risk, risk measurement and the basic elements or concepts on which portfolio theory is built. A risk-averse investor will demand compensation for uncertainty or risk. A risk neutral investor will be willing to accept a fair bet or would be willing to analyse investments in terms of expected value. A risk seeking investor will take an unfair bet, that is, would be willing to take on an uncertain investment that has a lower expected value for the chance of securing a large profit.

In this context it is important to understand that Utility is a measure of an investor's welfare. The text includes examples (pp. 162 – 167) to calculate utility using the basic investment and indicates how the utility equation can be used to rank investments.

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It is important that you follow through (and work out the calculations yourself) all the rules of risky assets and portfolios Now go to end of this topic to Portfolio Mathematics, which you may find useful for revision. The initial part of this reading uses the historical data to calculate firstly the return and standard deviation. Work through those calculations. The second part of Portfolio Mathematics describes calculation of expected return and expected standard deviation using probability. The table layout in this reading is a simple way to apply equations presented in your textbook (pp. 168 - 172).

Chapter 7 Capital allocation between risky assets & risk free asset

It is important to understand the concept of allocating investment funds between risk-free and risk-less assets. Combining risk free assets (Treasury bills or money market mutual funds) with risky mutual fund portfolios operationalises the concepts of producing portfolios of acceptable risk/return trade-offs for various investors.

The mix of a portfolio can be varied in order to reduce risk of the portfolio and this develops the Capital Allocation Line, the line that depicts all risk-return combinations available to investors. You should note that the line is straight and that it indicates as the risk increases, so does the return. Once the CAL has been derived, utility theory can then be used to determine the optimal portfolio for the investor. This can be done either graphically or algebraically. However, do you think it is so simple in reality?

The last part of the chapter examines a passive investment policy based upon the Capital Market Line (CML), a special version of the CAL. You should note that there are investment funds around whose prime purpose is to mimic a broad based index, such as the All Ordinaries Index. This section examines the pros and cons of such a policy.

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Portfolio Mathematics

Portfolio mathematics refers to the calculations of various values including portfolio returns, standard deviations, covariance and correlations. The formulae used will depend upon whether you are calculating past values of return etc or expected future values. If you want to calculate past values, you will have the actual historic returns. If you want to calculate expected future values, you will need estimates of future outcomes, and the probability of each outcome occurring. The first section below uses past data, the second section uses expected future outcomes.

Historic Data

Suppose you are examining the historic performance of two companies, Gamma and Delta. Their returns for the past 6 years are given below:

year % returnGamma

% returnDelta

1998 12.0 17.0

1997 11.0 13.0

1996 8.0 9.0

1995 15.0 17.0

1994 10.0 7.0

1993 7.0 5.0

total 63.0 68.0

The arithmetic average return for Gamma is 63/6 = 10.5% The arithmetic average return for Delta is 68/ 6 = 11.3%

The following table calculates the historic standard deviation of returns for

Gamma:

year % return deviation deviation squared

1998 12.0 1.5 2.25

1997 11.0 0.5 0.25

1996 8.0 -2.5 6.25

1995 15.0 4.5 20.25

1994 10.0 -0.5 0.25

1993 7.0 -3.5 12.25

total 63.0 41.50

The columns in the table above are calculated as follows:

The column headed 'deviation' is the deviation of the actual return from the average return. Thus, for 1998 = 12% - 10.5% = 1.5%.

The column headed 'deviation squared' is the square of the 'deviation' column.

Thus, for 1998, 1.52 = 2.25.

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The specific details for calculating the variance and standard deviation of returns depends on whether we are treating our data as a sample of the firm's returns or as the whole population of the firm's returns. (This concept would have been covered in the pre-requisite statistics subject).

If we are treating the data as a sample (which would be the accurate method as we are only dealing with returns for six years), the variance is calculated as 'the sum of the last column divided by one less than the number of observations'. That is, 41.50 / 5 = 8.30 percent squared.

This is the table format of using the equation 5.17 for calculating variance using historical data:

The standard deviation is the square root of the variance and is therefore 8.30 = 2.88%.

If we are treating the data as a population, the variance is calculated as 'the sum of the last column divided by the number of observations'. That is, 41.50 / 6 = 6.92 percent squared. The standard deviation is the square root of the variance and is thus 6.92 = 2.63%.

The process of calculating the numbers for Delta is exactly the same. The sample variance and standard deviation are 26.27 percent squared and 5.13% respectively.

When doing any calculations, it is always helpful to have a 'feel' for the answers, to know what sort of answer to expect. Thus, if the calculated answer is different to our expectations, it could suggest that we have made an error. For example, if we look at the historic data for the two companies here, the returns for Delta seem to be more 'spread out' or 'varied' than those for Gamma. Thus we should expect the variance and standard deviation for Delta to be higher than those for Gamma, which they are.

Expected future outcomes

We can also calculate the expected returns, standard deviations, covariance and correlations using forecast data.

Suppose that the two firms Epsilon and Zeta have the following expected outcomes for the coming year:

state probability Epsilon expected% return

Zeta expected% return

outstanding 0.05 25 16very good 0.15 17 11good 0.3 13 6average 0.2 8 3poor 0.2 5 -1

very poor 0.1 -2 -4

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Again, when doing calculations, its good to have a 'feel' for the numbers. The first thing to do when working with probabilities is to check they add up to 100%, or 1. The total of column (1) is 1, so we have accounted for all possible 'states' and expected returns.

The following table uses the forecast returns for Epsilon:

(1) (2) (3) (4) (5) (6)

state probability

expected % return

(1) * (2) deviation (4) * (4) (5) * prob

outstanding 0.05 25 1.25 14.9 222.01 11.1005very good 0.15 17 2.55 6.9 47.61 7.1415good 0.3 13 3.9 2.9 8.41 2.523average 0.2 8 1.6 -2.1 4.41 0.882poor 0.2 5 1 -5.1 26.01 5.202very poor 0.1 -2 -0.2 -12.1 146.41 14.641

total 1 10.1 41.49

The total of column (3) is the overall expected return for Epsilon for the coming year. That is, Epsilon is expected to earn 10.1% next year.

Column (4) is the deviation of column (2) from the expected return. For example, for the 'outstanding' result, the deviation is 25 — 10.1 = 14.9%. Column (5) is column (4) squared.

Column (6) is column (5) times the probability of each outcome occurring (that is, column (1). The total of column (6) is the variance of the forecast returns for Epsilon, 41.49 percent squared.

So, the equation for variance using probability is:

The standard deviation is, as usual, the square root of the variance and is thus = 6.44%.

Similar calculations for Zeta would find an expected return of 4.25% and a variance of 27.2875 percent squared and a standard deviation of 5.22%.

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Chapter 5

1. For the money market fund, your holding period return for the next year depends on the level of 30-day interest rates each month when the fund rolls over maturing securities. The one-year savings deposit offers a 7.5% holding period return for the year. If you forecast that the rate on money market instruments will increase significantly above the current 6% yield, then the money market fund might result in a higher HPR than the savings deposit. The 20-year Treasury bond offers a yield to maturity of 9% per year, which is 150 basis points higher than the rate on the one-year savings deposit; however, you could earn a one-year HPR much less than 7.5% on the bond if long-term interest rates increase during the year. If Treasury bond yields rise above 9%, then the price of the bond will fall, and the resulting capital loss will wipe out some or all of the 9% return you would have earned if bond yields had remained unchanged over the course of the year.

3. a. The “Inflation-Plus” CD is the safer investment because it guarantees the purchasing power of the investment. Using the approximation that the real rate equals the nominal rate minus the inflation rate, the CD provides a real rate of 3.5% regardless of the inflation rate.

b. The expected return depends on the expected rate of inflation over the next year. If the expected rate of inflation is less than 3.5% then the conventional CD offers a higher real return than the Inflation-Plus CD; if the expected rate of inflation is greater than 3.5%, then the opposite is true.

c. If you expect the rate of inflation to be 3% over the next year, then the conventional CD offers you an expected real rate of return of 4%, which is 0.5% higher than the real rate on the inflation-protected CD. But unless you know that inflation will be 3% with certainty, the conventional CD is also riskier. The question of which one is the better investment then depends on your attitude towards risk versus return. You might choose to diversify and invest part of your funds in each.

d. No. We cannot assume that the entire difference between the risk-free nominal rate (on conventional CDs) of 7% and the real risk-free rate (on inflation-protected CDs) of 3.5% is the expected rate of inflation. Part of the difference is probably a risk premium associated with the uncertainty surrounding the real rate of return on the conventional CDs. This implies that the expected rate of inflation is less than 3.5% per year.

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4. E(r) = [0.35 44%] + [0.30 14%] + [0.35 (–16%)] = 14%2 = [0.35 (44 – 14)2] + [0 .30 (14 – 14)2] + [0.35 (–16 – 14)2] = 630 = 25.10%

The mean is unchanged, but the standard deviation has increased, as the probabilities of the high and low returns have increased.

5. Probability distribution of price and one-year holding period return for a 30-year U.S. Treasury bond (which will have 29 years to maturity at year’s end):

Economy Probability YTM PriceCapital

GainCouponInterest HPR

Boom 0.20 11.0% $ 74.05 $25.95 $8.00 17.95%

Normal Growth 0.50 8.0% $100.00 $ 0.00 $8.00 8.00%

Recession 0.30 7.0% $112.28 $12.28 $8.00 20.28%

11. a [The expected dollar return on the investment in equities is $18,000 compared to the $5,000 expected return for T-bills.]

12. b

13. d

14. c

15. b

16. b The probability that the economy will be neutral is 0.50, or 50%. Given a neutral economy, the stock will experience poor performance 30% of the time. The probability of both poor stock performance and a neutral economy is therefore:

0.30 0.50 = 0.15 = 15%

17. b

Chapter 6

1. a. The expected cash flow is: (0.5 $70,000) + (0.5 200,000) = $135,000

With a risk premium of 8% over the risk-free rate of 6%, the required rate of return is 14%. Therefore, the present value of the portfolio is:

$135,000/1.14 = $118,421

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b. If the portfolio is purchased for $118,421, and provides an expected cash inflow of $135,000, then the expected rate of return [E(r)] is derived as follows:

Therefore, E(r) = 14%. The portfolio price is set to equate the expected rate or return with the required rate of return.

c. If the risk premium over T-bills is now 12%, then the required return is:6% + 12% = 18%

The present value of the portfolio is now:$135,000/1.18 = $114,407

d. For a given expected cash flow, portfolios that command greater risk premia must sell at lower prices. The extra discount from expected value is a penalty for risk.

2. When we specify utility by U = E(r) – 0.005A, the utility level for T-bills is 7%. The utility level for the risky portfolio is: U = 12 – 0.005A 182 = 12 – 1.62A

In order for the risky portfolio to be preferred to bills, the following inequality must hold:12 – 1.62A > 7 A < 5/1.62 = 3.09

A must be less than 3.09 for the risky portfolio to be preferred to bills.

3. Points on the curve are derived by solving for E(r) in the following equation:U = 5 = E(r) – 0.005A = E(r) – 0.015

The values of E(r), given the values of , are therefore:

2 E(r)

0% 0 5.000%5% 25 5.375%

10% 100 6.500%

15% 225 8.375%

20% 400 11.000%

25% 625 14.375%

The bold line in the following graph (labeled Q3, for Question 3) depicts the indifference curve.

25


E (r)

5

4

U(Q 3,A=3)U(Q 4,A=4)

U(Q 5,A=0)

U(Q 6,A<0)

4. Repeating the analysis in Problem 3, utility is now:U = E(r) – 0.005A = E(r) – 0.020 = 4

The equal-utility combinations of expected return and standard deviation are presented in the table below. The indifference curve is the upward sloping line in the graph above, labeled Q4 (for Question 4).

2 E(r)

0% 0 4.000%5% 25 4.500%

10% 100 6.000%

15% 225 8.500%

20% 400 12.000%

25% 625 16.500%

The indifference curve in Problem 4 differs from that in Problem 3 in both slope and intercept. When A increases from 3 to 4, the increased risk aversion results in a greater slope for the indifference curve since more expected return is needed in order to compensate for additional . The lower level of utility assumed for Problem 4 (4% rather than 5%) shifts the vertical intercept down by 1%.

5. The coefficient of risk aversion for a risk neutral investor is zero. Therefore, the corresponding utility is equal to the portfolio’s expected return. The corresponding indifference curve in the expected return-standard deviation plane is a horizontal line, labeled Q5 in the graph above (see Problem 3).

7. c [Utility for each portfolio = E(r) – 0.005 4

We choose the portfolio with the highest utility value.]

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8. d [When investors are risk neutral, then A = 0; the portfolio with the highest utility is the one with the highest expected return.]

9. b

10. The portfolio expected return and variance are computed as follows:

(1)WBills

(2)rBills

(3)WIndex

(4)rIndex

rPortfolio

(1)(2)+(3)(4)Portfolio

(3) 20% 2

Portfolio

0.0 5% 1.0 13.5% 13.5% 20% 4000.2 5% 0.8 13.5% 11.8% 16% 2560.4 5% 0.6 13.5% 10.1% 12% 1440.6 5% 0.4 13.5% 8.4% 8% 640.8 5% 0.2 13.5% 6.7% 4% 161.0 5% 0.0 13.5% 5.0% 0% 0

13. Sugarcane is now less useful as a hedge. The probability distribution is as follows:

Normal Year for Sugar Abnormal Year

Bullish StockMarket

Bearish StockMarket

Probability 0.5 0.3 0.2Stock

Best Candy 25.0% 10.0% 25.0%

Sugarcane 10.0% 5.0% 20.0%

Humanex’s Portfolio 17.5% 2.5% 2.5%

Using the distribution of portfolio rate of return, the expected return and standard deviation are calculated as follows:

E(r p) = (0.5 17.5) + (0.3 2.5) + [0.2 (–2.5)] = 9.0%

p = [0.5 (17.5 – 9) 2 + 0.3 (2.5 – 9) 2 + [0.2 (–2.5 – 9) 2] 1/2 = 8.67%

While the expected return has improved somewhat, the standard deviation is now significantly greater, and only marginally better than investing half of the portfolio in T-bills.

14. The expected return for Best Candy is 10.5% and the standard deviation is 18.9%. The mean and standard deviation for Sugarcane are now:

E(r) = (0.5 10) + [0.3 (–5)] + (0.2 20) = 7.5%

= [ 0.5 (10 – 7.5) 2 – 0.3 (–5 – 7.5) 2 + 0.2 (20 – 7.5) 2] 1/2 = 9.01%

The covariance between Best Candy and Sugarcane is:Cov(rBest , rCane ) = [0.5(25 – 10.5)(10 – 7.5)] + [0.3(10 – 10.5)(–5 – 7.5)] + [0.2(–25 – 10.5)(20 –7.5)] = –68.75

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15. Using the results from Problem 14, the portfolio expected rate of return is computed as follows:

E(rp) = (0.5 10.5) + (0.5 7.5) = 9%

We can use Rule 5 to compute the portfolio standard deviation as follows:

Chapter 7

1. Expected return = (0.7 18%) + (0.3 8%) = 15%Standard deviation = 0.7 28% = 19.6%

2.Investment proportions: 30.0% in T-bills

0.7 25% = 17.5% in Stock A

0.7 32% = 22.4% in Stock B

0.7 43% = 30.1% in Stock C

3. Your reward-to-variability ratio:

Client's reward-to-variability ratio:

4.

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11. a. If the period 1926 - 2002 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(rM) rf = 8.22%, M = 20.81% (we use the standard deviation of the risk premium from Table 7.4). Then y* is given by:

That is, 47.45% of the portfolio should be allocated to equity and 52.55% should be allocated to T-bills.

b. If the period 1983 - 2002 is assumed to be representative of future expected performance, then we use the following data to compute the fraction allocated to equity: A = 4, E(rM) rf = 8.38%, M = 16.26% and y* is given by:

Therefore, 79.24% of the complete portfolio should be allocated to equity and 20.76% should be allocated to T-bills.

c. In part (b), the market risk premium is expected to be higher than in part (a) and market risk is lower. Therefore, the reward-to-variability ratio is expected to be higher in part (b), which explains the greater proportion invested in equity.

12. Assuming no change in risk tolerance, that is, an unchanged risk aversion coefficient (A), then higher perceived volatility increases the denominator of the equation for the optimal investment in the risky portfolio (Equation 7.5). The proportion invested in the risky portfolio will therefore decrease.

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13. a. E(rC) = 8% = 5% + y(11% – 5%)

b. C = yP = 0.50 15% = 7.5%

c. The first client is more risk averse, allowing a smaller standard deviation.

18. b

19. b

20. a(0.6 $50,000) + [0.4 ($30,000)] $5,000 = $13,000

21. b

22. c

Expected return for equity fund = T-bill rate + risk premium = 6% + 10% = 16%Expected return of client’s overall portfolio = (0.6 16%) + (0.4 6%) = 12%Standard deviation of client’s overall portfolio = 0.6 14% = 8.4%

23. a

Reward to variability ratio =

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Topic 4 Portfolio selection


Objectives


1. discuss the effect of naive diversification on portfolio risk;

2. calculate the return and risk of a portfolio;

3. discuss the effect of changing the weightings and correlations of portfolio assets;

4. calculate the weightings of assets in the minimum variance portfolio;

5. calculate the Optimal Risky Portfolio with Two Risky Assets and a Risk-Free Asset;

6. select the optimal portfolio using the efficient frontier.

7. determine the Optimal Portfolio where there are restrictions on the Risk Free Investment.

Prescribed reading

Text: Chapter 8 Optimal Risky Portfolios

Reading 4: Reilly The importance of asset allocation

Review problems

Text: Chapter 8 Problems 1-8, 21-27

Comments

This is a very important topic and you should ensure that you have mastered the concepts covered in this topic.

Chapter 8 Optimal risky portfolios

In our previous topic we examined how an investor chooses between risk-free assets and 'the' optimal portfolio of risky assets. In this topic we shall examine how that 'optimal portfolio of risky assets' should be selected.

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P. 218 examines naive diversification. One better example of this is to invest in an ice cream company and an umbrella company. Prima facie, the ice cream company will perform well in summer and the umbrella company in winter. As well, if the summer proves to be wet, the investor should have made up the lost income on the ice cream by extra umbrella sales. The question then obviously becomes: How many different stocks do we invest in? See Fig 8.2 (p. 219). This suggests that after a portfolio has, about 20 different stocks, the effect on risk of adding extra stocks is fairly minimal.

Some risk factors affect ALL stocks and thus by adding extra stocks, risk is not reduced. This risk is called market/systematic/non diversifiable risk. Obviously this poses the question: Why do super funds, life offices, equity trusts etc. invest in more than 20 stocks?

It is very important that you master how portfolio risk is calculated and the underlying concepts behind this calculation. Providing the correlation between two stocks is less than +1, by adding the second stock will have risk reduction benefits. In this context, Fig 8.5 (p. 227) is very important.

Section 8.5 (p. 240) allows you to use different excel functions to simplify the calculations helps you to create covariance matrix and efficient frontier.

Going back to Portfolio Mathematics (in topic-3) you can now calculate the covariance and correlation of returns for those shares.

Using Historical Data for shares Gamma and Delta:

(1) (2) (1) (2)

year Gamma deviation Delta deviation

1998 1.5 5.7 8.551997 0.5 1.7 0.851996 -2.5 -2.3 5.751995 4.5 5.7 25.651994 -0.5 -4.3 2.151993 -3.5 -6.3 22.05

total 65.0

Treating the data as a sample

Covariance = = 65/5 = 13

Correlation is the covariance divided by both standard deviations =

= 13 / (2.88 x 5.13) = 0.88

Remember that correlation is always between —1 and 1. A correlation of 0.88 thus indicates that the returns for the two firms move in a reasonably similar manner.

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Now, using probabilities and expected returns for shares Epsilon and Zeta the covariance of the expected returns is calculated using the table below:

(1) (2) (3) (1) (2) (3)

state probability Epsilon deviation

Zeta deviation

outstanding 0.05 14.9 11.75 3.75very good 0.15 6.9 6.75 6.98625good 0.3 2.9 1.75 1.5225average 0.2 -2.1 -1.25 0.525poor 0.2 -5.1 -5.25 5.355very poor 0.1 -12.1 -8.25 9.9825

total 1 5.4 5.5 33.125

The total of the last column is the covariance, that is,

= 33.125.

The correlation is again the covariance divided by both standard deviations:

= 33.125 / (6.44 5.22) = 0.9854.

Since the correlation can only be between -1 and 1, a correlation of 0.9854 indicates the two firms are expected to move in a very similar way.

Can you now work out the minimum-variance portfolio using the above pairs of shares? What would be their weights in MVPs? What would be the expected returns and the risks of these portfolios?

In this context you should now read Reading 4 The importance of asset allocation by Reilly and Norton. It introduces this important concept, which will be examined more thoroughly in last topic Portfolio Management and Evaluation.

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Chapter 8

1. The parameters of the opportunity set are:

E(rS) = 20%, E(rB) = 12%, S = 30%, B = 15%,

From the standard deviations and the correlation coefficient we generate the covariance matrix [note that Cov(rS, rB) = SB]:

Bonds StocksBonds 225

4Stocks 459

The minimum-variance portfolio is computed as follows:

wMin(S) =

wMin(B) = 1 0.1739 = 0.8261

The minimum variance portfolio mean and standard deviation are:E(rMin) = (0.1739 20) + (0.8261 12) 13.39%

Min =

2.Proportion

in stock fundProportion

in bond fundExpected

returnStandardDeviation

0.00% 100.00% 12.00% 15.00%17.39% 82.61% 13.39% 13.92% minimum variance20.00% 80.00% 13.60% 13.94%40.00% 60.00% 15.20% 15.70%45.16% 54.84% 15.61% 16.54% tangency portfolio60.00% 40.00% 16.80% 19.53%80.00% 20.00% 18.40% 24.48%

100.00% 0.00% 20.00% 30.00%

Graph shown on next page.

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3.

The graph indicates that the optimal portfolio is the tangency portfolio with expected return approximately 15.6% and standard deviation approximately 16.5%.

4. The proportion of the optimal risky portfolio invested in the stock fund is given by:

The mean and standard deviation of the optimal risky portfolio are:\

E(rP) = (0.4516 20) + (0.5484 12) = 15.61%

p = [(0.45162 900) + (0.54842 225) + (2 0.4516 0.5484 45)]1/2

= 16.54%

5. The reward-to-variability ratio of the optimal CAL is:

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6. a. If you require that your portfolio yield an expected return of 14%, then you can find the corresponding standard deviation from the optimal CAL. The equation for this CAL is:

Setting E(rC) equal to 14%, we find that the standard deviation of the optimal portfolio is 13.04%.

b. To find the proportion invested in the T-bill fund, remember that the mean of the complete portfolio (i.e., 14%) is an average of the T-bill rate and the optimal combination of stocks and bonds (P). Let y be the proportion invested in the portfolio P. The mean of any portfolio along the optimal CAL is:

E(rC) = (l y)rf + yE(rP) = rf + y[E(rP) rf] = 8 + y(15.61 8)

Setting E(rC) = 14% we find: y = 0.7884 and (1 y) = 0.2116 (the proportion invested in the T-bill fund).

To find the proportions invested in each of the funds, multiply 0.7884 times the respective proportions of stocks and bonds in the optimal risky portfolio:

Proportion of stocks in complete portfolio = 0.7884 0.4516 = 0.3560Proportion of bonds in complete portfolio = 0.7884 0.5484 = 0.4324

7. Using only the stock and bond funds to achieve a portfolio expected return of 14%, we must find the appropriate proportion in the stock fund (wS) and the appropriate proportion in the bond fund (wB = 1 wS) as follows:

14 = 20wS + 12(1 wS) = 12 + 8wS wS = 0.25So the proportions are 25% invested in the stock fund and 75% in the bond fund. The standard deviation of this portfolio will be:

P = [(0.252 900) + (0.752 225) + (2 0.25 0.75 45)]1/2 = 14.13%This is considerably greater than the standard deviation of 13.04% achieved using T-bills and the optimal portfolio.

8. With no opportunity to borrow you wish to construct a portfolio with an expected return of 24%. Since this exceeds the expected return for the stock fund, you will have to sell short the bond fund, which has an expected return of 12%, and use the proceeds to buy additional stock. The graphical representation of your risky portfolio is point Q on the following graph:

Point Q is the stock/bond combination with expected return equal to 24%. Let wS equal the proportion invested in the stock fund and (1 wS ) equal the proportion invested in the bond fund required to achieve the 24% mean. Then:

36


24 = [20 wS] + [12 (1 wS)] = 12 + 8wS

wS = 1.50 and 1 wS = .50

Therefore, you would have to sell short an amount of the bond fund equal to 0.50 of your total funds, and then invest 1.50 times your total funds in stocks. The standard deviation of this portfolio would be:

Q = {[1.502 900] + [(.50)2 225] + [2 1.50 (.50) 45]}1/2 = 44.87%

If you were allowed to borrow at the risk-free rate (8%), then, in order to achieve the target expected return of 24% you would invest more than 100% of your funds in the optimal risky portfolio. On the following graph, this would be represented by moving out along the CAL to the right of P, to point R.

R is the point on the optimal CAL that has expected return equal to 24%. Using the formula for the optimal CAL we can find the corresponding standard deviation:

E(rC) = 8 + 0.4601C = 24 C = 34.78%

This standard deviation is considerably less than the 44.87% standard deviation for the portfolio created above without the ability to borrow at the risk-free rate.

What is the portfolio composition of point R on the optimal CAL? The mean of any portfolio along this CAL is: E(rC) = rf + y[E(rP) rf]

where y is the proportion invested in the optimal risky portfolio P, and E(rP) is the mean of that portfolio (15.61%). Substituting in the above equation, we have:24 = 8 + y(15.61 8) y = 2.1025

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This means that for every $1 of your own funds invested in portfolio P, you would borrow an additional $1.1025 and also invest the borrowed funds in portfolio P.

21. d. Portfolio Y cannot be efficient because it is dominated by another portfolio. For example, Portfolio X has both higher expected return and lower standard deviation.

22. c.

23. d.

24. b.

25. a.

26. c.

27. Since we do not have any information about expected returns, we focus exclusively on reducing variability. Stocks A and C have equal standard deviations, but the correlation of Stock B with Stock C (0.10) is less than that of Stock A with Stock B (0.90). Therefore, a portfolio comprised of Stocks B and C will have lower total risk than a portfolio comprised of Stocks A and B.

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Topic 5 Asset pricing models


Objectives


1. discuss the Capital Asset Pricing Model, including its development.

2. draw and interpret the SML;

3. discuss the CAPM with restricted borrowing, and multi-period investment horizon;

4. discuss how one can reduce the amount of firm-specific risk in the portfolio by combining securities with differing patterns of returns;

5. discuss how Arbitrage Profits may be earned, using examples;

6. calculate the rate of return, based upon an APT model;

7. compare and contrast CAPM and APT.

Prescribed reading

Text: Chapter 9 The Capital Asset Pricing Model (pp. 276-291 inclusive)

Chapter 10 Index ModelChapter 11 Arbitrage pricing theory and multifactor models of risk

and return

Review problems

Text: Chapter 9 Problems 1-5, 21-29Chapter 10 Problems 5-11, 16-19Chapter 11 Problems 4-7, 13-19

Comments

Chapter 9 The Capital Asset Pricing Model

This topic examines one of the more controversial topics in Finance today - the Capital Asset Pricing Model, usually abbreviated to CAPM, which is an equilibrium model for the pricing of assets based upon risk. CAPM rules out the possibility of arbitrage profits, that is, the exploitation of misprised securities.

Pp. 276-277 examines the assumptions upon which CAPM is based. On p. 277, the

formula for Beta is introduced. Again, this measure forms one of the

underlying concepts in Finance.

The simplified two-security example that develops the concept of demand for shares and how prices of securities would change with changes in demand should

39


be easy to understand. The presentation includes the assumptions that underlie the CAPM, major implications of model and development of the Security Market Line.

Read carefully the 'covariance matrix' discussed on p. 280, especially the equations on pp. 281-282, which are important.

P. 284 introduces The Security Market Line (SML). Given the relevant measure of risk is the risk that is related to the market portfolio, the Security Market Line describes that relationship. The slope of the SML is the market risk premium. The beta for the individual security can be calculated as the [Cov (ri,rm)] / Var rm.

It is important to compare the SML with the CML. Fig. 9.3 on p. 285 illustrates how the SML/CAPM can be used to determine if a stock is over/under priced. The example in text shows a security that is underpriced, offering a higher rate of return that is appropriate for its level of risk. If the condition were to exist, as investors sought to acquire the security, its price would rise and its return would decrease to levels consistent with the SML. This should be revision for you from Corporate Finance (FIN516).

The concept of using CAPM in accounting for risk (Risk Adjusted Discount Rate) in Capital Budgeting is also introduced. This is examined in much more detail in future finance subjects.

Section 9.2 Extensions of the CAPM, examines the effects of relaxing some of those assumptions made on pp. 276-277. Thus, we end up with a more realistic model.

However, remember just because a model is not realistic does not mean that it should be disregarded. It, in fact, may be very useful in examining reality, perhaps leading to a greater understanding of how 'reality' operates. Make sure you understand all the review questions.

You only need to understand conceptually about liquidity costs at this stage. So, only read up to p. 291.

Nevertheless, you should also read the summary in pp. 297 – 298.

Chapter 10 Index models

The single factor index model predicts stock returns based upon both the firm specific (also called non systematic/ diversifiable risk) and market risks (also called systematic/non diversifiable risk) of the security. Adding more securities to the portfolio may eliminate firm-specific risk. The desired level of market risk is obtained by manipulating the asset allocations of the risky securities in the portfolio.

Portfolio systematic risk is a weighted average of the betas of the securities in the portfolios, where weights are the asset allocation percentages. Furthermore, if the portfolio is adequately diversified, then firm-specific (or non systematic) risk can be virtually eliminated (hence called diversifiable), and thus beta (systematic or market risk) becomes the relevant risk measure of the portfolio (as it is non diversifiable).

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Section 10.3 in pp 323 - 328 presents the industry version of Index Model used extensively. You may find the section on predicting beta coefficients helpful in exploring the issues related to estimating the coefficients and the statistical significance of the beta and alpha coefficients.

Chapter 11 Arbitrage pricing theory and multifactor models of risk and return

Arbitrage Pricing Theory (APT) developed as a result of irregularities discovered with CAPM.

CAPM claims that risk is represented by one factor, b. APT postulates that various risk factors affecting the return of a security and these risk factors may vary from one stock to the next. Thus, in order to arrive at the theoretical return of a stock, one needs to know which risk factors affect it and the strength of each factor. Thus, it incorporates a much more complex view of risk than CAPM.

The arbitrage-pricing framework rules out the possibility of arbitrage profits, that is, the exploitation of misprised securities. Arbitrage opportunities exist if an investor can construct a zero investment portfolio with a sure profit. If such opportunities exist, an investor can take large positions to secure riskless profits. In efficient markets if profitable arbitrage opportunities exist traders will take positions to secure the riskless profit and we should expect such opportunities to disappear quite quickly. Therefore, Arbitrage pricing theory uses a no-arbitrage argument to derive the same expected return/risk relationship introduced before.

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Chapter 9 The Capital Asset Pricing Model

1. E(rP) = rf + b P [E(rM ) – rf ]

18 = 6 + b P(14 – 6) b P = 12/8 = 1.5

2. If the security’s correlation coefficient with the market portfolio doubles (with all other variables such as variances unchanged), then beta, and therefore the risk premium, will also double. The current risk premium is: 14 – 6 = 8%

The new risk premium would be 16%, and the new discount rate for the security would be:

16 + 6 = 22%

If the stock pays a constant perpetual dividend, then we know from the original data that the dividend (D) must satisfy the equation for the present value of a perpetuity:

Price = Dividend/Discount rate

50 = D/0.14 D = 50 0.14 = $7.00

At the new discount rate of 22%, the stock would be worth: $7/0.22 = $31.82

The increase in stock risk has lowered its value by 36.36%.

3. The appropriate discount rate for the project is:

rf + b[E(rM ) – rf ] = 8 + [1.8 (16 – 8)] = 22.4%

Using this discount rate:

Annuity factor (22.4%, 10 years)]

= $18.09

The internal rate of return (IRR) for the project is 35.73%. Recall from your introductory finance class that NPV is positive if IRR > discount rate (or, equivalently, hurdle rate). The highest value that beta can take before the hurdle rate exceeds the IRR is determined by:

35.73 = 8 + b(16 – 8) b = 27.73/8 = 3.47

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4. a. False. b = 0 implies E(r) = rf , not zero.

b. False. Investors require a risk premium only for bearing systematic (undiversifiable or market) risk. Total volatility includes diversifiable risk.

c. False. Your portfolio should be invested 75% in the market portfolio and 25% in T-bills. Then:bP = (0.75 1) + (0.25 0) = 0.75

5. a. Call the aggressive stock A and the defensive stock D. Beta is the sensitivity of the stock’s return to the market return, i.e., the change in the stock return per unit change in the market return. Therefore, we compute each stock’s beta by calculating the difference in its return across the two scenarios divided by the difference in the market return:

b. With the two scenarios equally likely, the expected return is an average of the two possible outcomes:

E(rA ) = 0.5 (–2 + 38) = 18%

E(rD ) = 0.5 (6 + 12) = 9%

c. The SML is determined by the market expected return of [0.5(25 + 5)] = 15%, with a beta of 1, and the T-bill return of 6% with a beta of zero. See the following graph.

The equation for the security market line is:

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E(r) = 6 + b(15 – 6)

d. Based on its risk, the aggressive stock has a required expected return of:

E(rA ) = 6 + 2.0(15 – 6) = 24%

The analyst’s forecast of expected return is only 18%. Thus the stock’s alpha is:

A = actually expected return – required return (given risk)

= 18% – 24% = –6%

Similarly, the required return for the defensive stock is:

E(rD) = 6 + 0.3(15 – 6) = 8.7%

The analyst’s forecast of expected return for D is 9%, and hence, the stock has a positive alpha:

D = actually expected return – required return (given risk)

= 9 – 8.7 = +0.3%

The points for each stock plot on the graph as indicated above.

e. The hurdle rate is determined by the project beta (0.3), not the firm’s beta. The correct discount rate is 8.7%, the fair rate of return for stock D.

21. a.

22. d. From CAPM, the fair expected return = 8 + 1.25(15 8) = 16.75%Actually expected return = 17% = 17 16.75 = 0.25%

23. d.

24. c.

25. d.

26. d. [You need to know the risk-free rate]

27. d. [You need to know the risk-free rate]

28. Under the CAPM, the only risk that investors are compensated for bearing is the risk that cannot be diversified away (systematic risk). Because systematic risk (measured by beta) is equal to 1.0 for both portfolios, an investor would expect the same rate of return from both portfolios A and B. Moreover, since both portfolios are well diversified, it doesn’t matter if the specific risk of the individual securities is high or low. The firm-specific risk has been diversified away for both portfolios.

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29. a. McKay should borrow funds and invest those funds proportionately in Murray’s existing portfolio (i.e., buy more risky assets on margin). In addition to increased expected return, the alternative portfolio on the capital market line will also have increased risk, which is caused by the higher proportion of risky assets in the total portfolio.

b. McKay should substitute low beta stocks for high beta stocks in order to reduce the overall beta of York’s portfolio. By reducing the overall portfolio beta, McKay will reduce the systematic risk of the portfolio, and therefore reduce its volatility relative to the market. The security market line (SML) suggests such action (i.e., moving down the SML), even though reducing beta may result in a slight loss of portfolio efficiency unless full diversification is maintained. York’s primary objective, however, is not to maintain efficiency, but to reduce risk exposure; reducing portfolio beta meets that objective. Because York does not want to engage in borrowing or lending, McKay cannot reduce risk by selling equities and using the proceeds to buy risk-free assets (i.e., lending part of the portfolio).

Chapter 10 Index Model

5. The standard deviation of each stock can be derived from the following equation for R2:

Therefore:

For stock B:

6. The systematic risk for A is:

The firm-specific risk of A (the residual variance) is the difference between A’s total risk and its systematic risk: = 980 – 196 784

The systematic risk is:

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B’s firm-specific risk (residual variance) is:

4800 – 576 4224

7. The covariance between the returns of A and B is (since the residuals are assumed to be uncorrelated):

The correlation coefficient between the returns of A and B is:

8. Note that the correlation is the square root of R2:

Cov(rA,rM ) = AM = 0.201/2 31.30 20 = 280

Cov(rB,rM ) = BM = 0.121/2 69.28 20 = 480

9. The non-zero alphas from the regressions are inconsistent with the CAPM. The question is whether the alpha estimates reflect sampling errors or real mispricing. To test the hypothesis of whether the intercepts (3% for A, and –2% for B) are significantly different from zero, we would need to compute t-values for each intercept.

10. For portfolio P we can compute:

P = [(0.62 980) + (0.42 4800) + (2 0.4 0.6 336]1/2

= [1282.08]1/2 = 35.81%

b P = (0.6 0.7) + (0.4 1.2) 0.90

Cov(rP,rM ) = bP

This same result can also be attained using the covariances of the individual stocks with the market:

Cov(rP,rM ) = Cov(0.6rA + 0.4rB, rM ) = 0.6Cov(rA, rM ) + 0.4Cov(rB,rM )= (0.6 280) + (0.4 480) = 360

11. Note that the variance of T-bills is zero, and the covariance of T-bills with any asset is zero. Therefore, for portfolio Q:

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16. c. The R2 of the regression is: 0.702 = 0.49Therefore, 51% of total variance is unexplained by the market; this is nonsystematic risk.

17. b. 9 = 3 + b (11 3) b = 0.75

18. d.

19. b.

Chapter 11 APT & multifactor models of risk and return

4. a. This statement is incorrect. The CAPM requires a mean-variance

efficient market portfolio, but APT does not.

b. This statement is incorrect. The CAPM assumes normally distributed security returns, but APT does not.

c. This statement is correct.

5. Substituting the portfolio returns and betas in the expected return-beta relationship, we obtain two equations with two unknowns, risk-free rate (rf ) and factor risk premium (RP):

12 = rf + (1.2 RP)9 = rf + (0.8 RP)

Solving these equations, we obtain:rf = 3% and RP = 7.5%

6. a. Shorting an equally-weighted portfolio of the ten negative-alpha stocks and investing the proceeds in an equally-weighted portfolio of the ten positive-alpha stocks eliminates the market exposure and creates a zero-investment portfolio. Denoting the systematic market factor as RM , the expected dollar return is (noting that the expectation of non-systematic risk, e, is zero):

$1,000,000 [0.02 + (1.0 RM )] $1,000,000 [(–0.02) + (1.0 RM )]

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= $1,000,000 0.04 = $40,000

The sensitivity of the payoff of this portfolio to the market factor is zero because the exposures of the positive alpha and negative alpha stocks cancel out. (Notice that the terms involving RM sum to zero.) Thus, the systematic component of total risk is also zero. The variance of the analyst’s profit is not zero, however, since this portfolio is not well diversified.

For n = 20 stocks (i.e., long 10 stocks and short 10 stocks) the investor will have a $100,000 position (either long or short) in each stock. Net market exposure is zero, but firm-specific risk has not been fully diversified. The variance of dollar returns from the positions in the 20 stocks is:

20 [(100,000 0.30)2 ] = 18,000,000,000The standard deviation of dollar returns is $134,164.

b. If n = 50 stocks (25 stocks long and 25 stocks short), the investor will have a $40,000 position in each stock, and the variance of dollar returns is:50 [(40,000 0.30)2 ] = 7,200,000,000

The standard deviation of dollar returns is $84,853.

Similarly, if n = 100 stocks (50 stocks long and 50 stocks short), the investor will have a $20,000 position in each stock, and the variance of dollar returns is:100 [(20,000 0.30)2 ] = 3,600,000,000

The standard deviation of dollar returns is $60,000.

Notice that, when the number of stocks increases by a factor of 5 (i.e., from 20 to 100), standard deviation decreases by a factor of = 2.23607 (from $134,164 to $60,000).

7 a.

b. If there are an infinite number of assets with identical characteristics, then a well-diversified portfolio of each type will have only systematic risk since the non-systematic risk will approach zero with large n. The mean will equal that of the individual (identical) stocks.

c. There is no arbitrage opportunity because the well-diversified portfolios all plot on the security market line (SML). Because they are fairly priced, there is no arbitrage.

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13. b. Since Portfolio X has b = 1.0, then X is the market portfolio and E(RM) =16%. Using E(RM ) = 16% and rf = 8%, the expected return for portfolio Y is not consistent.

14. c.

15. d.

16. d.

17. c. Investors will take on as large a position as possible only if the mispricing opportunity is an arbitrage. Otherwise, considerations of risk and diversification will limit the position they attempt to take in the mispriced security.

18. d.

19. d.

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Topic 6 Market efficiency


Objectives


1. describe Random Walks and the Efficient Market Hypothesis;

2. discuss the implications of the EMH for Investment Policy;

3. describe the Event Studies that have been carried out;

4. discuss whether Markets are efficient;

5. identify the key errors made by individuals in processing information and the biases uncovered by psychologists.

6. understand the types of technical indicators that are used in the market and how such indicators are used by investors.

7. describe the tests that have been carried out with regard to the Multifactor CAPM and APT;

8. understand Roll's critique;

9. understand the Fama-French Three-factor Model.

Prescribed reading

Text: Chapter 12 Market Efficiency and Behavioural FinanceChapter 13 Empirical evidence on security return

Review problems

Text: Chapter 12 Problems 6-12Chapter 13 Problems 12-14

Comments

Security market research is probably the most researched area in Accounting/Finance/Economics but what have the results been? While the latter question may not be completely answered in this Topic, you will certainly gain an overview of the volume and type of work that has been done.Chapter 12 Market Efficiency and Behavioural Finance

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For many years, investors, brokers etc. had wondered whether or not one could predict future share prices and thus earn predictable returns. This Chapter examines the multitudinous research that has been carried out in this area. Note the early example in 12.1 that suggests that in order to make consistently abnormal returns, one would have to have prior access to information, and act upon it before anyone else.

Make sure you have a good understanding of the Efficient Market Hypothesis (EMH). The concept of market efficiency is related to the concept of competition. In efficient markets, once information becomes available, participants will trade quickly on that information. Competition assures that prices will reflect that information very quickly. If the information does not become incorporated into price very quickly, market participants would act to eliminate the inefficiency.

There are three forms of market efficiency. In a weak form efficient market, prices will reflect all information that can be derived from trading data such as prices and volumes. In a semi-strong form market, prices will reflect all publicly available information regarding the firm's prospects. In a strong form market, prices would reflect all information relevant to the firms' prospects, even inside information.

Much of the remainder of the Chapter examines research into these three areas.

If markets are semi-strong form efficient, fundamental analysis should not result in consistent superior profits. Fundamental Analysis involves using information on the economy as well as information such as earning trends and profit trends to find undervalued securities.

Lastly, if markets are efficient, investors would tend to employ passive strategies such as buying indexed funds or employing a buy and hold strategy. Active management such as security analysis or attempting to time the market would not result in consistently superior profits if markets were efficient.

The section on 'Event Studies', p. 375 examine the pattern of prices, more usually 'Cumulative Abnormal Return', around the time an important event such as, earnings announcements, dividend announcements, bonus issues announcements and so forth. However, one may be able to make Abnormal Returns prior to the announcement date, but not after the date.

Obviously, much research has been carried out to determine whether or not one can use information to generate abnormal returns. We shall concentrate on a selection, only.

Returns over short horizons - this research tends to support the efficiency of the stock market at the weak level.

The small-firm effect: - the end of year effect (TOY) research has been replicated in Australia. It has been hypothesised that tax-loss selling causes this effect. Thus, in Australia, it should occur during July, as most companies have a tax year ending in June. But no, the effect has been observed to occur at the beginning of January, as well!!!

Market-to-book ratios: in particular see the last sentence in the first paragraph.

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Day-of-the-week effect: very similar to the 'end of year' effect. Note last sentence. This comment could be applied to many other anomalies. Can you think of why this anomaly might exist?

Inside information: while empirical work indicates that insiders may earn abnormal returns, the returns are not sufficient for 'outsiders' to profit from this knowledge.

Mutual fund performance: in the marketplace there are a large number of professional fund managers being paid to manage funds, give investment advice etc. Accordingly, one would imagine that the funds that they manage consistently earn abnormal returns. The vast majority of research indicates otherwise. Even fund managers who generate above abnormal returns in one year are unlikely to continue such performance.

Behavioural Finance is a relatively new school of thought that presents an argument that prices may not be efficient by questioning investor rationality. There is evidence to indicate that individuals do not always react in a rational manner. Also, limits to arbitrage may lead to misprising on securities. This chapter presents evidence uncovered by psychologists that show errors made by individuals in processing information and biases observed in human behaviour.

The concept of efficient markets is built on the assumption that investors are rational and always behave in a rational fashion. However, evidence indicates otherwise. Behaviour that is inconsistent with rational behaviour is centered in two major areas. First, investors make forecasting errors. Second, there is evidence of systematic behavioural biases.

If a few market participants did not behave rationally, we could still expect efficient prices if rational investors could exploit inefficiencies. There may be limits to arbitrage that are significant and inefficient pricing could exist for long periods.

Critiques of the behavioural finance are has been criticised in terms of strength of its arguments. The existence of bubbles may be a violation of efficiency but such bubbles are really only identifiable after the fact. Some have criticised the behaviour school on the grounds that it lacks structure.

Chapter 13 Empirical evidence on security return

The preliminary part of the Chapter emphasises the significance of CAPM and APT. You should read the Chapter, in order to gain an overview only of the methodology of the research and, more importantly, an understanding of the results.

You should have an understanding how tests of single and multiple factor models are structured. You should be able to identify the major anomalies that have been found in studies of returns on securities and be able to describe measurement problems associated with tests.

52




Chapter 12

6. b. Semi-strong form efficiency implies that market prices reflect all publicly available information concerning past trading history as well as fundamental aspects of the firm.

7. a. The full price adjustment should occur just as the news about the dividend becomes publicly available.

8. d. If low P/E stocks tend to have positive abnormal returns, this would represent an unexploited profit opportunity that would provide evidence that investors are not using all available information to make profitable investments.

9. c. In an efficient market, no securities are consistently overpriced or underpriced. While some securities will turn out after any investment period to have provided positive alphas (i.e., risk-adjusted abnormal returns) and some negative alphas, these past returns are not predictive of future returns.

10. c. A random walk implies that stock price changes are unpredictable, using past price changes or any other data.

11. d. A gradual adjustment to fundamental values would allow for the use of strategies based on past price movements in order to generate abnormal profits.

12. a.

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Chapter 13

12. (i) Betas are estimated with respect to market indexes that are proxies for the true market portfolio, which is inherently unobservable.

(ii) Empirical tests of the CAPM show that average returns are not related to beta in the manner predicted by the theory. The empirical SML is flatter than the theoretical one.

(iii) Multi-factor models of security returns show that beta, which is a one-dimensional measure of risk, may not capture the true risk of the stock of portfolio.

13. a. The basic procedure in portfolio evaluation is to compare the returns on a managed portfolio to the return expected on an unmanaged portfolio having the same risk, using the SML. That is, expected return is calculated from:

E(rP ) = rf + bP [E(rM ) – rf ]

where rf is the risk-free rate, E(rM ) is the expected return for the unmanaged portfolio (or the market portfolio), and P is the beta coefficient (or systematic risk) of the managed portfolio. The performance benchmark then is the unmanaged portfolio. The typical proxy for this unmanaged portfolio is an aggregate stock market index such as the S&P 500.

b. The benchmark error might occur when the unmanaged portfolio used in the evaluation process is not “optimized.” That is, market indices, such as the S&P 500, chosen as benchmarks are not on the manager’s ex ante mean/variance efficient frontier.

c. Your graph should show an efficient frontier obtained from actual returns, and a different one that represents (unobserved) ex-ante expectations. The CML and SML generated from actual returns do not conform to the CAPM predictions, while the hypothesized lines do conform to the CAPM.

d. The answer to this question depends on one’s prior beliefs. Given a consistent track record, an agnostic observer might conclude that the data support the claim of superiority. Other observers might start with a strong prior that, since so many managers are attempting to beat a passive portfolio, a small number are bound to produce seemingly convincing track records.

e. The question is really whether the CAPM is at all testable. The problem is that even a slight inefficiency in the benchmark portfolio may completely invalidate any test of the expected return-beta relationship. It appears from Roll’s argument that the best guide to the

54


question of the validity of the CAPM is the difficulty of beating a passive strategy.

14. The effect of an incorrectly specified market proxy is that the beta of Black’s portfolio is likely to be underestimated (i.e., too low) relative to the beta calculated based on the “true” market portfolio. This is because the Dow Jones Industrial Average (DJIA), and other market proxies, are likely to have less diversification and therefore a higher variance of returns than the “true” market portfolio as specified by the capital asset pricing model. Consequently, beta computed using an overstated variance will be underestimated. This result is clear from the following formula:

An incorrectly specified market proxy is likely to produce a slope for the security market line (i.e., the market risk premium) that is underestimated relative to the “true” market portfolio. This results from the fact that the “true” market portfolio is likely to be more efficient (plotting on a higher return point for the same risk) than the DJIA and similarly misspecified market proxies. Consequently, the proxy-based SML would offer less expected return per unit of risk.

55

Topic 7 Fixed income securities


Objectives


1. calculate the price and yield to maturity of a bond;

2. describe the various types of bonds and their characteristics;

3. calculate forward rates;

4. measure the Term structure;

5. describe the various Theories of Term Structure;

6. interpret the Term Structure;

7. calculate the Realised Compound Yield to Maturity;

8. describe interest rate risk, the effect of interest rate changes on bond prices and how duration might be used as a management tool;

9. calculate duration and be able to describe how it is used to manage fixed-income portfolios;

10. describe how bond portfolios can be managed using passive strategies;

11. describe how bond portfolios can be managed using active strategies.

Prescribed reading

Text: Chapter 14 Bond prices and yieldsChapter 15 The term structure of interest ratesChapter 16 Managing bond portfolios

Review problems

Text: Chapter 14 Problems 7-9, 29-31 Chapter 15 Problems 1-2, 6-10Chapter 16 Problems 1-3, 6-11

Comments

We have so far made extensive references to, and use of, the market portfolio. Now we shall take a more detailed look at some of the different types of securities that make up the market portfolio. We start with fixed income securities in this topic. Later we shall examine ordinary shares, options and futures contracts.

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Chapter 14 Bond prices and yields

This chapter presents a thorough discussion of the various types of bonds, bond characteristics, determinants of bond risk, bond ratings, and the pricing and yield calculations of various types of bonds. Bond characteristics and pricing should be revision for you from Corporate Finance (FIN516). This chapter builds on that knowledge and you should not only refresh your memory but also work through all examples, so you can to calculate yields and prices of various types of bonds and understand the relationship between the yield curve and bond prices.

It is interesting to note that bond prices that are quoted in the financial pages do not contain accrued interest. Most pricing examples that we use in finance also do not include discussion of accrued interest. However, actual transaction prices would include any interest that has accrued since the last coupon payment.

In Australia, zero coupons became prominent because initially they were tax-free. As they did not pay any explicit interest, then they were 'non taxable'. However, their increasing popularity caused the Tax Office to change this.

Obviously, the factors mentioned on p. 467 will affect interest premium, regardless of whether or not rating agencies exist.

Chapter 15 The term structure of interest rates

This chapter examines the factors that determine interest rates. Again, while this chapter builds on your previous knowledge, you should not only refresh your memory but also work through all examples so you can calculate forward rates and understand how term structure concepts apply to valuation of securities. You should be able to develop a thorough understanding of the concept of short-term and long-term rates.

It is important that you should be able to describe the major theories of term structure and be able to describe the effects that the theories would have on observed term structure. So read carefully pp. 493 – 500. Here Fig 15.5 is very useful.

In essence, the expectations theory is built on the assumption that short-term and long-term securities are perfect substitutes. The only factor that influences the long-term rate in that case is expected future short-term rates. Since the securities are perfect substitutes, if the long-term rates do not equal the product of the observed short-term rate and expected future short-term rates, arbitrage possibilities would exist.

If long-term bonds are riskier than short-term bonds, investors in such securities will demand a risk premium. Under the liquidity premium theory long-term rates are influenced by expected future short-term rates and also by the liquidity premium. The liquidity premium theory leads to a prediction of an upward bias in the yield curve.

57


Market segmentations theory and its related preferred habitat theory are alternative explanations of the term structure of interest rates. According to market segmentation, participants in the market prefer to stay in distinct segments of the market. Some institutional investors such as banks prefer short-term securities while others such as insurance companies prefer the long end of the market. According to market segmentation, trading in the unique segments determines the observed rates. The preferred habitat theory is a modification of the market segmentation theory. It asserts that investors do prefer certain segments of the market but if the premiums in different segments are adequate, investors will move from their preferred habitat.

Chapter 16 Managing bond portfolios

This is a more important chapter, covering active and passive bond portfolio management strategies.

Duration

The more important aspect of this topic is duration, which is a very important concept. Duration is a weighted average maturity of the payment stream from a bond-and hence can be described as an effective maturity. Duration allows us to compare bonds of different maturities and coupon rates and also assists in the management of interest rate risk. It measures the 'economic' life of a bond by taking into account a weighted average of the present value of all cash flows from the bond.

The maturity of a bond tells about the timing of the very last payment and ignores all payments before that. But duration incorporates all payments so that a bond with large coupons will have a lower duration than a bond with small coupons or zero coupon. This is important as an indicator of risk as the sooner the payments are received on a bond the lower the risk.

You need to be able to calculate duration. The spreadsheet 16.1 (p. 520) is a simple method by which to do this. Practice this in excel as well as using the formula 16.1. Work through all examples until you are proficient with concepts and calculations of duration, modified duration and their role in calculating percentage change in bond price for a given change in the yield. Do not forget that it is an approximation (equations 16.2 and 16.3, p. 522).

It is important that you understand and work through the examples of the five rules for duration in pp. 524 – 525.

However, there are drawbacks to duration. Duration is only a measure of interest rate risk for the bonds and does not take into account the change in the value of bond investments from changed income streams. Although long duration bonds are more price-sensitive to changes in YTM, it ignores the fact that short duration bonds are more volatile (more risky). Finally, duration has very limited use in other investment instruments, and hence its usefulness is limited in a mixed portfolio.

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Convexity

Next important concept is convexity. The text discusses the concept (pp. 527 – 532) and it should provide you with the basic understanding, which is all that is required at this stage.

This then brings you to bond strategies and management. Bond management can be divided into two major approaches:

1. The passive strategies.2. The active strategies.

This is consistent with modern investing approaches, direct versus indirect investing.

The important concept to master here is immunisation (pp. 534 – 543). Table 16.5 (p. 536) and its explanation in subsequent pages should be helpful to you.

Now you can try to build a bond portfolio. Here conservative investors would approach these issues very differently to aggressive investors. It is also prudent to consider the opportunities available in the international bond markets, which can be utilised with the help of mutual funds and closed-end funds.

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Chapter 14

7. a. (i) Current yield = Coupon/Price = $70/$960 = 0.0729 = 7.29%

(ii) YTM = 3.993% semiannually or 7.986% annual bond equivalent yield.

On a financial calculator, enter: n = 10; PV = –960; FV = 1000; PMT = 35Compute the interest rate.

(iii) Realized compound yield is 4.166% (semiannually), or 8.332% annual bond equivalent yield. To obtain this value, first find the future value (FV) of reinvested coupons and principal. There will be six payments of $35 each, reinvested semiannually at of 3% per period. On a financial calculator, enter:

PV = 0; PMT = $35; n = 6; i = 3%. Compute: FV = $226.39

Three years from now, the bond will be selling at the par value of $1,000 because the yield to maturity is forecast to equal the coupon rate. Therefore, total proceeds in three years will be $1,226.39.

Then find the rate (yrealized) that makes the FV of the purchase price equal to $1,226.39:

$960 (1 + yrealized)6 = $1,226.39 yrealized = 4.166% (semiannual)

b. Shortcomings of each measure:

(i) Current yield does not account for capital gains or losses on bonds bought at prices other than par value. It also does not account for reinvestment income on coupon payments.

(ii) Yield to maturity assumes the bond is held until maturity and that all coupon income can be reinvested at a rate equal to the yield to maturity.

(iii) Realized compound yield is affected by the forecast of reinvestment rates, holding period, and yield of the bond at the end of the investor's holding period.

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8. a. Zero coupon 8% coupon 10% coupon

Current prices $463.19 $1,000.00 $1,134.20

b.

Price 1 year from now $500.25 $1,000.00 $1,124.94

Price increase $ 37.06 $ 0.00 - $ 9.26

Coupon income $ 0.00 $ 80.00 $100.00

Pre-tax income $ 37.06 $ 80.00 $ 90.74

Pre-tax rate of return 8.00% 8.00% 8.00%

Taxes* $ 11.12 $ 24.00 $ 28.15

After-tax income $ 25.94 $ 56.00 $ 62.59

After-tax rate of return 5.60% 5.60% 5.52%

c.

Price 1 year from now $543.93 $1,065.15 $1,195.46

Price increase $ 80.74 $ 65.15 $ 61.26

Coupon income $ 0.00 $ 80.00 $100.00

Pre-tax income $ 80.74 $145.15 $161.26

Pre-tax rate of return 17.43% 14.52% 14.22%

Taxes $ 24.22 $ 37.03 $ 42.25

After-tax income $ 56.52 $108.12 $119.01

After-tax rate of return 12.20% 10.81% 10.49%

* In computing taxes, we assume that the 10% coupon bond was issued at par and that the decrease in price when the bond is sold at year end is treated as a capital loss and therefore is not treated as an offset to ordinary income.

9. a. On a financial calculator, enter the following:

n = 40; FV = 1000; PV = –950; PMT = 40

You will find that the yield to maturity on a semi-annual basis is 4.26%. This implies a bond equivalent yield to maturity equal to: 4.26% 2 = 8.52%

Effective annual yield to maturity = (1.0426)2 – 1 = 0.0870 = 8.70%

b. Since the bond is selling at par, the yield to maturity on a semi-annual basis is the same as the semi-annual coupon rate, i.e., 4%. The bond equivalent yield to maturity is 8%.


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c. Keeping other inputs unchanged but setting PV = –1050, we find a bond equivalent yield to maturity of 7.52%, or 3.76% on a semi-annual basis.


29. Market conversion value = value if converted into stock = 20.83 $28 = $583.24

Conversion premium = Bond price – market conversion value= $775.00 – $583.24 = $191.76

30. a. The call feature requires the firm to offer a higher coupon (or higher promised yield to maturity) on the bond in order to compensate the investor for the firm's option to call back the bond at a specified price if interest rate falls sufficiently. Investors are willing to grant this valuable option to the issuer, but only for a price that reflects the possibility that the bond will be called. That price is the higher promised yield at which they are willing to buy the bond.

b. The call feature reduces the expected life of the bond. If interest rates fall substantially so that the likelihood of a call increases, investors will treat the bond as if it will "mature" and be paid off at the call date, not at the stated maturity date. On the other hand if rates rise, the bond must be paid off at the maturity date, not later. This asymmetry means that the expected life of the bond is less than the stated maturity.

c. The advantage of a callable bond is the higher coupon (and higher promised yield to maturity) when the bond is issued. If the bond is never called, then an investor earns a higher realized compound yield on a callable bond issued at par than a non-callable bond issued at par on the same date. The disadvantage of the callable bond is the risk of call. If rates fall and the bond is called, then the investor receives the call price and then has to reinvest the proceeds at interest rates that are lower than the yield to maturity at which the bond originally was issued. In this event, the firm's savings in interest payments is the investor's loss.

31. a. (iii)

b. (iii) The yield on the callable bond must compensate the investor for the risk of call.

Choice (i) is wrong because, although the owner of a callable bond receives a premium plus the principal in the event of a call, the interest rate at which he can reinvest will be low. The low interest rate that makes it profitable for the issuer to call the bond makes it a bad deal for the bond’s holder.

Choice (ii) is wrong because a bond is more apt to be called when interest rates are low. Only if rates are low will there be an interest saving for the issuer.

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c. (ii) is the only correct choice.

(i) is wrong because the YTM is greater than the coupon rate when a bond sells at a discount and is less than the coupon rate when the bond sells at a premium.

(iii) is wrong because adding the average annual capital gain rate to the current yield does not give the yield to maturity. For example, assume a 10-year bond with a 6% coupon rate paying interest annually and a YTM of 8% per year. Its price is $865.80. The average annual capital gain is equal to ($1000 – 865.80)/10 years = $13.42 per year. Using this number results in an average capital gains rate per year of $13.42/$865.80 = 1.55%. The current coupon yield is $60/$865.80 = .0693 per year or 6.93%. Therefore, the “total yield” is: 1.55% + 6.93% = 8.48%

This is greater than the YTM.

(iv) is wrong because YTM is based on the assumption that any payments received are reinvested at the YTM and not at the coupon rate.

d. (iii)

e. (ii)

f. (iii)

Chapter 15

1. Expectations hypothesis: The yields on long-term bonds are geometric averages of present and expected future short rates. An upward sloping curve is explained by expected future short rates being higher than the current short rate. A downward-sloping yield curve implies expected future short rates are lower than the current short rate. Thus bonds of different maturities have different yields if expectations of future short rates are different from the current short rate.

Liquidity preference hypothesis: Yields on long-term bonds are greater than the expected return from rolling-over short-term bonds in order to compensate investors in long-term bonds for bearing interest rate risk. Thus bonds of different maturities can have different yields even if expected future short rates are all equal to the current short rate. An upward sloping yield curve can be consistent even with expectations of falling short rates if liquidity premiums are high enough. If, however, the yield curve is downward sloping and liquidity premiums are assumed to be positive, then we can conclude that future short rates are expected to be lower than the current short rate.

2. d.

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6.Maturity Price YTM Forward Rate

1 $943.40 6.00%

2 $898.47 5.50% (1.0552/1.06) – 1 = 5.0%

3 $847.62 5.67% (1.05673/1.0552) – 1 = 6.0%

4 $792.16 6.00% (1.064/1.05673) – 1 = 7.0%

7. The expected price path of the 4-year zero coupon bond is shown below. (Note that we discount the face value by the appropriate sequence of forward rates implied by this year’s yield curve.)

Beginning of Year

Expected Price Expected Rate of Return

1 $792.16 ($839.69/$792.16) – 1 = 6.00%

2 ($881.68/$839.69) – 1 = 5.00%

3 ($934.58/$881.68) – 1 = 6.00%

4 ($1,000.00/$934.58) – 1 = 7.00%

8. a. (1+y4 )4 = (1+ y3 )3 (1 + f 4 )

(1.055)4 = (1.05)3 (1 + f 4 )

1.2388 = 1.1576 (1 + f 4 ) f 4 = 0.0701 = 7.01%

b. The conditions would be those that underlie the expectations theory of the term structure: risk neutral market participants who are willing to substitute among maturities solely on the basis of yield differentials. This behavior would rule out liquidity or term premia relating to risk.

c. Under the expectations hypothesis, lower implied forward rates would indicate lower expected future spot rates for the corresponding period. Since the lower expected future rates embodied in the term structure are nominal rates, either lower expected future real rates or lower expected future inflation rates would be consistent with the specified change in the observed (implied) forward rate.

9. You would expect the yield on a callable bond to lie above the yield curve for noncallable bonds because the callable bond must offer a premium to investors in order to compensate them for the option granted to the issuer.

10. The given rates are annual rates, but each period is a half-year. Therefore, the per period spot rates are 2.5% on one-year bonds and 2% on six-month bonds. The semiannual forward rate is obtained by solving for f in the following equation:

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This means that the forward rate is 0.030 = 3.0% semiannually, or 6.0% annually. Therefore, choice d is correct.

Chapter 16

1. The percentage change in the bond’s price is:

or a 3.27%

decline.

2. a. YTM = 6%

(1) (2) (3) (4) (5)

Time until Payment (years)

Cash FlowPV of CF

(Discount rate = 6%)

WeightColumn (1)

Column (4)

1 $60.00 $56.60 0.0566 0.0566

2 $60.00 $53.40 0.0534 0.1068

3 $1,060.00 $890.00 0.8900 2.6700

Column Sums $1,000.00 1.0000 2.8334

Duration = 2.833 years

b. YTM = 10%

(1) (2) (3) (4) (5)

Time until Payment (years)

Cash FlowPV of CF

(Discount rate = 10%)

WeightColumn (1)

Column (4)

1 $60.00 $54.55 0.0606 0.0606

2 $60.00 $49.40 0.0551 0.1102

3 $1,060.00 $796.39 0.8844 2.6532

Column Sums $900.53 1.0000 2.8240

Duration = 2.824 years, which is less than the duration at the YTM of 6%.

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3. For a semiannual 6% coupon bond selling at par, we use the following parameters: coupon = 3% per half-year period, y = 3%, T = 6 semiannual periods. Using Rule 8, we find:

D = (1.03/0.03) [1 – (1/1.03)6] = 5.58 half-year periods = 2.79 years

If the bond’s yield is 10%, use Rule 7, setting the semiannual yield to 5%, and semiannual coupon to 3%:

= 5.5522 half-year periods = 2.7761 years

6. a. The call feature provides a valuable option to the issuer, since it can buy back the bond at a specified call price even if the present value of the scheduled remaining payments is greater than the call price. The investor will demand, and the issuer will be willing to pay, a higher yield on the issue as compensation for this feature.

b. The call feature reduces both the duration (interest rate sensitivity) and the convexity of the bond. If interest rates fall, the increase in the price of the callable bond will not be as large as it would be if the bond were noncallable. Moreover, the usual curvature that characterizes price changes for a straight bond is reduced by a call feature. The price-yield curve (see Figure 16.6) flattens out as the interest rate falls and the option to call the bond becomes more attractive. In fact, at very low interest rates, the bond exhibits negative convexity.

7. In each case, choose the longer-duration bond in order to benefit from a rate decrease.

a. The Aaa-rated bond will have the lower yield to maturity and therefore the longer duration.

b. The lower-coupon bond will have the longer duration and greater de facto call protection.

c. Choose the lower coupon bond for its longer duration.

8. a. (iv) [10 0.01 800 = 80.00]b. (ii) [½ 120 (0.015)2 = 0.0135 = 1.35%]c. (i)d. (i) [9/1.10 = 8.18]e. (iii)f. (i)g. (i)h. (iii)

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9. The table below shows the holding period returns for each of the three bonds

Maturity 1 year 2 years 3 yearsYTM at beginning of year 7.00% 8.00% 9.00%

Beginning of year prices $1,009.35 $1,000.00 $974.69Prices at year end (at 9% YTM) $1,000.00 $990.83 $982.41Capital gain –$9.35 –$9.17 $7.72Coupon $80.00 $80.00 $80.001-year total $ return $70.65 $70.83 $87.721-year total rate of return 7.00% 7.08% 9.00%

You should buy the 3-year bond because it provides a 9% holding-period return over the next year, which is greater than the return on either of the other bonds.

10. a. Modified duration years

b. For option-free coupon bonds, modified duration is a better measure of the bond’s sensitivity to changes in interest rates. Maturity considers only the final cash flow, while modified duration includes other factors, such as the size and timing of coupon payments, and the level of interest rates (yield to maturity). Modified duration, unlike maturity, indicates the approximate percentage change in the bond price for a given change in yield to maturity.

c. i. Modified duration increases as the coupon decreases.ii. Modified duration decreases as maturity decreases.

d. Convexity measures the curvature of the bond’s price-yield curve. Such curvature means that the duration rule for bond price change (which is based only on the slope of the curve at the original yield) is only an approximation. Adding a term to account for the convexity of the bond increases the accuracy of the approximation. That convexity adjustment is the last term in the following equation:

11. a. PV of the obligation = [$10,000 Annuity factor (8%, 2)] = $17,832.65Duration = 1.4808 years, which can be verified using Rule 6 or a table such as Table 15.3.

b. A zero-coupon bond maturing in 1.4808 years would immunize the obligation. Since the present value of the zero-coupon bond must be $17,832.65, the face value (i.e., the future redemption value) must be:

$17,832.65 1.081.4808 = $19,985.26

c. If the interest rate increases to 9%, the zero-coupon bond would decrease in value to:

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The present value of the tuition obligation would decrease to $17,591.11. The net position decreases in value by $0.19.

If the interest rate decreases to 7%, the zero-coupon bond would increase in value to:

The present value of the tuition obligation would increase to $18,080.18. The net position decreases in value by $0.19.

The reason the net position changes at all is that, as the interest rate changes, so does the duration of the stream of tuition payments.

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Topic 8 Security analysis


Objectives


1. describe the macro economic factors that affect a stock's price;

2. describe how an analyst could use economic indicators;

3. calculate the intrinsic value of a stock using the methods specified in the text;

4. use P/E ratios in valuing stocks, evaluating stocks and be aware of their shortcomings;

5. describe the effect that inflation has upon equity valuation;

6. describe the research that has occurred into the behaviour of the Aggregate Stock Market;

7. calculate the 'standard' financial ratios;

8. describe the shortcomings of using financial ratios;

9. describe the significance of the 'SUE' research.

Prescribed reading

Text: Chapter 17 Macroeconomic and industry analysisChapter 18 Equity valuation models Chapter 19 Financial statement analysis

Review questions

Text: Chapter 17 Problems 1-5, 14-15Chapter 18 Problems 1-9Chapter 19 Problems 1-4

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Comments

Chapter 17 Macroeconomic and industry analysis

The price of a share is affected by the performance of the company. Obviously, the performance of the company is affected by the economy. Thus, in valuing a share, one must examine the effect of the economy. This is usually described as the top down approach to share valuation. Global, Economy then Industry then Company. The rationale for this approach is the assumption that a company is unlikely to be performing well in an industry or market that is performing poorly. There is some empirical support for such a claim.

After GFC the importance of macroeconomic and industry analysis have increased. Not all of the indicators in Table 17.2 (p. 578) are available in Australia. Obviously, if one can find a large positive correlation between an indicator and the revenue of a company, then the revenue can be predicted with a high degree of accuracy. Of course, this may be dependent upon having accurate forecasts of the indicator. Case studies carried out by students in Investments Analysis have indicated correlations > 0.90. Historically, a high correlation may exist - but one needs to be careful in assuming this will continue. Is it logical for a high correlation to exist? Might the characteristics of the company change in the future, thus leading to a lower correlation? In calculating the correlation one is often in a bind as to how many observations to include. If too few, the answer may be misleading due to too few observations. If too many, again the answer may be misleading because the nature of the company may have changed over the period, for example, a retailer becoming an investment company.

The importance of industry analysis cannot be understated particularly in post GFC era.

Chapter 18 Equity valuation models

This is probably the more important chapter of the three.

See p. 602. In the case of Microsoft shares, why was its market value more than its book value? Why would someone pay more than 4.5 times the book value to acquire a share in Microsoft? More importantly, why for the average firm in the PC software industry it was 4.9?

Closely follow through the valuation models. They ARE important! Make sure you understand all concepts and can do all examples and review questions.

Follow through the Raytheon’s case commencing on p. 615. It uses actual historical information to calculate the intrinsic value of Raytheon and then compares it to the actual value. This is what is done in reality.

Next is Price/Earnings Ratio or P/E Ratio. This is a very widely used ratio. Note the intrinsic value arrived for Raytheon on p. 628, different from that originally calculated on p. 617. This is due to the various assumptions made under each method. Quite often P/E ratios within industries are compared. For example, if

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ABC has a P/E of 9, while DEF has a P/E of 15, it is cheaper to buy ABC. But one needs to ask why. Are the companies really comparable? Why is there such a large difference between the two? Analysts usually argue that P/Es within an industry should be fairly similar - although research indicates that this is not the case, in reality.

Chapter 19 Financial statement analysis

This chapter should be largely revision for you. You should know how to analyse financial statements and be aware of the shortcomings of the methodology.

One normally views an increase in ROE with favour. However, beware, an increase in ROE can be caused by an increase in Financial Leverage. This latter increase may not be viewed favourably though, due to increase probability of financial distress.

If you have forgotten the comparability problems in financial statement analysis, then read 19.7, pp. 672 – 677.

Much research has occurred about the ability to predict corporate failure. Examples are Altman and Beaver in the U.S.A. and Lincoln, and Castagna and Matolcsy in Australia. In recent times the failure of many companies in USA, Europe and Australia have initiated, and will continue to contribute in future, many research projects. While some of the research indicates a high ability to predict corporate failure or 'at riskiness', some years before the event, the models do not seem to have great 'public' use. However, Altman has, apparently, devised proprietary models that are better indicators than his public ones and Lincoln provides a service advising of the 'at riskness' of private companies.

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Chapter 17

1. Expansionary (looser) monetary policy to lower interest rates would stimulate both investment and expenditures on consumer durables. Expansionary fiscal policy (i.e., lower taxes, increased government spending, increased welfare transfers) would stimulate aggregate demand directly.

2. a. Gold Mining. Gold traditionally is viewed as a hedge against inflation. Expansionary monetary policy may lead to increased inflation, and thus could enhance the value of gold mining stocks.

b. Construction. Expansionary monetary policy will lead to lower interest rates which ought to stimulate housing demand. The construction industry should benefit.

3. a. Lowering reserve requirements would allow banks to lend out a higher fraction of deposits and thus increase the money supply.

b. The Fed would buy Treasury securities, thereby increasing the money supply.

c. The discount rate would be reduced, allowing banks to borrow additional funds at a lower rate.

4. a. Expansionary monetary policy is likely to increase the inflation rate, either because it may over stimulate the economy, or ultimately because the end result of more money in the economy is higher prices.

b. Real output and employment should increase in response to the expansionary policy, at least in the short run.

c. The real interest rate should fall, at least in the short-run, as the supply of funds to the economy has increased.

d. The nominal interest rate could either increase or decrease. On the one hand, the real rate might fall [see part (c)], but the inflation premium might rise [see part (a)]. The nominal rate is the sum of these two components.

5. A depreciating dollar makes imported cars more expensive and American cars less expensive to foreign consumers. This should benefit the U.S. auto industry.

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Chapter 18

1. Choice (a): P0 = D1/(k – g) = $2.10/(0.11 – 0) = $19.09

2. (c)

3. a. k = D1/P0 + g0.16 = $2/$50 + g g = 0.12 = 12%

b. P0 = D1/(k – g) = $2/(0.16 – 0.05) = $18.18

The price falls in response to the more pessimistic dividend forecast. The forecast for current year earnings, however, is unchanged. Therefore, the P/E ratio falls. The lower P/E ratio is evidence of the diminished optimism concerning the firm's growth prospects.

4. a. g = ROE b = 16% 0.5 = 8%D1 = $2(1 – b) = $2(1 – 0.5) = $1P0 = D1/(k – g) = $1/(0.12 – 0.08) = $25

b. P3 = P0(1 + g)3 = $25(1.08)3 = $31.49

5. a. This director is confused. In the context of the constant growth model[i.e., P0 = D1/(k – g)], it is true that price is higher when dividends are higher holding everything else including dividend growth constant. But everything else will not be constant. If the firm increases the dividend payout rate, the growth rate g will fall, and stock price will not necessarily rise. In fact, if ROE > k, price will fall.

b. (i) An increase in dividend payout will reduce the sustainable growth rate as less funds are reinvested in the firm. The sustainable growth rate (i.e., ROE plowback) will fall as plowback ratio falls.

(ii) The increased dividend payout rate will reduce the growth rate of book value for the same reason -- less funds are reinvested in the firm.

6. a. k = rf + b(rM) – rf ] = 6% + 1.25(14% – 6%) = 16%g = 2/3 9% = 6%D1 = E0(1 + g) (1 – b) = $3(1.06) (1/3) = $1.06

b. Leading P0/E1 = $10.60/$3.18 = 3.33Trailing P0/E0 = $10.60/$3.00 = 3.53

c.

The low P/E ratios and negative PVGO are due to a poor ROE (9%) that is less than the market capitalization rate (16%).

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d. Now, you revise b to 1/3, g to 1/3 9% = 3%, and D1 to:E0 1.03 (2/3) = $2.06Thus:V0 = $2.06/(0.16 – 0.03) = $15.85V0 increases because the firm pays out more earnings instead of reinvesting a poor ROE. This information is not yet known to the rest of the market.

7. Since beta = 1.0, then k = market return = 15%

Therefore:15% = D1/P0 + g = 4% + g g = 11%

8. a.

b. The dividend payout ratio is 8/12 = 2/3, so the plowback ratio is b = 1/3.

The implied value of ROE on future investments is found by solving:

g = b ROE with g = 5% and b = 1/3 ROE = 15%

c. Assuming ROE = k, price is equal to:

Therefore, the market is paying $40 per share ($160 – $120) for growth opportunities.

9. Using a two-stage dividend discount model, the current value of a share of Sundanci is calculated as follows.

where:E0 = $0.952D0 = $0.286E1 = E0 (1.32)1 = $0.952 1.32 = $1.2566D1 = E1 0.30 = $1.2566 0.30 = $0.3770E2 = E0 (1.32)2 = $0.952 (1.32)2 = $1.6588D2 = E2 0.30 = $1.6588 0.30 = $0.4976E3 = E0 (1.32)2 = $0.952 (1.32)3 1.13 = $1.8744D3 = E3 0.30 = $1.8743 0.30 = $0.5623

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Chapter 19

1. ROE = Net profits/Equity = Net profits/Sales Sales/Assets Assets/Equity

= Net profit margin Asset turnover Leverage ratio = 5.5% 2.0 2.2 = 24.2%

2. ROA = ROS ATO

The only way that Crusty Pie can have an ROS higher than the industry average and an ROA equal to the industry average is for its ATO to be lower than the industry average.

3. ABC’s Asset turnover must be above the industry average.

4. ROE = (1 – Tax rate) [ROA + (ROA – Interest rate)Debt/Equity]ROEA > ROEB

Firms A and B have the same ROA. Assuming the same tax rate and assuming that ROA > interest rate, then Firm A must have either a lower interest rate or a higher debt ratio.

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Topic 12 Portfolio management and evaluation

Topic 9 International diversification

Objectives


1. describe the characteristics of the world capital market;

2. describe the advantages to an investor of holding an international portfolio;

3. describe the disadvantages to an investor of holding an international portfolio;

4. calculate the return, in domestic currency, of holding overseas investments;

5. describe the international market indices, how they are calculated and how an investor might use them;

6. describe how we might determine an 'Asset Allocation' policy in an international portfolio setting;

7. discuss the factors that affect the return on an international portfolio;

8. discuss the applicability of CAPM and APT to international investment.

Prescribed reading

Text: Chapter 25 International Diversification

Reading 6: Eiteman et al Risk of International Investment

Review problems

Text: Chapter 25 Problems 1-6

Thought questions

International diversification

1. What is the purpose of international diversification? Why should institutional and individual investors acquire foreign securities?

2. Discuss in some detail why international diversification should work. Specifically, why would you expect low correlation in the rates of return for domestic and foreign securities?

3. Would you expect a difference in the correlation of returns between U.S. and foreign securities from alternative countries, such as, Japan, Canada, and South Africa? Why? Be specific.

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4. What were the empirical findings regarding changes in the correlations over time between the stock price series for various countries? What are the implications of these results for a portfolio manager interested in international diversification?

5. Would you expect there to be a trend in the correlations between U.S. stock price series and the stock price series for different countries? Why or why not, and what would influence such a trend?

6. What would news of a small increase in the correlations between the securities market in the United States and other countries mean to you as a portfolio manager?

7. Briefly discuss the major problems involved in international diversification. Which of the problems is greatest for individuals? Which is most important to institutions? Why?

8. It is contended that international investing introduces an additional risk component. Discuss what it is and how it can increase or decrease your return.

9. What alternatives are available to direct investment in foreign shares?

Comments

Chapter 25

The Chapter commences by examining why one would not just invest in one's own country.

U.S. equities, the largest equity market in the world, accounts for 48% of the world equity capitalisation, while Australia accounts for about 3%. This, alone, would suggest that there might well be equity investments, overseas, that have a better risk/return.

Fig. 25.6 (p.926) provides another reason. By investing in overseas stocks, portfolio risk can be reduced. (Recall portfolio theory?) Table 25.11 (p. 923) indicates the reason. The correlations of returns between the equity markets throughout the world are low. More recently the correlation for Australia varied between 0.44 (Japan) and 0.79 (U.K.). However, the correlation between U.S. and U.K. stayed quite high at 0.83. Can you think why?

Second part of the table is more revealing as the correlation are based in hedged currency.

In Australia, investors can invest directly overseas, probably with a minimum of about $A10, 000 or through an Equity Trust. Some trusts invest in specific countries, some in geographical regions, while others invest in a number of countries.

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By investing overseas, a number of costs and risk are incurred:

Exchange rate risk: a movement in the rate could make a once favourable investment, a loss maker

Monitoring costs: cost of deciding in which stock to invest, placing the order, and then monitoring the stock's performance will probably be higher and more tedious

Political risk: effect of change in government, will industries be nationalised?

As well, one needs to review the law of the overseas country. Are there restrictions on foreign shareholders, repatriating dividends and capital? What is the taxation law?

Pp. 912 – 919 examine exchange rate risk and its components. Obviously, an investment in a foreign company may well generate a high return, but when converted back to $A, it could be a loss.

So you need to formulate an international investment policy. With any portfolio, an investor will want to compare the returns of the portfolio with a benchmark. This will be examined in greater depth in the next topic. However, this topic examines some of the benchmarks in existence, how they are constructed and their shortcomings.

Reading 6, 'Risk of international investment' by Eiteman et al provides deeper understanding of risk of international investment and international diversification. This may be a revision for you if you have attempted Fin518, if not read through carefully.

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Chapter 25 International Diversification

1. Initial investment = 2,000 $1.50 = $3,000

Final value = 2,400 $1.75 = $4,200

Rate of return = ($4,200/$3,000) 1 = 0.40 = 40%

2. a.

3. c.

4. a. $10,000/2 = £5,000

£5,000/£40 = 125 shares

b. To fill in the table, we use the relation:

1 + r(US) = [(1 + r(UK)]

Price per Pound-Denominated Dollar-Denominated Return (%)

for Year End Exchange Rate

Share (£) Return (%) $1.80/£ $2.00/£ $2.20/£

£35 -12.5% -21.25% -12.5% -3.75%£40 0.0% -10.00% 0.0% 10.00%

£45 12.5% 1.25% 12.5% 23.75%

c. The dollar-denominated return equals the pound-denominated return when the exchange rate is unchanged over the year.

5. The standard deviation of the pound-denominated return (using 3 degrees of freedom) is 10.21%. The dollar-denominated return has a standard deviation of 13.10% (using 9 degrees of freedom), greater than the pound-denominated standard deviation. This is due to the addition of exchange rate risk.

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6. a. First we calculate the dollar value of the 125 shares of stock in each scenario. Then we add the profits from the forward contract in each scenario.

Price per Dollar Value of Stock

at Given Exchange Rate

Share (£) Exchange Rate: $1.80/£ $2.00/£ $2.20/£

£35 7,875 8,750 9,625£40 9,000 10,000 11,000

£45 10,125 11,250 12,375

Profits on Forward Exchange:

[ = 5000(2.10-E1)]

1,500 500 -500

Price per Total Dollar Proceeds



£35 9,375 9,250 9,125£40 10,500 10,500 10,500

£45 11,625 11,750 11,875

Finally, calculate the dollar-denominated rate of return, recalling that the initial investment was $10,000:

Price per Rate of return (%)



£35 -6.25% -7.50% -8.75%£40 5.00% 5.00% 5.00%

£45 16.25% 17.50% 18.75%

b. The standard deviation is now 10.24%. This is lower than the unhedged dollar-denominated standard deviation, and is only slightly higher than the standard deviation of the pound-denominated return.

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FIN531 201090 SG