Investment Mgmt L1

8/3/2019 Investment Mgmt L1

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THE INVESTMENT FRAMEWORK


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INVESTMENT MANAGEMENT 200057

Week 1 Investment Framework

Kevin Daly

Unit Coordinator

Email: [email protected]


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LEARNING OBJECTIVES

After completion of this Lecture you should be able to:

understand the nature of an investment

describe the key steps in the investment process

recognise the major investment asset classes

understand the role and function of financial markets


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LEARNING OBJECTIVES (CONT.)

understand the concept of return and be able todistinguish between realised returns and expected

returns understand the relationship between expected return

and risk

understand the basic notion of uncertainty and beable to calculate sample variance

understand the role and importance of the normaldistribution


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LECTURE OUTLINE

1 Introduction

2 Overview of the investment process

3 The allocation decision

4 Performance measurement

5 Review stage

6 Summary


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1 INTRODUCTION

What is the nature of investment?

y allocate wealth among assets to increase returns

y individuals have to make choice between current and

future consumption

y when current consumption exceeds wealth

borrow

y when wealth exceeds current consumption

save and invest proceeds

y this represents the first choice that investors mustmake.

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1 INTRODUCTION

What is the nature of investment?

y the second choice is between investment assets

y investment assets differ in terms of risk and return

y

return arises due to time value of money

rate of inflation

uncertainty of future cash flows

y the greater the risk of the investment, the greater the

return.

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2 OVERVIEW OF INVESTMENT PROCESS

The investment process consists of 3 steps:

y Allocation decision

i.e. what assets to invest in

Recall that excess wealth is saved for future investment, Thesesaved funds are known as the investment pool.

y Performance measurement

i.e. did the investments perform as expected

y Review stage

i.e. what changes need to be made

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2 OVERVIEW OF INVESTMENT PROCESS

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3 THE ALLOCATION DECISION

Concept of markets

y arise due to timing problem

i.e. the need to store excess funds or borrow to meet fund

deficiencies

y

reliant upon legal system to enforce agreements betweeninvestors (with excess funds) and borrowers (with

deficient funds)

y derivative markets

allow adjustment of risk and timing of investment cash flows

y international markets development of market for foreign exchange

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How are investment assets classified?

y Classes and Instruments

Equity

e.g. shares

traded on stock exchange Cash

e.g. bank accepted bills

traded in the money market

Fixed Interest

e.g. treasury bonds traded in bond markets

Property

e.g. real estate investment trusts

traded on stock exchange 11


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3 THE ALL

OCATION DECISION

Investor preferences

y investors differ in terms of risk aversion and desired

holding period preferences

high risk aversion (low risk tolerance) investors prefer investingin low risk assets such as fixed interest investments (e.g. bonds)

low risk aversion (high risk tolerance) may be more willing to

take on relatively high risk asset class investments like equity

and property.

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Investor preferences (cont.)

y Holding periods may be short-term or long-term in

nature

the allocation decisions differs substantially depending

upon the holding period.

short-term approaches take advantage of temporary

imbalanced in markets

long-term focus more on risk and return.

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4 PERFORMANCE MEASUREMENT

Defining returns

y Measuring the return on an investment

Return is the increase in wealth from holding a security over a given

period.

Return = (Ending value - Starting value) / Startingvalue

which can be rearranged to yield;

Future value = Starting value x (1 + Return)

or, FV = PV (1 + Return)

Example: Asset purchased for $1,000 and sold 4 months later for$1,200 has a return of (1200-1000)/1000 = 0.20 over the 4 month

holding period.

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Defining returns


Return is usually expressed as a percentage.

ie. 0.20 is equivalent to a 0.20 x 100 = 20% return.

To make returns comparable across different size holding periods,

they often expressed as an annual return.

Simple annual return is found by multiplying the holding period

return by the number of holding periods per year.

Simple annual return is 0.20 x 3 = 60%.

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Defining returns


Alternatively, we can assume that the money is rolled-over (ie.

reinvested) in an identical investment.

Example: consider an investment purchased for $1,000 and sold 4months later for $1,200.

The 4-month return is (1,200-1,000) / 1,000 = 0.20.

If this money is reinvested for another 4 months, it will accrue to;

Value (8 months) = Value (4 months) x 1.20 = $1,440, and so on.

At the end of a year, the effective annual return is;y (1+r)n-1 = (1.20)3 - 1 = 72.8%

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Defining returns (cont.)

y Continuous Compounding

If compounding approaches infinity () then the effective

rate with continuous compounding is:(1+nominal rate/)-1 = enominal rate-1

Example: If the nominal rate is 10% pa and there is

continuous compounding then the effective rate is:

e0.10-1 2.718280.10-1 = 10.51%pa

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y Discrete vs. continuous compounding

Continuous compounding is preferred because it:

is more consistent with the theory of return generationcontinuously through time

draws in the effect of positive outliers

continuously compounded returns imply a symmetric return

distribution, consistent with a normal distribution.

reduces the effect low priced investment securities have on thevolatility of realised returns.

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y Formal return definitions

Example: assume you purchase a share for $4.00 and at the

end of 4 months the share is worth $5.00. return = (5.00 - 4.00)/4.00 * 100 = 25%

Formally:

rt = (Pt - Pt-1)/ Pt-1

rt = (Pt / Pt-1) - 1

Note: Pt / Pt-1 is known as the price relative.

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y Formal return definitions

A continuously compounded return measured over 1 period:

rt= ln (Pt/Pt-1)

Example: A share bought for $4 and sold for $5 four months later

represents a continuously compounded return over the four

months of:

rt = ln(5.00/4.00) * 100 = 22.3%

Note: the continuously compounded return is always less than

the discrete return

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y Intermediary cash flows

Some investments have cash flows which accrue to the investor over

the period.

Some examples include; eg. dividends on shares,

eg. coupon payments on fixed interest securities,

eg. rental income from property investments

These are included in the calculation of the shareholders return.

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y Intermediary cash flows

Example: Say you buy a share for $8. If the company then pays a

dividend of $0.20 and at the end of the period the share price is $10

the return is:

formally: rt = ln[(Pt + CFt)/Pt-1]

y where CF is the intermediary cash flow accruing to the holder of the

security.

rt = ln[(10 + 0.20)/8.00]*100 = 24.30%.

That is, ln(10/8) = 22.31% of the return was due to the appreciation

of the share price and the remaining 1.99% was due to the

dividend. 23


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y Expected returns

Example: An investor predicts that an investment will earn either -

5%, 8% or 12%, with respective probabilities of 30%, 45% and 25%.

Given these values, the expected return for the investment is; E(r) = 0.3(-0.05)+0.45(0.08)+0.25(0.12) = 0.051.

which can be formally expressed as;

E(r) = p1(r1) + p2(r2) + ... + pn(rn)

=

24

( )

1

np ri i

i !


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Defining risk

y Variance

is simply the weighted average of the squared deviation of the

random variable from its expected value with each value

weighted by its probability.

Standard deviation is the square root of variance


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( )CV

E r

W

!

Defining risk (cont.)

y Coefficient of variation

captures the relative uncertainty of the investment.

for a risk averse investor, a low CV is preferable as it indicates

that less risk for each unit of expected return.


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Performance measures across time

y investors are concerned with aggregating returns across a

multiple of time periods.

Arithmetic sum

Geometric sum:

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r rt t

t

n

!

!

1

r rt t

t

n

!

-

!

( )1 11


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Performance measures across time (cont.)

y to obtain an average performance across time periods,

arithmetic or geometric averaging is used;

Arithmetic mean:

Geometric mean:

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r

n

rt t

t

n

!

!

1

1

r rt t

t

nn

!

-

! ( )1 1

1

1


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Performance measures across time (cont.)y Example: Assume the returns on an asset over 3 consecutive

holding periods are;

yr1: 4%, yr2: -6%, yr3: 5%

The arithmetic and geometric cumulative return over the 3-years

are;

Arithmetic cumulative return

= 0.04 -0.06 + 0.05 = 0.03 or 3%

Geometric cumulative return= (1+0.04)(1-0.06)(1+0.05)-1 = 0.0265 or 2.65%

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Performance measures across time (cont.)y Example: Assume the returns on an asset over 3 consecutive

holding periods are;

yr1: 4%, yr2: -6%, yr3: 5%

The arithmetic and geometric average (mean) return over the 3-

years are;

Arithmetic mean return

= (0.04 -0.06 + 0.05) / 3 = 0.01 or 1%

Geometric mean return= [(1+0.04)(1-0.06)(1+0.05)]1/3-1 = 0.0088 or 0.88%

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Performance measures across time (cont.)y The geometric return is often preferred to the arithmetic

return as it is more consistent with the actual return received

by the investor.

Example: Assume the following values of an investment;

Arithmetic mean return =(100-50)/2 = 25%

Geometric mean return = [(1+100%).(1-50%)]1/2-1= 0%

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y Arithmetic average return assumptions:

provide a good indication of the expected rate of return for an

investment during a future individual year

y Geometric average return assumptions: assume you reinvest all profits back into the stock

reinvested funds earn the rate of return the stock earns in

subsequent periods.

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y Geometric versus arithmetic returns

If rates of return are the same for all years the geometric mean will

equal arithmetic mean.

If returns vary over the years, geometric mean is lower than

arithmetic mean.

Higher volatility creates a greater difference.

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4 PERFORMANCE MEASUREMENT Performance measures across time (cont.)

y Calculating risk over time

common to use standard deviation

is a function of the return in each holding period, from the average

return over all holding periods. higher standard deviations indicate higher risk.

Note: the variance is the standard deviation squared.

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1

2( ( ))

n

i

r E rt

nW

!

!


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Performance measurement for portfolios

y Portfolio returns

Portfolio:

is prime focus of interest

is how asset returns combine and relate

is a combination of two or more securities.

Portfolio return:

is the weighted average of the returns on the securities

comprising the portfolio.

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Performance measurement for portfolios (cont.)

y Equal-weighted portfolio return

Example: Consider three securities with annual returns of 5%, 10%

and -5%

Equally-weighted portfolio return is: (5+10-5)/3 = 3.3%

Note: we have assigned equal weights to each of the securities

comprising the portfolio.

Formally:

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1

1 N

i

R riN !

!


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y Value-weighted portfolio return

Example: Assume the three assets in the previous example

contribute to overall portfolio value by 10%, 40% and 50%respectively.

Value-weighted portfolio return is:

[(0.1x5)+(0.4x10)+(0.5x-5)] = 2.0%

Formally:

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1

N

i

ViR riVp!

!


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y Price-weighted portfolio return

Example: Assume the original prices of the three assets in the

previous example were $2, $6 and $8 respectively. The total priceof the portfolio was therefore $2 + $6 + $8 = $16.

Price-weighted portfolio return is:

[(2/16x5)+(6/16x10)+(8/16x-5)] = 1.875%

Formally:

381

N

i

PiR riPp!

!


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y Value-weighted index weights large companies more heavily

than small companies.

Value-weighted index is a better reflection of what happened in the

market.

represents the performance of the average dollar invested in the

corresponding market

No rationale behind equal- and price-weighted portfolio methods.

Value-weighted measures are more accurate.

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y Covariance measures the degree to which asset returns

move together.

If the assets are affected by the same general economic factors

then there will be some degree of (positive) correlation betweenthem.

Note: independence = zero correlation.

The covariance between two assets (i and j) is;

, ,

1

( ) . ( )n

ij i k i j k jkk

cov p r E r r E r!

! - -


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y Correlation is a relative measure of how assets co-

vary with each other.

It is simply the correlation scaled by the product of the two

standard deviations. Correlation is bound by negative 1 and positive 1.

The correlation between two assets, i and j is;

covij

ijji

VW W

!


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The distribution of returns

y What would a histogram plot of the returns for an investment

look like?

y Symmetric? Are the returns clustered towards the middle?

Extreme returns?

y The properties of the returns is known as the return

distribution.

y This distribution can be summarised according to 5 measures;

Mean and median, variance, skewness and kurtosis.

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The distribution of returns (cont.)

y Mean is the average return.

y Median is the value ranked at the 50th percentile.

y Variance measures how dispersed the returns are from

the average return

y Skewness is a measure of symmetry.

y Kurtosis measures the relative number of observations

that fall in the extreme ends of tails of the distribution.

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y The normal (Gaussian) distribution

Completely described in terms of the first two moments.

The distribution is symmetric and mesokurtic; that is no skewness (or

asymmetry) or excess kurtosis skewness = 0

kurtosis = 3

68.27%, 95.45% and 99.7% of observations fall within one, two and

three standard deviations of the mean.

Since the normal distribution is symmetric, the median coincideswith the mean.

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y Statistical Inferences such as probabilities

Assuming a normal distribution makes the process of

statistical inference much easier.

Example: assume that an investment security has a mean

return of 16% and standard deviation of 10%.

What is the probability of making a loss?

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y Example (cont.) Use standard normal tables

Pr (loss) = Pr (Ri < 0)

Using zi = [Ri -E(Ri )] / (Wi)

where zi is the standard normal deviate.

Here zi = (0 - 0.16) / 0.10

= -1.6 (refer to prob tables)

= 0.054 (about 5%)

Hence the probability of loss is approximately 5%

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y Empirical evidence of returns

Return distributions are:

typically not symmetric

observed to have positive skewness or skewed

to right

not mesokurtic

observed to have leptokurtosisfat tails and peakedness

especially for high frequency stock returns

non-normality worst at short sample intervals. (But monthly

returns are not too bad.)

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5 THE REVIEW STAGE

What is the review stage?

y Occurs at the end of the holding period

y the key issue here is the comparison of expected return

with the actual return earned by the investment over theholding period

y typically performance measures used are risk and return.

y the purpose is to identify what changes must be made to

the allocation before the next holding period?

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6 SUMMARY

Summary of investment process

y Consists of three steps: Allocation decision, performance

measurement and the review stage.

y Continuously compound returns are preferred to discrete

returns.

y Geometric mean returns are typically preferred to

arithmetic mean returns.

y A value-weighted portfolio return is preferred to equal- or

price-weighted portfolio return.

y Returns are typically non-normally distributed.

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AUSTRALIAN FINANCIAL MARKETS

y In this part of the Lecture we will identify the major

Australian financial markets

y understand the importance of these markets via

selected statistics

y describe the basic legal and physical environment inwhich the markets operate.

y be aware of the historical performance of each of the

major Australian asset classes.

y identify the securities associated with each

Australian asset classes.

y appreciate the basics that underlie the Australian tax

system, with particular emphasis on the dividend

imputation system


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ASSET CLASSES & MARKETS

the 4 major asset classes and the markets each is

traded in;

y The equity market

where shares are traded

y The debt market which comprises;

Money market (cash securities), and

the Bond market (fixed interest securities)

y Property markets

real estate investments


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EQUITYMARKETS INAUSTRALIA

Australian Stock Exchange (ASX)

y ASX formed in 1987 from 6 existing state exchanges

y Exchange in each capital city-linked.

y

Primary market- company/organisation issues/floatsshares.

initial public offers (IPOs)

rights issues

dividend reinvestment plans

company options

y Secondary market- buy/sell securities by investors

other than original issuers.


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INTERNET RESOURCES FOR COMPANY

INFORMATION: REFER TOWEBADDRESS BELOW.

Australian Stock Exchange (ASX) - lists bothcurrent and delisted companies and namechanges. Shares and closing prices are available,as are recent company announcements, which

can be downloaded in full-text PDF (from July 1,2003), floats (forthcoming as well as recent), withlinks to PDFs of prospectuses. The ASX Fact Fileis produced annually. It contains marketstatistics, including market capitalization,

turnover, indices, top 50 domestic equitysecurities by market capitalization, and overseascompanies listed on the ASX.http://www.lib.unimelb.edu.au/collections/ecocom/ir_company.html


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Australian Stock Exchange (ASX)y Example of ASX pricing information

y the following is an extract from Example 2.1

y Company: Qantas Airways Ltd

y Issuer code: QAN

y Opening price for day: $3.968

y Price change since open (%): 0.76%

y Lowest (highest) price for the day: $3.96 (4.00)

y Volume of trades for the day: 2 569 305 shares


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Australian Stock Exchange (ASX)

y Two forms of regulation designed to ensure

confidence in share market transactions

Corporations Act 2001

provides a framework in which the ASX operates

ASX self regulation

Business and Listing rules for companies

rules for market participants (eg. brokers)

these rules cover accounting disclosures, reporting

requirements, and corporate governance issues.y ASX provides continuous surveillance of companies,

and reports to theAustralian Securities and

Investments Commission (ASIC).


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Trading on the ASX

y SEATS is an auction system that matched buyersand sellers.

y The system matches buyers and sellers until there

are no situations where the bid (buy) prices aregreater than the offer (sell) prices.

y The list of buyers and sellers is known as the orderbook. Suppose a stockbroker receives an order for 10,000 shares

at $5.00.

The buy order will be executed if there are sufficient sellorders in place at a price of $5.00 or less to meet the orderfor the 10,000 shares.

y Some common orders are limit, market orders andshort sales.


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Trading on the ASX - Limit Orders Limit orders are orders to trade a specific quantity of shares

at a particular price.


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Trading on the ASX - Market Orders Market orders are orders to trade a specific quantity of

shares at best possible price

Suppose buy order for 18,000 shares in

XYZ at market.


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Trading on the ASX - Short-sales Short-sales amounts to selling borrowed shares now at the

current market price and returning the shares to the lender

at some future point in time.

Allows investors to profit from a future fall in the share

price.

Example 2.1: Suppose share currently trading for $10.

Investor believes this price will fall in future and therefore

short-sells the share.


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Historical equity performance

y performance of equity market measured using an

index.

y Differences in index performance relate to

Breadth of the index

Broadest equity index is the All Ordinaries (500 stocks)

Narrowest is the ASX20

Index weighting system

equal, value or price-weighted

Capitalisation changes

impact of rights and bonus issues on value of index

Dividend effects

impact of dividend payments on value of index


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y Capitalisation changes

Example: Company ABC has 1m shares on issue at a cum-

rights price of $2. The company makes a rights issue on the

basis of 1 share for every 4 held. The subscription price is$1.50.

Cum-rights price

4 shares worth (4 x $2) $8.00

Ex-rights price

5 share worth (4 x $2 + $1.50) $9.50

Hence 1 share worth ($9.50/5) $1.90


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y Capitalisation changes

Example: Company ABC has 1m shares on issue at a cum-

bonus price of $2. The company makes a bonus issue on the

basis of 1 share for every 4 held. Cum-bonus price

4 shares worth (4 x $2) $8.00

Ex-bonus price

5 share worth (4 x $2) $8.00

Hence 1 share worth ($8.00/5) $1.60


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Taxation of Australian equity instruments

y Dividend Imputation

Replaced classical tax system in 1987

Designed to remove double-tax on dividends

Steps: Company pays tax on behalf of shareholders

Shareholders notionally pay income tax on dividends

Tax rebate on company tax already paid

Net tax is only personal tax


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y Dividend after all taxes paid is:

Dividend after all taxes = Dividend paid x (1-tp)/(1-tc)

y where:

tc is the corporate tax rate

tp is the personal tax rate

Dividend paid is the dollar amount of the dividend.


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y Example: Assume a fully franked dividend of $70 is

received and that tax has been paid at the corporate

tax rate of 30%.

y Assume a personal tax rate of 47%.

y Franked dividend of $70

Assessable income: 70/(1-tc) 100.00

Taxed at tp (47%) 47.00

Less tax credit (30%) 30.00

Net personal tax (17.00)

After tax dividend $53.00


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tax rate of 30%.




Taxed at tp (30%) 30.00


Net personal tax (0.00)



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tax rate of 30%.




Taxed at tp (15%) 15.00


Net personal tax 15.00



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RECENT SHARE PRICE INDICES


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Documents

Investment Mgmt L1