Chapter 10

Copyright © 2011 Pearson Prentice Hall. All rights reserved.

Chapter 10

Capital Markets and the Pricing of Risk

Figure 10.1 Value of $100 Invested at the End of 1925

Source: Chicago Center for Research in Security Prices (CRSP) for U.S. stocks and CPI, Global Finance Data for the World Index, Treasury bills and corporate bonds.

5-2

10.2 Common Measures of Risk and Return

• Probability Distribution When an investment is risky, there are different returns

it may earn. Each possible return has some likelihood of occurring. This information is summarized with a probability distribution, which assigns a probability, PR , that each possible return, R , will occur.

• Assume BFI stock currently trades for $100 per share. In one year, there is a 25% chance the share price will be $140, a 50% chance it will be $110, and a 25% chance it will be $80.

5-3

Table 10.1

5-4

Figure 10.2 Probability Distribution of Returns for BFI

5-5

Expected Return

• Expected (Mean) Return

Calculated as a weighted average of the possible returns, where the weights correspond to the probabilities.

Expected Return RRE R P R

5-6

Variance and Standard Deviation

• Variance The expected squared deviation from the mean

• Standard Deviation The square root of the variance

• Both are measures of the risk of a probability distribution

( ) ( ) SD R Var R

2 2( )

RRVar R E R E R P R E R

5-7

Alternative Example 10.1

• Problem

TXU stock is has the following probability distribution:

What are its expected return and standard deviation?

Probability Return

.25 8%

.55 10%

.20 12%

5-8

Alternative Example

• Solution

Expected Return

• E[R] = (.25)(.08) + (.55)(.10) + (.20)(.12)

• E[R] = 0.020 + 0.055 + 0.024 = 0.099 = 9.9%

Standard Deviation

• SD(R) = [(.25)(.08 – .099)2 + (.55)(.10 – .099)2 + (.20)(.12 – .099)2]1/2

• SD(R) = [0.00009025 + 0.00000055 + 0.0000882]1/2

• SD(R) = 0.0001791/2 = .01338 = 1.338%

5-9

10.3 Historical Returns of Stocks and Bonds

• Computing Historical Returns

Realized Return

• The return that actually occurs over a particular time period.

1 1 1 1 1

1

Dividend Yield Capital Gain Rate

t t t t tt

t t t

Div P Div Div PR

P P P

5-10

10.3 Historical Returns of Stocks and Bonds (cont'd)

• Computing Historical Returns

If a stock pays dividends at the end of each quarter, with realized returns RQ1, . . . ,RQ4 each quarter, then its annual realized return, Rannual, is computed as:

annual 1 2 3 41 (1 )(1 )(1 )(1 ) Q Q Q QR R R R R

5-11

Chapter 10, problem 6

Using the data in the table below, calculate the return for investing in Boeing stock from January 2, 2003 to January 2, 2004, assuming all dividends are reinvested in the stock immediately.

Date Price Dividend

1/2/03 33.88

2/5/03 30.67 0.17

5/14/03 29.49 0.17

8/13/03 32.38 0.17

11/12/03 39.07 0.17

1/2/04 41.99

5-12

Figure 10.4 The Empirical Distribution of AnnualReturns for U.S. Large Stocks (S&P 500), Small Stocks, Corporate Bonds, and Treasury Bills, 1926–2008

5-13

Average Annual Return

Where Rt is the realized return of a security in year t, for the years 1 through T

• Using the data from Table 10.2, the average annual return for the S&P 500 from 1996–2004 is:

1 2 1

1 1

T

T tt

R R R R RT T

1 (0.230 0.334 0.286 0.210 0.091

9 0.119 0.221 0.287 0.109) 11.4%

R

5-14

The Variance and Volatility of Returns

• Variance Estimate Using Realized Returns

The estimate of the standard deviation is the square root of the variance.

2

1

1( )

1

T

tt

Var R R RT

5-15

Table 10.3 and 10.4:Return and volatility, 1926–2008

5-16

Using Past Returns to Predict the Future: Estimation Error

• We can use a security’s historical average return to estimate its actual expected return. However, the average return is just an estimate of the expected return.

Standard Error

• A statistical measure of the degree of estimation error

Example: The expected return and standard deviation of the S&P 500 annual return was 12.36% and 20.36%, respectively. Given that that these empirical estimates were calculated based on the past 79 years(1926–2004), what is the 95% confidence interval for next year’s S&P 500 return?

What is the probability that return will go down by more than 5%?

5-17

Table 10.5 Volatility Versus Excess Return of U.S. Small Stocks, Large Stocks (S&P 500), Corporate Bonds, and Treasury Bills, 1926–2008

5-18

Figure 10.5 The Historical Tradeoff Between Risk and Return in Large Portfolios, 1926–2005

Source: CRSP, Morgan Stanley Capital International5-19

Figure 10.6 Historical Volatility and Return for 500 Individual Stocks, by Size, Updated Quarterly, 1926–2005

5-20

10.5 Common Versus Independent Risk The Vancouver insurance industry is highly competitive. Manulife

has 100,000 houses insured against theft, and 100,000 houses insured against earthquake. Against a year with large claims of above $100M, the company can reinsure itself with a reinsurance company in Swiss at a premium of 1% of claim value.

Suppose that in Vancouver there is a 0.1% probability of a theft and a 0.1% probability of an earthquake in any given year. If an average house in the city costs $600,000, what would you expect the premiums to be for each type of insurance given that the competitive market is such that in 95% of the years the insurance company’s revenues are higher than the costs of claims?

5-21

10.5 Common Versus Independent Risk

Common Risk and Independent Risk in the Corporate Environment

Risk that affects all securities versus risk that affects a particular security.

Diversification – the process of averaging out of independent risks in a large portfolio

5-22

10.6 Diversification in Stock Portfolios

• Firm-Specific Versus Systematic Risk

Firm Specific News

• Good or bad news about an individual company

Market-Wide News

• News that affects all stocks, such as news about the economy

5-23

10.6 Diversification in Stock PortfoliosImportant financial terminology

Independent Risks

• Due to firm-specific news Also known as:

» Firm-Specific Risk

» Idiosyncratic Risk

» Unique Risk

» Unsystematic Risk

» Diversifiable Risk

Common Risks

• Due to market-wide news Also known as:

» Systematic Risk

» Undiversifiable Risk

» Market Risk

5-24

10.6 Diversification in Stock Portfolios (cont'd)


When many stocks are combined in a large portfolio, the firm-specific risks for each stock will average out and be diversified.

The systematic risk, however, will affect all firms and will not be diversified.

5-25

10.6 Diversification in Stock Portfolios


Consider two types of firms:

• Type S firms are affected only by systematic risk. There is a 50% chance the economy will be strong and type S stocks will earn a return of 40%; There is a 50% change the economy will be weak and their return will be –20%. Because all these firms face the same systematic risk, holding a large portfolio of type S firms will not diversify the risk.

• Type I firms are affected only by firm-specific risks. Their returns are equally likely to be 40% or –20%, based on factors specific to each firm’s local market. Because these risks are firm specific, if we hold a portfolio of the stocks of many type I firms, the risk is diversified.

5-26

Example 10.6

5-27

Figure 10.7 Volatility of Portfolios of Type S and I Stocks

5-28

No Arbitrage and the Risk Premium

• The risk premium for diversifiable risk is zero, so investors are not compensated for holding firm-specific risk.

If the diversifiable risk of stocks were compensated with an additional risk premium, then investors could buy the stocks, earn the additional premium, and simultaneously diversify and eliminate the risk.

5-29

No Arbitrage and the Risk Premium (cont'd)

• The risk premium of a security is determined by its systematic risk and does not depend on its diversifiable risk.

This implies that a stock’s volatility, which is a measure of total risk (that is, systematic risk plus diversifiable risk), is not especially useful in determining the risk premium that investors will earn.

5-30

10.7 Measuring Systematic Risk

• Estimating the expected return will require two steps:

Measure the investment’s systematic risk

Determine the risk premium required to compensate for that amount of systematic risk

5-31

Measuring Systematic Risk (cont'd)

• Efficient Portfolio A portfolio that contains only systematic risk. There is

no way to reduce the volatility of the portfolio without lowering its expected return.

• Market Portfolio An efficient portfolio that contains all shares and

securities in the market• The S&P 500 is often used as a proxy for the

market portfolio.

5-32


• Beta (β)

The expected percent change in the excess return of a security for a 1% change in the excess return of the market portfolio.

• Beta differs from volatility. Volatility measures total risk (systematic plus unsystematic risk), while beta is a measure of only systematic risk.

5-33

Chapter 10, problem 31

Suppose the market portfolio is equally likely to increase by 30% or decrease by 10%.a.Calculate the beta of a firm that goes up on average by 43% when the market goes up and goes down by 17% when the market goes down.b.Calculate the beta of a firm that goes up on average by 18% when the market goes down and goes down by 22% when the market goes up.c.Calculate the beta of a firm that is expected to go up by 4% independently of the market.

5-34


• Beta (β)

A security’s beta is related to how sensitive its underlying revenues and cash flows are to general economic conditions. Stocks in cyclical industries, are likely to be more sensitive to systematic risk and have higher betas than stocks in less sensitive industries.

5-35

Table 10.6 Betas with Respect to the S&P 500 for Individual Stocks (based on monthly data for 2004–2008)

5-36

Estimating the Risk Premium

• Market Risk Premium

The market risk premium is the reward investors expect to earn for holding a portfolio with a beta of 1.

Market Risk Premium Mkt fE R r

5-37

Estimating the Risk Premium (cont'd)

• Estimating a Traded Security’s Expected Return from Its Beta

Risk-Free Interest Rate Risk Premium

( )

f Mkt f

E R

r E R r

5-38

Example

• Problem

Assume the economy has a 60% chance of the market return will 15% next year and a 40% chance the market return will be 5% next year.

Assume the risk-free rate is 6%.

If Microsoft’s beta is 1.18, what is its expected return next year?

5-39

10.8 Beta and the Cost of Capital

• A firm’s cost of capital for a project is the expected return that its investors could earn on other investments with the same risk. Systematic risk determines expected returns, thus the

cost of capital for an investment is the expected return available on securities with the same beta.

• The cost of capital for investing in a project is:

( ) f Mkt fr r E R r

5-40

Example

5-41

How the CAPM is related capital market efficiency

• Efficient Capital Markets When the cost of capital of an investment depends only

on its systematic risk and not its unsystematic risk.

• The CAPM states that the cost of capital of any investment depends upon its beta. The CAPM is a much stronger hypothesis than an efficient capital market. The CAPM states that the cost of capital depends only on systematic risk and that systematic risk can be measured precisely by an investment’s beta with the market portfolio.

5-42

Empirical Evidence on Capital Market Competition

• If the market portfolio were not efficient, investors could find strategies that would “beat the market” with higher returns and lower risk.

• However, all investors cannot beat the market, because the sum of all investors’ portfolios is the market portfolio.

• Hence, security prices must change, and the returns from adopting these strategies must fall so that these strategies would no longer “beat the market.”

5-43

Empirical Evidence on Capital Market Competition (cont'd)

• An active portfolio manager advertises his/her ability to pick stocks that “beat the market.” While many managers do have some ability to “beat the market,” once the fees that are charged by these funds are taken into account, the empirical evidence shows that active portfolio managers have no ability to outperform the market portfolio.

5-44

Documents

Chapter 10