978-0077861704 Chapter 13 Lecture Note Part 2

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Chapter 13 – Return, Risk, and the Security Market Line

1. Systematic Risk and Beta

A. The Systematic Risk Principle

The principle – The reward for bearing risk depends only on the

systematic risk of the investment.

The implication – The expected return on an asset depends only on

that asset’s systematic risk.

A corollary – No matter how much total risk an asset has, its

expected return depends only on its systematic risk.

Lecture Tip: Exchange Traded Funds (ETFs) are essentially

mutual funds that can be traded through a broker just like stock.

Currently, ETFs are traded on a wide variety of indexes, including

domestic stock, international stock, corporate bond, government

bond, energy, and many others. One major advantage of ETFs

over traditional index mutual funds is that they trade like stock

throughout the day, whereas mutual funds take orders during the

day, but the fund trades at the closing value of the assets. ETFs

have become a popular way for investors to manage their asset

allocation and achieve diversification.

B. Measuring Systematic Risk

Beta coefficient – measures how much systematic risk an asset has

relative to an asset of average risk.

Lecture Tip: Students sometimes wonder just how high a stock’s

beta can get. In earlier years, one would say that, while the

average beta for all stocks must be 1.0, the range of possible

values for any given beta is from – to +.

Today, the Internet provides another way of addressing the

question. Go to screen.yahoo.com/stocks.html. This site allows you

to search many financial markets by fundamental criteria. For

example, as of February 20th, 2012, a search for stocks with betas

of at least 2.00 turns up 1,330 stocks.

Lecture Tip: The point that “the market does not reward risks that

are borne unnecessarily,” should be strongly emphasized, possibly

with a reference back to Figure 13.1. Many investment companies

offer investors a choice between income-oriented mutual funds,

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Chapter 13 – Return, Risk, and the Security Market Line

containing both bonds and stocks in established companies with

higher dividend payouts, and growth-oriented funds that are

typically composed of stocks of smaller companies that retain most

of their earnings for reinvestment in the firm. Investors that desire

growth-oriented funds typically assume a much greater degree of

systematic risk and expect higher returns. However, both types of

funds eliminate the unsystematic portion of risk through

diversification.

C. Portfolio Betas

Portfolio betas are a weighted average of the individual asset betas.

Example:

Stock Amount Invested Portfolio Weight Beta Product

IBM 6000 50.00% 1.586 .793

GM 4000 33.33% 1.139 .380

Wal-Mart 2000 16.67% .674 .112

Portfolio 10,000 100.00% 1.285

Lecture Tip: Remember that the cost of equity depends on both the

firm’s business risk and its financial risk. So, all else equal,

borrowing money will increase a firm’s equity beta because it

increases the volatility of earnings. Robert Hamada derived the

following equation to reflect the relationship between levered and

unlevered betas (excluding tax effects):

L = U (1 + D/E)

where: L = equity beta of a levered firm;

U = equity beta of an unlevered firm;

D/E = debt-to-equity ratio

2. The Security Market Line

A. Beta and the Risk Premium

A riskless asset has a beta of 0.When a risky asset with >0 is

combined with a riskless asset, the resulting expected return is the

weighted sum of the expected returns, and the portfolio beta is the

weighted sum of the betas. By varying the amount invested in each

asset, we can get an idea of the relation between portfolio expected

returns and betas. This relationship is illustrated in Figure 13.2A.

As can be seen, all of the risk-return combinations lie on a straight

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Chapter 13 – Return, Risk, and the Security Market Line

line. Remind the students that the equation for a line is:

y = mx + b

where: y = expected return

x = beta

m = slope = risk-premium per unit of beta

b = y-intercept = risk-free rate

Introducing this equation now prepares the students for the SML

and the CAPM.

Lecture Tip: The example in the book illustrates a greater than

100% investment in asset A. This means that the investor has

borrowed money on margin (technically at the risk-free rate) and

used that money to purchase additional shares of asset A. This can

increase the potential returns, but it also increases the risk. The

maximum amount that an investor can borrow on margin is 50% of

the total value of the position. If the value of the portfolio drops

such that the loan amount is greater than 50% of the value of the

portfolio (or some other amount established by the broker), then

the investor will receive a margin call and will have to add

additional cash to the brokerage account. Also, students may have

heard about margin accounts in relation to futures contracts –

buying stock on margin and posting margin for futures trades are

different types of trades and have different mechanics involved

with how margin calls are issued.

The Reward-to-Risk Ratio is the expected return per unit of

systematic risk. In other words, it is the ratio of risk premium to

systematic risk.

The basic argument is that since systematic risk is all that matters

in determining expected return, the reward-to-risk ratio must be the

same for all assets. If it were not, people would buy the asset with

the higher reward-to-risk ratio (driving the price up and the return

down).

The fundamental result is that in a competitive market where only

systematic risk affects E(R), the reward-to-risk ratio must be the

same for all assets in the market. Consequently, the expected

returns and betas of all assets much plot on the same straight line.

B. The Security Market Line

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Chapter 13 – Return, Risk, and the Security Market Line

The line that gives the expected return/systematic risk

combinations of assets in a well functioning, active financial

market is called the security market line.

Lecture Tip: Although the realized market risk premium has on

average been approximately 8.2%, the historical average should

not be confused with the anticipated risk premium for any

particular future period. There is abundant evidence that the

realized market return has varied greatly over time. The historical

average value should be treated accordingly. On the other hand,

there is currently no universally accepted means of coming up with

a good ex ante estimate of the market risk premium, so the

historical average might be as good a guess as any. In the late

1990’s, there was evidence that the risk premium had been

shrinking. In fact, Alan Greenspan was concerned with the

reduction in the risk premium because he was afraid that investors

had lost sight of how risky stocks actually are. Investors had a

wake-up call in late 2000 and 2001.

Market Portfolios: Consider a portfolio of all the assets in the

market and call it the market portfolio. This portfolio, by

definition, has “average” systematic risk with a beta of 1. Since all

assets must lie on the SML when appropriately priced, the market

portfolio must also lie on the SML. Let the expected return on the

market portfolio = E(RM). Then, the slope of the SML = reward-to-

risk ratio = [E(RM) – Rf] / M = [E(RM) – Rf] / 1 = E(RM) – Rf

The Capital Asset Pricing Model: Go back to the discussion of the

equation of a line:

E(Rj) = Rf + slope(j)

E(Rj) = Rf + (E(RM) – Rf)(j)

The CAPM states that the expected return for an asset depends on:

-The time value of money, as measured by Rf

-The reward per unit risk, as measured by E(RM) – Rf

-The asset’s systematic risk, as measured by 

3. The SML and the Cost of Capital: A Preview

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Chapter 13 – Return, Risk, and the Security Market Line

A. The Basic Idea

We must determine an investment’s risk and then use the CAPM to

determine the expected return on assets of similar risk.

Lecture Tip: Students should remember that in an efficient market,

security investments have a NPV = 0 on average. However, the

NPV does not imply that a company’s investments in new projects

must have an NPV of zero. Firms attempt to invest in projects with

a positive NPV, and those that are consistently successful will

trade at higher prices, all else equal. The ability to generate

positive NPV projects reflects the fundamental differences in

physical asset markets and financial asset markets. Physical asset

markets are generally less efficient than financial asset markets.

B. The Cost of Capital

Cost of capital – the minimum expected return an investment must

offer to be attractive. Sometimes referred to as the required return.

4. Summary and Conclusions

APPENDIX A: CALCULATING BETA COEFFICIENTS

In the chapter we noted that a beta coefficient measures the amount of systematic risk

present in a particular risky asset relative to the average risky asset. (Later, it was

suggested that the market portfolio would serve as an appropriate proxy for the average

risky asset.) Since risk is a function of the changes in, or “movement of,” an asset’s price,

systematic risk must be attributable to the movement in a risky asset’s price relative to the

movement in the price of the average risky asset (or the market portfolio).

Given the above, we should not be surprised to find that the beta coefficient is nothing

more than a statistical measure of the relationship between the returns on asset j and the

market portfolio. This relationship is most often quantified via the use of simple linear

regression. Specifically, we estimate the following model:

Rjt = j + jRMt + j

Where:Rjt = the return on stock j in period t,

RMt = the return on the market portfolio in period t,

j, j = the intercept and the slope coefficients, respectively, and

j = the error term.

The model above is called the “market model” and is usually estimated using daily,

weekly, or monthly historical returns. (Although there are no universally accepted

guidelines, most people use approximately 250 daily returns, 104 weekly returns, or 60

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Chapter 13 – Return, Risk, and the Security Market Line

monthly returns to estimate the model.) The estimated  coefficient in the model above is

the beta referred to in the chapter.

Although, it is beyond the scope of this book, it is possible to show that, given certain

assumptions about the distribution of returns, the beta coefficient is equal to the

correlation between returns on stock j and the market portfolio, times the product of the

standard deviations of the returns on stock j and the market portfolio, divided by the

variance of the market returns. In equation form,

j = j,MjM / 2M

Consider the following monthly stock return data.

Month RjRM

1 .003 .013

2 .024 .017

3 .021 .012

4 -.015 .004

5 .005 .011

6 .022 .015

7 -.021 .011

8 .017 -.010

9 .018 .011

10 .028 .013

11 .032 .021

12 -.017 -.013

Expected Return .00975 .00875

Standard Deviation .0185 .0103

Correlation .50276

According to the above equation, j = .50276(.0185)(.0103)/(.0103)2 = .903. Since, in a

strict mathematical sense, the beta coefficient is simply an index measuring the statistical

relationship between the returns on stock j and the market portfolio, we interpret the

results to mean that the systematic risk of stock j is about 90 percent of that of the

average stock. (Digression: This is the source of the terms “aggressive” and “defensive”

as applied to stocks. Aggressive stocks are stocks with betas greater than 1.0; they are

more volatile than the average stock and are, therefore, more suited to investors willing to

take risks, i.e., to be aggressive. Of course, the opposite holds true for defensive stocks.)

Notice that the beta equation also suggests that beta has the following properties.

1. The beta of the market portfolio, M, must equal one.

2. The beta of the risk-free asset must equal zero.

Finally, it should be noted that most people need not bother to calculate betas for stocks

they are interested in. Beta coefficients are computed by several firms (for example,

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Chapter 13 – Return, Risk, and the Security Market Line

Merrill Lynch, Standard and Poor’s Corporation, Value Line, and Moody’s) and appear in

various publications and on the Internet.

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