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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,MjM / 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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