The Security Market Line (SML)equation shows the relationship between a se-
curity’s market risk and its required rate of return. The return required for any
security i is equal to the risk-free rateplus the market risk premiumtimes the
security’s beta: rirRF(RPM)bi.
Even though the expected rate of return on a stock is generally equal to its re-
quired return, a number of things can happen to cause the required rate of return
to change: (1) the risk-free rate can changebecause of changes in either real
rates or anticipated inflation, (2) a stock’s beta can change,and (3) investors’
aversion to risk can change.
Because returns on assets in different countries are not perfectly correlated, global
diversificationmay result in lower risk for multinational companies and globally
diversified portfolios.
In the next two chapters we will see how a security’s expected rate of return affects its
value. Then, in the remainder of the book, we will examine ways in which a firm’s
management can influence a stock’s risk and hence its price.
Questions
Define the following terms, using graphs or equations to illustrate your answers wherever
feasible:
a.Stand-alone risk; risk; probability distribution
b.Expected rate of return, rˆ
c.Continuous probability distribution
d.Standard deviation, ; variance, ^2 ; coefficient of variation, CV
e.Risk aversion; realized rate of return,
f.Risk premium for Stock i, RPi; market risk premium, RPM
g.Capital Asset Pricing Model (CAPM)
h.Expected return on a portfolio, ˆrp; market portfolio
i.Correlation coefficient, ; correlation
j.Market risk; diversifiable risk; relevant risk
k.Beta coefficient, b; average stock’s beta, bA
l.Security Market Line (SML); SML equation
m. Slope of SML as a measure of risk aversion
The probability distribution of a less risky expected return is more peaked than that of a riskier
return. What shape would the probability distribution have for (a) completely certain returns
and (b) completely uncertain returns?
Security A has an expected return of 7 percent, a standard deviation of expected returns of 35 per-
cent, a correlation coefficient with the market of 0.3, and a beta coefficient of 1.5. Security B
has an expected return of 12 percent, a standard deviation of returns of 10 percent, a correlation
with the market of 0.7, and a beta coefficient of 1.0. Which security is riskier? Why?
Suppose you owned a portfolio consisting of $250,000 worth of long-term U.S. government bonds.
a.Would your portfolio be riskless?
b.Now suppose you hold a portfolio consisting of $250,000 worth of 30-day Treasury bills.
Every 30 days your bills mature, and you reinvest the principal ($250,000) in a new batch of
bills. Assume that you live on the investment income from your portfolio and that you want
to maintain a constant standard of living. Is your portfolio truly riskless?
c.Can you think of any asset that would be completely riskless? Could someone develop such
an asset? Explain.
If investors’ aversion to risk increased, would the risk premium on a high-beta stock increase
more or less than that on a low-beta stock? Explain.
If a company’s beta were to double, would its expected return double?
Is it possible to construct a portfolio of stocks which has an expected return equal to the risk-
free rate?
3–7
3–6
3–5
3–4
3–3
3–2
r
3–1
140 CHAPTER 3 Risk and Return
138 Risk and Return
