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CHAPTER 5
RISK AND PORTFOLIO MANAGEMENT
Teaching Guides for Questions and Problems in the Text
QUESTIONS
5-1. Nondiversifiable risk (also referred to as systematic risk) is the risk that is not reduced
through the construction of diversified portfolios. This risk is associated with general
movements in securities returns (market risk), changes in interest rates (interest rate risk),
inflation (purchasing power risk), fluctuations in the value of foreign currency (exchange
rate risk), and reinvestment rate risk. These sources of risk may be managed by other
techniques (e.g., duration to manage interest and reinvestment rate risks associated with
bonds), but they are not affected through the construction of diversified portfolios.
5-2. A diversified portfolio consists of a variety of assets (e.g., bonds, stocks, and real
estate). A diversified portfolio may also consist solely of stocks if the securities are issued
by a variety of firms in different industries.
5-3. The return from an investment can be either income, price appreciation, or a
combination of both. The expected return is the return the investor anticipates when the
5-4. The investor will select the security that offers the highest return for a given level of
5-5. To achieve diversification, the correlation among investment returns should be low or
5-6. Risk may be measured by the dispersion around the expected return (i.e., the standard
deviation) or by beta. (Betas are discussed in the next question.) Indifference curves
5-7. A beta coefficient is an index of systematic risk. It is a measure of the volatility of a
stock's return relative to the market return. The larger the beta coefficient, the more volatile
is the stock's return relative to the return on the market. A beta of 0.5 means that the return
on the stock is less volatile than the market return. A beta of 1.0 indicates that movement in
the return on the market and the return on the stock have been identical. A beta of 1.5
5-8. If the correlation coefficient between a stock and the market is 0.0, then movements in
5-9. In order to induce the investor to accept more risk, the anticipated return must be
higher. Thus, there is a positive relationship between return and risk as measured by either
5-10. The capital asset pricing model is a two variable model in which return is dependent
PROBLEMS
5-1. a. The expected return on an investment is the sum of the dividend yield and the
b. If taxes on the returns and the costs of realizing the returns are the same, there is no
A.
The small cost associated with on-line trading has almost erased the impact of brokerage
commissions for many investors. There remains, however, the question of the size of the
trade, since many small trades are not cost effective.
5-2. a. The expected return on a portfolio is the weighted average of the assets included in
b. The substitution of real estate for AT&T stock in this problem increases the expected
5-3. a. Expected return of the portfolio:
b. Standard deviation of the portfolio:
c. Position Expected Return Standard Deviation
All A 10% 3.0
5-4. This problem repeats the previous problem but adds more possible combinations.
a. Position Expected Return Standard Deviation
All A 12% 1.00
All B 20% 6.00
Computations of the standard deviations:
b. The substitution of stock A reduces both risk and expected return.
c. Position Expected Return Standard Deviation
All A 12% 1.0
All B 20% 6.0
50%A/50%B 16% 2.73
Computations of the standard deviations:
50%A-50%B:
Again the substitution of stock A reduces both risk and expected return, but the reduction
in risk is greater in this example because the correlation between the two returns is more
negative (i.e., the correlation coefficient is -0.6 instead of 0.2).
5-5. Total invested: $10 + 24 + 41 + 19 = $94
Weight of each stock in portfolio (assuming one share
of each stock):
A: $10/$94 = 11%
Portfolio beta:
Weight of each stock in the portfolio:
A: $10/$159 = 6%
B: $48/$159 = 30%
C: $82/$159 = 52%
D: $19/$159 = 12%
Portfolio beta:
5-6. The return according to the security market line is
rs = rf + (rm - rf)beta.
The return on the stock should be
5-7. Expected returns:
A: (-10)(.2) + (5)(.4) + 15(.3) + 25(.1) = 7.0%
B: (-5)(.2) + (5)(.4) + 7(.3) + 39(.1) = 7.0%
The expected returns are equal.
The standard deviations:
A: the weighted squared differences:
B: the weighted squared differences:
(-5 - 7)2(.2) = (-122).2 = 144(.2) = 28.8
(5 - 7)2(.2) = (-22).4 = 4(.4) = 1.6
(7 - 7)2(.2) = (-02).3 = 0(.3) = 0.0
5-8. The coefficient of variation facilitates comparisons of standard deviations, by
converting an absolute number into a relative number. This is done by dividing the standard
deviation by the mean. In this problem, there are two sets of stocks, and in both cases
Stock B has the higher return. It also has the higher standard deviation, which indicates
more variability of the returns and more risk. The question is the additional return
sufficient to justify bearing the risk. Calculating the coefficient of variation will help
answer that question.
a. Stock A: average return 3.00%
In this pairing, Stock B has a higher standard deviation but the coefficients of variation are
equal.
b. Stock A: average return 2.00%
5-9. Students may use any regression package such as Excel and its regression program to
obtain the beta coefficients.
a. The estimated equations are
The beta coefficients (i.e., the slopes of the lines) are
Stock X has the lower beta; it has less systematic risk.
b. In period 10 the return on the market was -5%. Using the estimated equations the
returns on each stock would be
c. The R squared for the two equations are 0.41 and 0.82, respectively. These indicate that
for at least stock X something other than the market primarily explains the stock's return.
5-10. The following correlation coefficients were calculated using Excel. I let my students
use whatever method they prefer to perform the calculations, since the purpose of the
problem is to demonstrate the change in the values of the coefficients.
For the entire 20 year time period, the correlation coefficient is 0.721. For the five years
a. The students add beta coefficients to the stocks they selected in Part 1.
b. Next the student determines the beta of the portfolio. Having the same amount invested
in each stock reduces the amount of calculations, if an equal dollar amount is invested in
each stock, an average of the individual stock’s beta will give the portfolio beta. If an
c. Beta coefficients may differ depending on the source. Part c tries to verify this reality
g. Diversification is important because it reduces unsystematic risk. To reduce
unsystematic risk, the return on the assets in the portfolio must not be highly, positively
This case essentially repeats the material on risk and return, and helps determine is a
particular combination of risk and return is inefficient. The expected returns and betas are
1. Position Expected Return Beta
All in T-bill 7% 0.0
Summary of the portfolio returns and their betas:
return beta
All in T-bill 7% 0.00
2. All that has to be shown is that a portfolio offers an inferior return for a given amount
of risk (or for a given return requires more risk) to determine an inefficient portfolio. For
example, all in B produces a return of 11 percent with a beta of 1.3 while 50 percent in A
and 50 percent in C produces a higher return (11 percent) and lower risk (beta of 1.05). A
portfolio invested entirely in B is inefficient3. Combination of half the funds in A and half
the funds in C generates a return of 11.5% and has a beta of 1.05. What combination of the
Treasury bill and stock C offers a beta of 1.05? Answer:
11.9 percent exceeds 11.5 percent, so that portfolio is superior to 50 percent invested in A
and C. (30 percent in the bill and 70 percent in stock A produces a point that lies above the
4. To illustrate that a return of 12 percent and a beta of 1.4 is inefficient, all that is
necessary is to find a portfolio with either a higher return with a beta of 1.4 or a lower beta
with a higher return. For example, 89 percent in stock C and 11 percent in stock A
5. While investors may acquire one asset at a time, it is
important to see the acquisition in a portfolio context. Since diversification is an important
objective when constructing a portfolio, the impact of the individual security on the
portfolio's risk as well as its return should be considered before acquiring the asset. The
1. The first question asks for the portfolio's standard deviation as the portfolio of the
portfolio is shifted from the domestic index fund to the foreign fund. The equation for the
standard deviation of a portfolio consisting of two securities was given in Chapter 6 in
The portfolio standard deviations for the various combinations of U.S. and Japanese
securities are
Proportion Invested in Portfolio Standard
the U.S. Fund Deviation
100% 10.00%
90 9.65
80 9.47
70 9.49
(These answers were derived using the Investment Analysis Calculator available through
the publisher’s home page.)
2. This question illustrates the impact of a lower correlation coefficient. If the coefficient
is -0.2, the portfolio standard deviations for the various combinations are
Proportion Invested in Portfolio Standard
the U.S. Fund Deviation
100% 10.00%
90 8.82
80 8.20
70 8.26
In both 1 and 2, the substitution of the foreign securities initially reduces risk as measured
by the portfolio's standard deviation. In both cases, risk is the least at a combination of 80
percent U.S. securities and 20 percent foreign securities.
3. This question reverses the first question. Diversification also applies to foreign
investors, so that they may reduce their risk exposure by investing in the securities of other
4. a. If investors anticipate that the value of the dollar will rise, that argues against
investing in foreign securities denominated in the foreign currency. (Anything such as the
b. One reason for investing in foreign securities is the potential they offer for diversifying a
domestic portfolio. Increased globalization of financial markets may increase the
