Session 6: Risk and the Cost of Capital
Read: Chapter 10: Risk and Return
Chapter 11: Portfolio Choice and Diversification
1. Answer the following questions:
a. Briefly explain the difference between beta as a measure of risk and variance as a
measure of risk.
b. What is the correlation coefficient between the two stocks that gives the maximum
reduction in risk for a two-stock portfolio?
c. Historical nominal return for stock A is –8%, +10% and +22%. The nominal return for
the market portfolio is +6%, +18% and 24%. Calculate the beta for stock A.
d. The correlation coefficient between stock B and the market portfolio is 0.8. The
standard deviation of the stock B is 35% and that of the market is 20%. Calculate the
beta of the stock.
2. Answer the following questions:
a. How many variance terms and how many covariance terms do you need to calculate
the risk of a 100-share portfolio?
b. Suppose all stocks had a standard deviation of 30 percent and a correlation with each
other of .4. What is the standard deviation of the returns on a portfolio that has equal
holdings in 50 stocks?
c. What is the standard deviation of a fully diversified portfolio of such stocks?
3. Your eccentric Aunt Gerlinda has left you €50,000 in Deutsche Bank shares plus €50,000
cash. Unfortunately, her will requires that the shares not be sold for one year and the
€50,000 cash must be entirely invested in one of the securities listed below. What is the
safest attainable portfolio under these restrictions?
Correlation
Coefficients
Alcan BP Deutsche
Bank KLM LVMH Nestle Sony
Standard
Deviation
(%)
Alcan 1 0.39 0.55 0.54 0.61 0.26 0.36 30.20
BP 1 0.23 0.29 0.22 0.3 0.14 23.90
Deutsche
Bank 1 0.36 0.48 0.16 0.39 38.10
KLM 1 0.49 0.32 0.19 54.50
LVMH 1 0.02 0.5 42.00
Nestle 1 0.1 15.50
Sony 1 47.50
4. ExxonMobil offers an expected return of 10 percent and Coca-Cola offers an expected
return of 15 percent. The standard deviation of returns is 18.2 percent for ExxonMobil and
27.3 percent for Coca-Cola. The correlation between the returns of ExxonMobil and Coca-
Cola has been about .4. In what proportions should the investor divide his portfolio to
achieve the minimum risk?
