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FINM7403 CAPM Tutorial Solutions
BKM Chapter 9 problem sets, Q10*, 11*, 12*, 13*, 14*, 15*, and 16*
Question 10
Suggested solution:
Not possible. Portfolio A has a higher beta than Portfolio B, but the expected return for Portfolio A is lower than
the expected return for Portfolio B. Thus, these two portfolios cannot exist in equilibrium.
Question 11
Suggested solution:
Possible. If the CAPM is valid, the expected rate of return compensates only for systematic (market) risk,
represented by beta, rather than for the standard deviation, which includes nonsystematic risk. Thus, Portfolio
A’s lower rate of return can be paired with a higher standard deviation, as long as A’s beta is less than B’s.
Question 12
Suggested solution:
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Not possible. The reward-to-variability ratio for Portfolio A is better than that of the market. This scenario is
impossible according to the CAPM because the CAPM predicts that the market is the most efficient portfolio.
Using the numbers supplied:
.16 .10 .18 .100.5 0.33
.12 .24A M
S S− −= = = =
Portfolio A provides a better risk-reward trade-off than the market portfolio.
Question 13
Suggested solution:
Not possible. Portfolio A clearly dominates the market portfolio. Portfolio A has both a lower standard deviation
and a higher expected return.
Question 14
Suggested solution:
Not possible. The SML for this scenario is: E(r) = 10 + β × (18 – 10)
Portfolios with beta equal to 1.5 have an expected return equal to:
E(r) = 10 + [1.5 × (18 – 10)] = 22%
The expected return for Portfolio A is 16%; that is, Portfolio A plots below the SML (α A = –6%) and, hence, is
an overpriced portfolio. This is inconsistent with the CAPM.
Question 15
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Suggested solution:
Not possible. The SML is the same as in Problem 14. Here, Portfolio A’s required return is: .10 + (.9 × .08) =
17.2%
This is greater than 16%. Portfolio A is overpriced with a negative alpha:
α A = –1.2%
Question 16
Suggested solution:
Possible. The CML is the same as in Problem 12. Portfolio A plots below the CML, as any asset is expected to.
This scenario is not inconsistent with the CAPM.
BKM Chapter 9 CFA Problems 2, 12*
Problem 2
Suggested solution:
E(r) = rf + β × [E(r M ) − rf ]
Furhman Labs: E(r) = .05 + 1.5 × [.115 − .05] = 14.75%
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Garten Testing: E(r) = .05 + 0.8 × [.115 − .05] = 10.20%
If the forecast rate of return is less than (greater than) the required rate of return, then the security is overvalued
(undervalued).
Furhman Labs: Forecast return – Required return = 13.25% − 14.75% = −1.50%
Garten Testing: Forecast return – Required return = 11.25% − 10.20% = 1.05%
Therefore, Furhman Labs is overvalued and Garten Testing is undervalued.
Problem 12
Suggested solution:
a.
Expected Return Alpha
Stock X 5% + 0.8 × (14% − 5%) = 12.2% 14.0% − 12.2% = 1.8%
Stock Y 5% + 1.5 × (14% − 5%) = 18.5% 17.0% − 18.5% = −1.5%
b. i. Kay should recommend Stock X because of its positive alpha, compared to Stock Y, which has a negative
alpha. In graphical terms, the expected return/risk profile for Stock X plots above the security market line
(SML), while the profile for Stock Y plots below the SML. Also, depending on the individual risk
preferences of Kay’s clients, the lower beta for Stock X may have a beneficial effect on overall portfolio
risk.
ii. Kay should recommend Stock Y because it has higher forecasted return and lower standard deviation
than Stock X. The respective Sharpe ratios for Stocks X and Y and the market index are:
Stock X: (14% − 5%)/36% = 0.25
Stock Y: (17% − 5%)/25% = 0.48
Market index: (14% − 5%)/15% = 0.60
The market index has an even more attractive Sharpe ratio than either of the individual stocks, but, given the
choice between Stock X and Stock Y, Stock Y is the superior alternative.
When a stock is held as a single stock portfolio, standard deviation is the relevant risk measure. For such a
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portfolio, beta as a risk measure is irrelevant.
Although holding a single asset is not a typically recommended investment strategy, some investors may hold
what is essentially a single-asset portfolio when they hold the stock of their employer company. For such
investors, the relevance of standard deviation versus beta is an important issue.

Excel Modelling: Testing the CAPM
You are required to test the Capital Asset Pricing Model on 25 U.S. portfolios formed on Size and Operating
Profitability for the sample period from January 1963 to December 2020. You need to download returns data
from Professor Kenneth French’s website.1 The data includes:
1) 25 portfolios formed on U.S. Size and Operating Profitability returns (use monthly value-weighted
including dividend returns).
2) Fama/French 3 factors returns (monthly value-weighted returns).
Complete the following task:
A. Perform the CAPM test. Does the CAPM work empirically for the sample period from January 1963 to
December 2020? Present the evidence to support the conclusion. (20 marks)
The US Federal Reserve (FED) controls three tools of monetary policy - open market operations, the discount
rate, and reserve requirements. While the Board of Governors of the FED is responsible for the discount rate and
reserve requirements, the Federal Open Market Committee (FOMC) is responsible for the open market operations.
The FOMC holds eight regularly scheduled meetings per year. At these meetings, the Committee reviews
economic and financial conditions and determines the appropriate stance of monetary policy. Based on the
assessments, they will make important interest rate announcements. FOMC announcements are perhaps the most-
watched events in the financial markets across the globe.
Download from the CAPM folder the “FOMC_dates.csv” file which contains all of the FOMC scheduled meeting
dates from 1997 to 2020.
Perform the CAPM test for FOMC periods as well as non-FOMC periods. Does the CAPM work? Present
evidence to support the conclusion. You need to perform the CAPM test on the same 25 portfolios in Part I from
1997 to 2020. (10 marks)
Please see Excel Spreadsheet
1 https://mba.tuck.dartmouth.edu/pages/faculty/ken.french/data_library.html. Please read the data descriptions
carefully.