FINANCIAL ECONOMICS
1. Download the data from Canvas and calculate the (arithmetic) average excess returns
for the five risky portfolios during the period 1/1927-12/1963.
2. Calculate the betas of the five portfolios during 1/1927-12/1963. Use the SLOPE func-
tion in Excel that computes the slope coefficient βi of a linear regression
Ri − Rf = αi + βi (Rm − Rf ) + εi
Note that you have been provided the excess market returns.
3. Calculate the alphas of the five portfolios during 1/1927-12/1963 using the INTERCEPT
function in Excel. (The intercept is, by definition, the alpha.)
4. Calculate the expected excess returns predicted by CAPM for this period. According
to the CAPM equation we should have E[Ri] − Rf = βi (E[Rm] − Rf ). Compute this
for all five portfolios, including the market portfolio. (You can take the average excess
return of the market portfolio from step 1 as your estimate of the expected excess market
return.)
5. Plot the security market line predicted by CAPM, as well as the actual position of the
five portfolios in (beta, expected excess return) space.
6. Now repeat the steps above for the time period 1/1964-12/2021.
Your solution for Q1 should include the following:
(a) Provide tables reporting the mean excess return, beta, alpha, and the CAPM predicted
excess return for the five portfolios. Round the numbers to three decimal places. For each
of the two time periods you should have a completed table as below: [25 pts]
Table 1: CAPM test
Small Big
Low High Low High Market
mean excess return
beta
alpha
CAPM pred. excess return
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(b) Provide graphs of the security market line and the actual position of the five portfolios
for both time periods. [25 pts]
(c) Provide a brief comment on the difference between the CAPM predicted mean excess
returns and the actual mean excess returns in the two periods. You can also do this
comparison by looking at the magnitude of the alphas (which represent the difference
between the predicted and actual mean excess returns). Compare the two time periods:
does CAPM hold in either period? [5 pts]
(d) Which portfolio has the highest alpha? Provide a brief comment. [10 pts]
Q2. Portfolio choice [35 pts]
Suppose you are a fund manager, managing an active fund with an expected return of 16%
and a standard deviation of 25%. There is also an index fund tracking the FTSE 100, which
has an expected return of 12% and a standard deviation of 20%. The risk-free rate is 4%.
(a) Calculate the Sharpe ratio of your active fund and the index fund. Compare the ratios
and provide an interpretation in no more than four sentences. [10 pts]
Your client has 75% of their wealth invested in your fund and the remaining 25% in the
risk-free asset. They consider switching their risky investment to the index fund.
(b) Calculate the expected return and the risk (standard deviation) of a portfolio with 75%
invested in the index fund and 25% in the risk-free asset. [5 pts]
(c) Suppose your client does not want to exceed the risk level found in part (b). Calculate
the maximum expected return that they can achieve under this condition by combining
your fund with the risk-free asset. What portfolio allocation (i.e., what combination of
the risk-free asset and one of the risky funds) should your client choose? [10 pts]
(d) What is the fee (as a percentage of the investment in your fund) you could charge your
client to make them indifferent between investing in your fund or the index fund?
[10 pts]
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