FINANCIAL ECONOMICS
Download the data from Canvas and calculate the (arithmetic) average excess returns for the five risky portfolios during the period 1/1927-12/1963.
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
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.)
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] − R).
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.)
Plot the security market line predicted by CAPM, as well as the actual position of the five portfolios in (beta, expected excess return) space.
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 2
Provide graphs of the security market line and the actual position of the five portfolios for both time periods. [25 pts]
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]
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%.
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.
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]
Suppose your client does not want to exceed the risk level found in part
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]
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?
