To carry out this problem set, you will need a computer running Microsoft Excel. Please use the data
provided in the answer template available on Blackboard. This problem set is due by 07:59am PT on
Wednesday, April 26, 2023. Your solutions should be in the form of a single Excel file with each
question answered in a separate sheet. Make sure to include the names of all people in your team
somewhere obvious inside the file. Submit the file on Blackboard. It is all team members’
responsibility that the problem set is submitted on time. It is sufficient if one of the team members
makes a submission.
Question 1
Please use data in sheet beta_portfolios for this question. The data description is included in the Excel
file which you should read carefully.
The Capital Asset Pricing Model (CAPM) predicts that differences in the exposure to market returns
should explain all cross-sectional expected return differences between different assets. In this
question, you will evaluate CAPM using annual data on portfolios sorted by CAPM beta from 1964 to
2019.
a) Compute the average return, volatility, average beta, and the Sharpe ratio for each portfolio.
b) As a mean-variance investor who needs to pick one of the five beta-sorted portfolios, which
portfolio would you choose?
c) Show graphically that CAPM does not hold. To do this, plot the security market line (SML) –
predicted by the data on the market return and the riskless rate –along with the average returns and
average betas of portfolios.
d) What does the relation between the expected portfolio returns and betas imply for mispricing
under the assumption that the CAPM is the right model? Which portfolios are overpriced, and which
portfolios are underpriced?
2
Question 2
Please use data in sheet beta_portfolios for this question. The data description is included in the Excel
file which you should read carefully.
In this exercise, we will implement a simplified version of the “Betting against Beta” (BaB) strategy.
For this purpose, we construct a zero-cost market-neutral (zero-beta) strategy by taking a levered
position in portfolio 1 (the lowest-beta portfolio) and a delevered short position in portfolio 5 (the
highest-beta portfolio) using the portfolio betas in each year.
a) Compute the returns of a levered version of portfolio 1 that has the same beta as the market
portfolio. What is the average annual return of this portfolio? Assume that the riskless rate can be
used for both borrowing and lending.
b) Compute the returns of a delevered version of portfolio 5 that has the same beta as the market
portfolio. What is the average annual return of this portfolio? Assume that the riskless rate can be
used for both borrowing and lending.
c) Consider a zero-cost strategy that is long in the levered portfolio from a) and short in the delevered
portfolio from b). What are the average return, Sharpe ratio, and beta of this strategy?
d) Interpret the results from c) in an economy where the only systematic risk is exposure to market
risk, and therefore the CAPM is the right model of risk and return.
Question 3
Please use data in sheet beta_portfolios for this question. The data description is included in the Excel
file which you should read carefully.
a) Some researchers have argued that the CAPM does not appear to hold due to high borrowing costs
for investors. That is, the cost of borrowing to lever up low-beta portfolios is higher than the riskless
rate. Repeat the exercise in a), b), and c) of Question 2 assuming that the borrowing costs of investors
is higher than the riskless rate by 6 percent.
b) How does your conclusion in d) of Question 2 change in terms of the feasibility of exploiting
mispricing in a CAPM world