Homework
Single-factor and multi-factor models
Unless stated otherwise, round your answers to two decimal points, and do not round intermediate calculations.
Problem 1. [20 points]
The following are estimates for two stocks.
Stock | Expected Return | Beta | Firm-Specific Standard Deviation |
|||||
A | 10 | % | 0.95 | 35 | % | |||
B | 17 | 1.50 | 45 | |||||
The market index has a standard deviation of 19% and the risk-free rate is 12%.
Problem 2. [20 points]
Suppose that the index model for stocks A and B is estimated from excess returns with the following results:
and σM = 29%; R-squaredA = 0.29; R-squaredB = 0.14
Assume you create portfolio P with investment proportions of 0.60 in A and 0.40 in B.
Problem 3. [10 points]
Consider a security of which we expect to pay a constant dividend of $18.49 in perpetuity. Furthermore, its expected rate of return is 20.1%. Using the equation for present value of a perpetuity, we know that the price of the security ought to be , where D is the constant dividend and k is the expected rate of return.
Assume that the risk-free rate is 3%, and the market risk premium is 6.4%.
What will happen to the market price of the security if its correlation with the market portfolio doubles, while all other variables, including the dividend, remain unchanged?
Problem 4: Fama-French Three-Factor Model. [50 points]
Download the Excel spreadsheet Portfolio_Returns.xlsx from Blackboard. The file contains the monthly excess returns in percent of a wide range of stocks and of QQQ (Nasdaq ETF), IWM (Russell ETF), and MCHI (China ETF).
Since some companies have not been publicly listed for the entire time period from January 2014 to December 2018, we cannot use them for our analysis. Please research the QQQ, IWM, and MCHI ETFs to see if you can use them as a replacement for missing stocks. For example, Alibaba (BABA) has not been listed for the entire time period, however, MCHI can serve as a decent albeit not perfect replacement in your analysis.
Additionally, the file contains the time series ExcMkt, SMB,and HML, representing the excess market return, the small-minus-big return, and the high-minus-low return.
For the following part, consider only your three largest holdings by market value.
For the following part, consider your entire portfolio.
Remember: is a proxy to how much market risk your portfolio carries; is your exposure to small over big firms; is your exposure to firms with a high book value compared to their market capitalization. These three betas are assumed to be non-diversifiable risk factors, and in the long run investors should be rewarded for their risk of having greater betas.