Factor Models
Unless stated otherwise, round your answers to three decimals, and do not round intermediate calculations.
Fama-French Three-Factor Model.
In this problem, you will analyze the risk-factors associated with some stocks in your portfolio. To limit the amount of work, consider only the three largest holdings in your portfolio by market value.
Download the Excel spreadsheet. The file contains the monthly
excess returns in percent for a wide range of stocks and for QQQ (Nasdaq ETF), IWM (Russell ETF), and MCHI (China ETF). 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 – these are the factors of the Fama-French Three-Factor model.
Since not all companies are going to be available in the Excel file, 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 we will study. However, MCHI can serve as a decent albeit not perfect replacement in your analysis. (If none of these fit, do not use the stock and instead include your next-largest holding.)
With your three largest positions and the data from the Excel file, solve the following problems:
a) Calculate using the single-factor model.
b) Estimate their risk (systematic and firm-specific) according to the single-factor model.
c) Calculate the weights of the stocks in your portfolio. Remember, stocks you’re selling short have negative weights, and the weights need to sum up to one.
d) Produce a return time series for your portfolio of the largest three stocks, using . Estimate your portfolio’s sensitivity to Fama-French’s three factors, that is, run the regression
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.
e) Analyze your results. This includes, but is not limited to: classifying your portfolio in terms of aggressiveness, small vs large cap, value vs growth; identifying which of your holdings potentially contribute to the portfolio classification how; going back to your portfolio philosophy statement and discussing if your holdings reflect your investment goal; using the expected values of to compute the expected return of your portfolio in the coming month.
