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Homework AD 717

Week 5 - 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 stocks in a portfolio. To limit the amount of work, consider a portfolio of five stocks that you would put into a portfolio. You may decide their weight in a hypothetical portfolio.

Download the Excel spreadsheet Portfolio_Returns.xlsx from Blackboard. The file contains the monthly excess returns Ri   = ri  — rf  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.

With data from the Excel file, solve the following problems:

a)    Calculate a, β using the single-factor model for each of the five stocks by running a regression in Excel.

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 Rp (t) =

w1 R1 (t) + w2 R2 + w3 R3 . Estimate your portfolio’s sensitivity to Fama-French’s three factors, that is, run the regression

Rp (t) =  ap  + βMRM (t) +  βSMLSML(t) + βHMLHML(t) + ep.

Remember: βm  is a proxy to how much market risk your portfolio carries; βSML  is your exposure to small over big firms; βHML  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; using the expected values of   RM, SML, HML to compute the expected return of your portfolio in the coming month.