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1 Fed rate hike and factor timing
Your analyst gives you the following information on three stocks that are correctly priced according to a 2-factor model,
rA = 0.07+1f1 +5f2 +eA
rB = 0.04+0.5f1 +3f2 +eB
rC = 0.10+1.5f1 +3f2 +eC
The factors satisfy E(f1) = E(f2) = 0, cov(f1,f2) = 0. The idiosyncratic risks satisfy E(eA) = E(eB) = E(eC) = 0, and they are uncorrelated with each other or either of the factors. Assume the following:
• Factor 1 is the stock market factor
• Factor 2 is the Federal Reserve interest rate factor (don’t worry about how to con-
struct the factor, just assume your analyst has constructed it)
You want to invest in stocks A, B, C (assume they are the only assets available to invest). However, you are concerned that the stock market might tank due to Fed rate hike. Using the above three securities, construct a stock portfolio that is unaffected by Fed rate hike. Specifically, construct a portfolio with beta=1 for the stock market factor while beta=0 for the interest rate factor. Show the portfolio weights.
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