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 construct 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.