Question

You run a regression of the excess returns of ABC stock on the excess returns of the market portfolio M and obtain an output:

RAbc - Rf= -.04 + 1.0 × (RM-Rf) + error

The expected return of the market portfolio is 10% and the risk-free rate is 5%.

1. What ABC stock's Alpha?
2. What is ABC stock's expected return?
3. If you are a fund manager and you want to build your portfolio such that it has an alpha of 2% and a beta of zero. What must be your portfolio’s weights on ABC stock, the market, and risk-free asset?

**This is all the information that was given**

Answer 1

1.
alpha=-4%

2.
returns=5%-4%+1.0*(10%-5%)=6%

3.
beta of zero
and alpha of 2%
mean return of 2%+0%+5%=7%

So, we want return of 7% and beta of 0

Let weight of A be w and weight of rf be 1-w

Returns=w*Ra+(1-w)*5%=w*(5%-4%+1*(10%-5%))+(1-w)*5%=1%w+5%

1%w+5%=7%
=>w=2

Hence, weight of stock A=2 and weight of risk free rate is -1 i.e., you borrow at risk free rate and invest in Stock A