The investment fund Omega has an equity portfolio with a strong tilt towards value stocks, i$.$e$.$ stocks

with low prices relative to book values. The investment strategy is based on buying the $50$ stocks

with the lowest price$-$to$-$book ratios every year and hold these stocks for one year. Over the last

$15$ years, on average, this investment strategy $($return minus risk$-$free rate of interest$)$ has given a

statistically significant abnormal return of $5\%(\backslash$alpha $).$ The CAPM beta of the portfolio over the same

period was $0\mathrm{.}6.$ The realized risk premium $($excess return$)$ on the market portfolio was $5\%,$ and its

variance was $0\mathrm{.}04.$ The R$2-$value of a regression of the portfolio return on the market portfolio return

is $0\mathrm{.}70.$

a$)$ Write down the return on the portfolio in terms of a regression equation using the information

you are given in the above text.

b$)$ Decompose the variance of the portfolio into a systematic and an unsystematic component.