The expected returns on treasury bills, the market, SMB and HML are given by:

$E(r_{\text{B}\text{I}\text{L}\text{L}})=2\%,E(r_m)=10\%,E(SMB)=2\%,E(HML)=5\%.$

You estimate expected returns on two mutual funds. You also estimate the funds' factor exposures

via the Fama$-$French $3-$factor model regression: $r_{it}-r_{ft}={}_i+{}_{mkt}(r_{m,t}-r_{f,t})+s_i(SM{B}_t)+h_i$

$(HM{L}_t)+lo{n}_t$

A$.$ Which fund has better performance measured by CAPM alpha?

B$.$ What is the expected benchmark return based on the Fama$-$French three$-$factor model?

C$.$ Which fund has better performance measured by Fama$-$French $3-$factor alpha?

Suppose the t$-$statistic for Fund $2\text{'}$s ${}_{mkt}$ for the null hypothesis that $=0$ is $30.$ What is the $t-$

statistic for the null hypothesis that $=1?$ Please solve on paper not on excel!