Please Answer all of the problems below:

$15.$ You estimate that a passive portfolio invested to mimic the S&P $500$ stock index provides an expected rate of return of $13\%$ with a standard deviation of $25\%.$

a$)$Draw the CML and your fund$$s CAL on an expected return$/$standard deviation diagram.

b$)$ What is the slope of the CML$?$

c$)$ Characterize in one short paragraph the advantage of your fund over the index fund.$$

$18.$You manage an equity fund with an expected risk premium of $10\%$ and a standard deviation of $14\%.$ The rate on Treasury bills is $6\%.$ Your client chooses to invest $$60,000$ of her portfolio in your equity fund and $$40,000$ in a T$-$bill money market fund. What are the expected return and standard deviation of your client$$s portfolio?$$

$19.$ What is the reward$-$to$-$volatility $($Sharpe$)$ ratio for the equity fund in the previous problem $($Problem $18).$