Question $4$

Consider the following variance$-$covariance matrix between two stocks A and B$.$ The expected

returns on the two stocks are $14\%$ and $10\%$ and the share prices for A and B are $75$ and $20,$

respectively.

$($a$)$ Nigel has $700$ of cash. He borrows $20$ shares of A and then uses the cash and the proceeds

from short selling the $20$ borrowed shares of A to purchase B$.$ Calculate his portfolio's

expected return and volatility.

$($b$)$ Suppose that the market consists of only Stock A and Stock B and the risk$-$free interest rate is

$4\%.$ Determine the weights of the two stocks in the tangent portfolio.

$($c$)$ Alexis wants to invest $10,000$ in an efficient portfolio with an expected return of $9\%.$ What is

the volatility on Alexis' portfolio?