Suppose that you have invested all your available wealth of $50,000$ in

Sainsbury, which has an expected return of $12\%$ and a volatility of $20\%.$ You

know that the risk$-$free rate is $4\%,$ the expected return of the market portfolio is

equal to $14\%$ and its volatility is $16\%.$ Assume that the CAPM assumptions hold

in the market.

i$.$ What alternative portfolio has the lowest possible volatility while having the

same expected return as Sainsbury? What is the volatility of this new

portfolio? $(5$ marks$)$

ii$.$ What alternative portfolio has the highest possible expected return if you

want to maintain the current volatility of $20\%?$ What is the expected return

of this new portfolio?