An investor has $500$m which they want to invest wisely. The investor has contacted three young and very eager investment managers to research the market opportunities and propose an optimal investment portfolio. The best candidate out of the three investment mangers will have the chance to become the investor$$s wealth manager. The investor will not hire candidates that propose either inefficient or infeasible portfolios.

Assume that all securities are priced correctly according to the CAPM and that the risk free rate is $2\%.$ The expected excess return on the market portfolio i$.$e$.$ the market risk premium, is $12\%$ and the standard deviation is $20\%.$ The three candidates have proposed portfolios with the following characteristics:

Candidate:

Frank $($FR$)$

Jenny $($JE$)$

John $($JO$)$

Expected Return

$0\mathrm{.}07($FR$)$

$0\mathrm{.}20($JE$)$

$0\mathrm{.}12($JO$)$

Standard Deviation

$0\mathrm{.}10($FR$)$

$0\mathrm{.}30($JE$)$

$0\mathrm{.}15($JO$)$

$($a$)$ Which candidate will be hired by the investor and why?

$($b$)$ How can the expected return of the wining portfolio be achieved? Specify the amount of money invested in each asset$/$portfolio of assets?

$($C$)$What is the beta of the winning portfolio?

$($d$)$ If the investor holds their position for one year what is their expected wealth at the end of the year?

Show all of your calculations and explain your approach.