$($ Investment Management $)($ Finance$)$

The expected return on the market portfolio is $E(R_M)=20\%$ and its standard deviation is

${}_M=5\%.$ The return on the risk$-$free asset is $R_F=2\%.$

a$.$ Based on the CAPM $($capital asset pricing model$),$ calculate the required expected

return on assets A and $B,$ with corresponding betas: ${}_A=-0\mathrm{.}06$ and ${}_B=1\mathrm{.}2$

b$.$ Suppose that asset $C$ has a required rate of return of $R_C=17\%.$ What must be the beta

of this asset $({}_C)$ so that its required rate of return is consistent with the CAPM $($capital

asset pricing model$)$ theory?

c$.$ Suppose that there is no risk$-$free asset, but you have found a portfolio $P,$ with weights on

the assets of the whole market $x_p$ such that: $($i$)E(R_P)=4\%$ and $($ii$)x_P^{\text{'}}{x}_M=0.$ Find the

required rate of return for assets $A,B$ and $C,$ assuming that their betas are the same as

the ones you computed above.