$$ Expected return on market portfolio: $16\%$

$$ Standard deviation of the market portfolio: $20\%$

$$ Risk free rate: $4\%$

a$)$ If the simple CAPM is valid, is it possible to have an asset with an expected return of $7\%$ and a standard deviation of $4\%?(3$ marks$)$

b$)$ If the simple CAPM is valid, is it possible to have an asset with an expected return of $12\%$ and a beta of less than $0\mathrm{.}5?(2$ marks$)$

c$)$ If the client wants the standard deviation of the portfolio to equal half that of the market portfolio, what expected return can NMI provide subject to the risk constraint? $(3$ marks$)$

d$)$ If the client wants the portfolio's expected return to be double that of the market portfolio, what would be the portfolio's standard deviation?