An investor is considering investing in either share $A$ or share $B.$ The return depends on the general economic development and below you will find some information about the shares:

$\backslash$table$[[$Boom$,$Probability,Return A$,$Return B$],[$Hay$,0\mathrm{.}2,25\%,35\%],[$Normal$,0\mathrm{.}6,10\%,20\%],[$Recession$,0\mathrm{.}2,0\%,-5\%]]$

A$.$ Without making any calculations, can you provide a rationale for which stock has the highest risk?

B$.$ Calculate the expected return and risk $($standard deviation$)$ for each stock. If you're only going to invest in one of the stocks, is one of them unambiguously preferable?

C$.$ Calculate the expected return and standard deviation of a portfolio of $75\%$ A and $25\%$ B$.$ You choose which method you want to use to calculate the values.

D$.$ Why is the diversification gain in this case relatively low?

E$.$ Suppose you place $50\%$ in stock A and the rest risk$-$free. Risk$-$free rate is $3\%.$ What will be the expected return and standard deviation for this