Consider the following information about the returns of three assets:

State Probability Asset A Asset B Asset C

Boom $0\mathrm{.}325\%10\%-2\mathrm{.}5\%$

Good $0\mathrm{.}415\%5\%5\%$

Level $0\mathrm{.}210\%2\%10\%$

Slump $0\mathrm{.}1-5\%-10\%15\%$

Next, we build up the following two portfolios:

Portfolio $1$: $50\%$ on Asset A and $50\%$ on Asset B

Portfolio $2$: $50\%$ on Asset A and $50\%$ on Asset C

a$.$ What are the expected return and standard deviation of the two portfolios? $(20$ marks$)$

b$.$ Use $($a$)$ results to explain the relationship between the risk deduction effect of diversification and the correlation, i$.$e$.,$ explain how$/$why the correlation affects the risk deduction effect of diversification?