Consider the following scenario analysis for asset A and asset B$.($d$)$ i$.$

Determine the minimum variance portfolio consisting of asset A and asset B$.$ Explain how you can construct a $$40,000$ portfolio with the two assets.

State of economy

Probability Return on asset A Return on asset B

Recession Normal

Expansion$0\mathrm{.}20\mathrm{.}50\mathrm{.}320\%18\%50\%15\%20\%10\%$Assume that of your $$40,000$ portfolio, you invest $$15,000$ in asset A and $$25,000$ in asset B$.$

$($a$)$ Write down the probability distribution of your future portfolio value.

$($b$)$ Find the correlation between the return on the two assets.

$($c$)$ Find

i$.$ the expected rate of return of your portfolio, and

ii$.$ the volatility of your portfolio.

ii$.$ Compare the minimum variance portfolio with your portfolio in terms of expected rate of return and volatility.

$($e$)$ Suppose now you want to construct a $$40,000$ portfolio with different targets. Determine all the possibilities of constructing such a portfolio $($with exact amounts stated for the two assets$)$ that you can achieve the following targets:

i$.$ The expected return $($in dollar term$)$ is $$4,800.$ ii$.$ The portfolio variance is $0\mathrm{.}0175.$