Suppose you also have researched longer back on the historical rate of returns (HPYs) of Equity, Aggregate Bond and also Cash and estimated the return of each asset class in different economic scenarios as in the following table, and you also predict the likelihood (probability) of the scenarios in the next year from research 

Scenarios	Probability	Historical annual rate of return
		Equity	Aggregate Bond	Cash
Recession	10%	-10.00%	-3.00%	0.75%
Slow growth	30%	-2.00%	-1.00%	0.50%
Good growth	40%	4.00%	4.00%	0.63%
High growth	20%	15.00%	2.00%	0.13%

Estimate:

Expected rate of return (HPY) of Equity, Bond and Cash.

Standard deviation of the returns of Equity, Bond and Cash. Also estimate the covariance & correlation between Equity & Bond returns based on the data in the table.

Given your estimation on each individual fund’s (Equity & Bond) expected return, risk and correlation in b., now if your clients want to put money into both of these 2 funds and combine them into an investment portfolio H, and you have suggested her to allocate 65% in Equity and 35% in Bond (asset allocation/investment decision), what will be her portfolio H's expected return & risk?

Now, suppose you want to provide clients visualization of the effect of your asset allocation decision on her Portfolio H's performance in terms of both return and risk .

Change the weights into each of the above assets from 0% to 100% with increment of 2% to obtain the possible investment opportunities (portfolios). Present these investment opportunities in a table (Please do NOT allow short-selling). Depict the investment opportunities in a graph in which the x-axis is the portfolio standard deviation of return and the y-axis the expected portfolio return.

Among all investment opportunities (portfolios), find out the portfolio (i.e. % in each asset investment, expected returns and risk of the portfolio) with 1) minimum variance (risk) or 2) Best return-risk relationship (the one with the highest Sharpe ratio, and we assume that short selling is NOT allowed) 

I need answer for Q4, Tyvm!

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To calculate the expected rate of return HPY of Equity Bond and Cash we multiply the historical annual rate of return by the probability of each scenario and sum the results We also need to calculate ... View the full answer