QUESTION 3. Suppose you also have researched longer back on the historical rate of returns (HPYs) of Equity, Crypto and also the Global All-Asset market index and estimated the return of each fund and the Global index in different economic scenarios as in the following table, and you have also known the likelihood (probability) of the scenarios via research provided by economic institutions which you found. (2 marks)

Scenarios	Probability	Historical annual rate of return
		Equity	Crypto	Global
Recession	23%	-4%	-5%	-2%
Slow growth	25%	0%	4%	0%
Good growth	32%	5%	3%	1%
High growth	20%	8%	7%	5%

Estimate:

1. Expected (forecasted) rate of return (HPY) of Equity, Crypto and the Global index. (0.5 mark)

2. Variance and standard deviation of the annual expected returns of Equity, Crypto and the Global index. Also estimate the covariance & correlation between Equity & Cryptos returns based on the data in the table (1 marks)

3. Given your estimation on each individual funds (Equity & Crypto) 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 (Name Portfolio O), and you have suggested her to allocate 65% in Equity and 35% in Crypto (asset allocation/investment decision), what will be your Portfolio O's expected return & risk? (0.5 mark)

QUESTION 4. Now, suppose you want to provide clients visualization of the effect of your asset allocation decision on your Portfolio O's performance in terms of both return and risk (2 marks).

1. Change the weights into each of the above stocks by 2% a time to obtain some 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 and the y-axis the expected portfolio return. (1 mark)

2. Among all possible investment opportunities (portfolios), find out the one with 1) minimum variance (risk) (see Topic 2) 2) Best return-risk relationship (optimum or highest Sharpe ratio) (hint: use Excel Solver, with the annual risk-free rate = 0.1%). (1 marks).

QUESTION 5. Now you want to combine the highest Sharpe ratio portfolio (or Optimum risky Portfolio O) you found out above with a risk-free asset to create a Portfolio C for your client to get an even more efficient portfolio. The risk-free asset, the one-year Global Government bond, provides a risk-free annual rate of return of 0.1%. (3 marks)

1. Suppose your client says her risk tolerance of 6%, what is the return of her combined portfolio C? (1 marks)

2. How much weight (your clients wealth distribution) should you put into Portfolio O (the risky asset) and in the risk-free asset in the above situation to create Portfolio C? (1 mark)

3. How does the weight in each asset (Equity, Crypto & the Global government bond) in portfolio C look like? Give the interpretation on the portfolios weights for 100$ investment in portfolio C (1 mark).