3 chosen US companies: APPLE (AAPL), Microsoft (MSFT), and Google (GOOG)

Collect data on stock prices and other information for the last five years to December 2021. In addition to stock data also include a suitable market index and a risk-free rate. You may use monthly data. Please provide the source of your data.

a) Compute the following based on the data you collected:

(i) Average return

(ii) Standard deviation of return

(iii) Correlation between each pair of securities

(iv) Excess return

(v) Sharpe ratio

Explain the formula/methods used in your data analysis. Did you encounter any problems in your analysis? (10 marks)

b) Choose the stock with the highest Sharpe ratio label this as Stock X. Using the concepts learned in Chapter 7, you are going to construct a portfolio for one of your clients. His degree of risk aversion, A = 3. The constructed risky portfolio will maximize the Sharpe ratio and will contain two risky assets Stock X and the market portfolio (M) combined with the risk-free asset.

(i) What would be the optimal asset allocation for the client? (5 marks)

(ii) What should be the clients optimal capital allocation? (5 marks)

c) Complete the table below for the mean and standard deviation of the given portfolios (7 marks)

Hint: Use the weights in decimals in the calculations and then convert your answers into percentages.

Percentage in X	Percentage in M	E(rP) (%)	P (%)
125	-25
100	0
75	25
50	50
25	75
0	100
-25	125

(i) Discuss your results (2 marks)

(ii) Next, sketch the following relationships:

a. Between the expected return on the portfolios and the weight, w, invested in asset X.

b. Between the standard deviation of the portfolios and the weight in X.

c. Between the mean and standard deviation of the portfolios in a single graph (the mean-standard deviation plane)

(iii) discuss your plots

d) which portfolios are efficient?

e) Construct a minimum variance portfolio. What are the weights in the two securities? (2 marks)

f) Calculate the expected return and the standard deviation of the minimum-variance portfolio (2 marks)