Homework 8: Due August 7 2020

Download into an excel worksheet the historical daily price data on (1) AMZN and (2) GS from yahoo finance for the year ended on August 3, 2020. Compute daily returns on the two stocks for each trading day. Now, using the CORREL function in MS Excel, compute the correlation between the returns on the two stocks. Also compute the expected return, variance and the standard deviation of returns on each of the two stocks using the AVERAGE and the VAR and STDEV function in MS Excel. Annualize the expected returns and the standard deviations of the two stocks by assuming that the number of trading days in the year is 252.

Now suppose Ms. X has 300 shares of AMZN stock and Mr. Y has 3000 shares of GS stock. Ms. X and Mr. Y decide to get married, and want to allocate their combined wealth between the two stocks in such a way that the standard deviation of the returns on their portfolio is minimized.

(a): Based on the closing prices on August 3, 2020, what is the value of (i) Ms. Xs and (ii) Mr. Ys stock holdings?

(b): What is the current portfolio composition? That is, denoting AMZN as Security 1, and GS as Security 2, what are the current fractions invested in the two stocks in the combined portfolio?

(c): Work out portfolio composition of the risk minimizing portfolio? What are the portfolio weights? What is the dollar amount invested in AMZN and in GS?

(d): Work out the number of shares in each of the two stocks that the risk minimizing portfolio will contain.

(e): Work out the expected value of their portfolio at t=1 (one year from today)

(f): Work out the range within which their t=1 wealth will lie with a probability of 2/3 assuming that the future wealth is normally distributed.[1]

(d): Check that your answer for the risk minimizing portfolio weights does in fact minimize the risk with the help of the MS Excel file 2-Security Portfolios.xlsx on the course web site by entering your solution in an appropriate row in that file, and showing that the portfolio risk increases if the portfolio weights differ from the optimal by 0.0001 in either direction. Print out the appropriate area of the Excel file and attach it with your solution. Note that you will lose 60% of the credit for this homework if you do not attach a printout of the appropriate part of Excel spreadsheet that shows that you have verified that your portfolio weights in fact minimize the risk.

[1] The lower end of the 95% confidence interval is [E(Wealth₁) 2*SD(Wealth₁)] and the upper end is [E(Wealth₁) + 2*SD(Wealth₁)].