Question
Download into an excel worksheet the historical daily price data on (1) XOM and (2) USAK from www.finance.yahoo.com from first trading day in July 2019
Download into an excel worksheet the historical daily price data on (1) XOM and (2) USAK from www.finance.yahoo.com from first trading day in July 2019 to July 27, 2022. Compute daily returns on the two stocks for each trading day using Adjusted Closing Prices. Make sure that the each observation on the price of each of the two stocks pertains to the same trading day as that on the other stock by VLOOKUP function in MS Excel. 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 a year is 252. Now suppose Investor X has 600 shares of XOM stock and Investor Y has 1800 shares of USAK stock. Investor X and Investor 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 July 27, 2022, compute the value of (i) Investor Xs (ii) Investor Ys stock holdings, and (iii) W0, the value at t=0 (i.e., on 7/27/2022) of their combined wealth. (b): What is the current portfolio composition? That is, denoting XOM as Security 1, and USAK as Security 2, work out x1 and x2, the current fractions of the total invested in the two stocks in the combined portfolio. (c): Work out portfolio composition of the risk minimizing portfolio. That is, work out the risk minimizing portfolio weights. Also work out the dollar amounts invested in XOM and in USAK in the risk-minimizing portfolio. (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). (Hint: Remember properties of Expectations.) (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. (Hint: Remember properties of Standard Deviations.) (g): Check that your answer for the risk minimizing portfolio weights does in fact minimize the risk showing that the portfolio risk increases if the portfolio weights differ from the optimal by 0.0001 in either direction.
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