1.Suppose r₁and r₂are returns of two stocks, both following normal distributions as given below,

The correlation coefficient of the two stock returns is -.4. Mr. Wong would like to invest $10,000 on the two stocks. He is anaggressiveinvestor and would like toshort$5000 of stock 1. (a reminder: choose the weight for stock 1 as -0.5 and weight for stock 2 as 1.5). Please answer the following questions:

(1)Figure out the exactdistributionof Mr. Wong's portfolio return (please write the expected value and variance of his portfolio return explicitly).

(2)Calculate the twoprobabilitiesof his portfolio return being negative and greater than 8%.

(3)However, Mrs. Wong is very conservative.She wishes to form a portfolio with the lowest variance by using the two stocks. Please use your knowledge in Portfolio Theory to find out the portfolio weights of thisminimum variance portfolio.