Mean variance portfolio theory

3. an investor is interested to purchase stock shares from company A. he expects to sell the shares after one year. To estimate the stock’s mean return, three scenarios, their probabilities and the rate of return for each one, are indentified.

To reduce the risk of loss, an insurance investment is available. This insurance offers opposite rates of return than those of the stock.the table shows the scenarios with the corresponding rates of return.

Scenario        probability     stocks      insurance 

Low growth        0.4              20%           -10%

Med growth       0.2              20%             0%

High growth       0.4              10%              20%

A)     Find the coverance and correlation coeffiient between the stock and the insurance

B)      Since the rate return of the insurance are opposite to those of the stock, the investor consider to invest equal amount in stock shares and insurance.in this case what is the mean return and th variance of return of this portfolio

C)      Find the weight that gives minimum risk(standard deviation) of the portfolio

D)     What is the mean return and the variance of return of this new portfolio?