Question:

a) My investment portfolio consists of one share of Microsoft stock and one share of Dell stock. My forecast for the end of the year is Microsoft at an expected value of $20 a share with a standard deviation of $2 and Dell at an expected values of $18 a share with a standard deviation of $3. The correlation between Microsoft and Dell annual stock price changes is 0.40. What is the probability that Microsoft stock will finish the year with a price greater than Dell (Assume that Dell and Microsoft stock prices follow a normal distribution)?

b) I have invested my portfolio in two stocks: Apple and Microsoft which currently sell for $135 and $28 a share, respectively. Based on the historical data, my forecast for one year from today is: I expect a share of Apple to sell for $150 and a share of Microsoft to sell for $30. However, there is a lot of uncertainty involved in those predictions. I summarize the uncertainty this way:

(i) The price next year of a share of Apple has a normal distribution with a mean= $150 and a standard deviation= $12.

(ii) The price next year of a share of Microsoft has a normal distribution with a mean= $30 and a standard deviation= $3.

In addition, Apple and Microsoft are both computer companies, so we would expect a positive correlation in their price movements. In fact, the correlation is 0.25.

Today I own 4 shares of Apple and 10 shares of Microsoft. Determine the mean and standard deviation of the value of my portfolio one year from today.