6. A portfolio consists of $10,000 of stock A and $20,000 of stock B. Stock A has an expected return of 12% and a standard deviation of 14%, while stock B has an expected return of 10% and a standard deviation of 12%.

a. Find the mean and standard deviation of the portfolio return when the correlation between the two stocks return is -1, 0, 1?

b. Assume that the stock returns are jointly normally distributed, what is the probability that the portfolio return is less than 0% when the correlation between the two stocks return is 0%.

c. How do correlations between the stocks affect the mean and variance of the portfolio return? If we use the standard deviation of portfolio return as a measure of portfolio risk, what is the largest portfolio risk is? What is the smallest portfolio risk?