Portfolios

X is the yieldper dollar of stockin company EX.X is approximately normally distributed with mean 0.04 and standard deviation 0.01.W is theyield per dollar of stockin company WAY.W is approximately normally distributed with mean 0.05 and standard deviation 0.02.(X and W are in dollars, i.e. the mean yields are 0.04 and 0.05 dollars, respectively.)X and W are independent.

Consider three alternative portfolios.You want to choose the portfolio that has the highest probability of yieldingmore than5 dollars.

Portfolio 1.Buy 200 dollars of EX.The yield on this portfolio is denoted Y1.

Portfolio 2.Buy 200 dollars of WAY.The yield on this portfolio is denoted Y2.

Portfolio 3.Buy 100 dollars EX and 100 dollars of WAY.The yield on this portfolio is denoted Y3.

1. Q is the yieldper dollar of stockin company QUEUE.Q is approximately normally distributed with the same mean as W and the same standard deviation as W (Q's mean is 0.05 and its standard deviation is 0.02).However, X and Q have a covariance ofminus0.0001.You are wondering whether you should replace the 100 dollars of WAY with 100 dollars of QUEUE in portfolio 3.Recalculate the probability that the yield will bemore than5 dollars with portfolio 3 (with stock in QUEUE instead of WAY).Four decimals