Question

9. The standard deviation of annual returns for Stock #1 is 76% and for Stock #2 is 40%. The correlation of Stock #1's returns to Stock #2's returns is +1. If you buy $40 worth of Stock #1, how much worth of Stock #2 must you trade in order to created a hedged portfolio of the two stocks? If you want buy Stock #2, make it a positive number and if you want to short-sell Stock #2, type a negative number. Round to the nearest dollar (but, as always, don't type the dollar sign).

11. The standard deviation of annual returns for Stock Y is 39%.  The standard deviation of annual returns for Stock Z is 62%. The correlation between the two stocks' returns is +1. If you decide to buy $3900 worth of Stock Z, figure out how much of Stock Y you need to buy or sell in order to create a net-short hedge portfolio. Then, for your answer, type the initial value of the portfolio. Since the portfolio is net-short, type your answer as a negative number.

Answer 1

Hedged Portfolio formula:

Weight on stock 1 = [(0.4^2)-(1*0.76*0.4)]/[(0.76^2)+(0.4^2)-(2*1*0.76*0.4)] = (0.16-0.304)/(0.5776+0.16-0.608) = -0.144/0.1296 = -1.11

Weight on stock 2 = 1 - Weight on stock 1 = 1-(-1.11) = 2.11

If buy $40 in stock 1, Short sell of stock 2 = Value in stock 1*Weight on stock 2/Weight on stock 1 = 40*2.11/-1.11 = -76

Part 2)

Weight on stock y = [(0.62^2)-(1*0.39*0.62)]/[(0.39^2)+(0.62^2)-(2*1*0.39*0.62)] = (0.3844-0.2418)/(0.1521+0.3844-0.4836) = 0.1426/0.0529 = 2.7

Weight on stock Z = 1 - Weight on stock Y = 1-(2.7) = -1.7

If you buy 3,900 worth of stock z, short sell worth of stock y = Value in stock z*Weight on stock y/Weight on stock z = 3,900*2.7/-1.7 = -2,453