Question

The standard deviation of annual returns for Stock Y is 44%.  The standard deviation of annual returns for Stock Z is 74%. The correlation between the two stocks' returns is +1. If you decide to buy $4400 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

Given,

Standard deviation of stock Y SD(Y) = 44%

Standard deviation of stock Z SD(Z) = 74%

Correlation between stock Y and Z Corr(Y,Z) = 1

money invested in stock Z = $4400

Let weight of Y be w then weight of stock Z in portfolio is (1-w)

Standard deviation of a portfolio with correlation 1 is w1*SD1 + w2*SD2

So here Standard deviation of portfolio = w*0.44 + (1-w)*0.74

Since required net short hedge portfolio, so standard deviation of portfolio = 0

So, w*0.44 + (1-w)*0.74 = 0 => w = 0.74/0.3 = 2.4667

weight of Z = (1-w) = -1.4667

let amount of stock Y = Y

So, weight of Y is Y/(Y+4400) = 2.4667

So, Y = -7400

So a total of $7400 stock Y must be short.

So answer is -7400