Question

Consider two stocks X and Y with the following expected returns (in percent) and standard deviations. How much of your $10,000 total investment should you invest in stock Y if you would like a portfolio with zero risk and the correlation between the two stocks is -1 (perfectly negatively correlated)?

Stock Expected return Standard deviation

X 10 75
Y 20 50

Answer 1

X $4000

Y $6000

Step-by-step explanation:

Let w be invested in Stock X,

Correlation = -1

Standard Deviation = w(0.75) - (10,000 - w)(0.50)

So,

For standard Deviation to be 0,

0 = 0.75w - 5,000 + 0.50w

w = $4,000

Amount invested in Stock X = $4,000

Amount invested in Stock Y = $6,000