Question

Suppose Avon and Nova stocks have volatilities of

47%

and

22%​,

​respectively, and they are perfectly negatively correlated. What portfolio of these two stocks has zero​ risk?

Answer 1

Avon volatility = 47%

Nova volatility = 22%

perfectly negatively correlated means correlation between Avon and Nova is (-1)

i.e., R_{Avon & Nova} = -1

If Stocks are perfectly negatively correlated then

=

Lets assume,

W_Avon = w

W_Nova = 1 - w

Volatility is consider as risk so, = 0 (given)

now put values in above formula,

0 = 47w - ( 22 - 22w )

0 = 47w - 22 + 22w

47w + 22w = 0 + 22

69w = 22

w = 22 / 69

w = 0.3188

1 - w = 1 - 0.3188 = 0.6812

Portfolio has 31.88% of Avon Stock and 68.12% of Nova Stock for zero risk.