Question

The following equally likely outcomes have been estimated for the returns on Portfolio G and Portfolio H: Scenario Portfolio G Portfolio H 1 5.0% 9.0% 2 3.0% -7.0% 3 9.0% 15.0% 4 9.0% -4.0% Which of the two portfolios is riskier?

Answer 1

Expected returns=Sum(probability*returns)
Standard Deviation=Sqrt(Sum(probability*(returns-expected returns)^2)))

1.
Expected returns of G=1/4*5%+1/4*3%+1/4*9%+1/4*9%=6.500%

Expected returns of H=1/4*9%+1/4*(-7%)+1/4*15%+1/4*(-4%)=3.250%

2.
Standard Deviation of G=sqrt(1/4*(5%-6.5%)^2+1/4*(3%-6.5%)^2+1/4*(9%-6.5%)^2+1/4*(9%-6.5%)^2)=2.598%

Standard Deviation of H=sqrt(1/4*(9%-3.25%)^2+1/4*(-7%-3.25%)^2+1/4*(15%-3.25%)^2+1/4*(-4%-3.25%)^2)=9.066%

H is riskier as it has higher standard deviation per unit of return