Question

5. The market portfolio expected return is 6% and its standard deviation is 15%. The risk-free rate is 0.5%. What are the expected return and the standard deviation of the portfolio that invests 50% in the risk-free asset and 50% in the market?

Answer 1

Answer )

For portfolio ,

Return = W₁* R₁ + W₂* R₂ , where W₁ & W₂ = portion invested in security 1 and 2

R₁ & R₂ = return from security 1 and 2

Standard deviation of portfolio (_p² ) = W₁² * ₁² + W₂² * ₂² + 2 * W₁ *W₂ * ₁₁* r₁₂ , where

W₁ & W₂ = portion invested in security 1 and 2

₁ & ₂ = standard deviation of security 1 and 2

r₁₂ = corelation between two securities

Given data , W₁ = W₂ = 50% = 0.5;

₁ = 15% = 0.15 and ₂ = 0;

R₁ = 6% and R₂ = 0.5%

Return = 0.5 * 6% + 0.5 * 0.5% = 3.25%

Standard deviation of portfolio (_p² ) = (0.5)² * 0.15 = 0.0375

_p = 0.193649 =19.365% .