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 = W_{1}* R_{1} + W_{2}*
R_{2} , where W_{1} & W_{2} = portion
invested in security 1 and 2

R_{1} & R_{2} = return from security 1 and
2

Standard deviation of portfolio (_{p}^{2}
) = W_{1}^{2} *
_{1}^{2} + W_{2}^{2} *
_{2}^{2} + 2 * W_{1} *W_{2} *
_{1}_{1}*
r_{12} , where

W_{1} & W_{2} = portion invested in security
1 and 2

_{1}
&
_{2} = standard deviation of security 1 and 2

r_{12} = corelation between two securities

Given data , W_{1} = W_{2} = 50% = 0.5;

_{1}
= 15% = 0.15 and
_{2} = 0;

R_{1} = 6% and R_{2} = 0.5%

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

Standard deviation of portfolio (_{p}^{2}
) = (0.5)^{2} * 0.15 = 0.0375

_{p}
= 0.193649 =**19.365% .**

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