Greg has $10,000 to invest in a risk-free asset and in the market portfolio.The risk-free rate is 4.8%.The market portfolio has an expected return of 13.6% with a standard deviation of 15%.What are the expected return and standard deviation for a portfolio with 30% of the funds invested in the risk-free asset?
A)Expected return = 10.50%; standard deviation = 10.96%
B)Expected return = 10.96%; standard deviation = 10.50%
C)Expected return = 4.50%; standard deviation = 7.44%
D)Expected return = 7.44%; standard deviation = 4.50%

Question

Quizplus · Accepted Answer

The expected return of the portfolio can be calculated using the formula: E(Rp) = w_rf * R_rf + w_m * E(R_m), where w_rf is the weight of the risk-free asset, R_rf is the risk-free rate, w_m is the weight of the market portfolio, and E(R_m) is the expected return of the market portfolio. With 30% in the risk-free asset, the expected return is: E(Rp) = 0.3 * 4.8% + 0.7 * 13.6% = 10.96%. The standard deviation of the portfolio is only affected by the market portfolio portion, so it's 0.7 * 15% = 10.5%.

Greg Has $10,000 to Invest in a Risk-Free Asset and in the Market