Question

The expected return on the market portfolio is 13 percent with a standard deviation of 16 percent. What are the expected return and standard deviation for a portfolio with 40 percent of the investment in the market portfolio borrowed at the risk-free rate of 5 percent?

Expected return = 26.67%; expected return = 18.33%

Expected return = 18.33%; standard deviation = 26.67%

Expected return = 22.40%; standard deviation = 16.20%

Expected return = 16.20%; standard deviation = 22.40%

Answer 1

Given that,

Expected return on market Rm = 13%

Standard deviation of market SDm = 16%

Risk free rate Rf = 5%

When 40% of the portfolio investment is borrowed at risk free rate,

Weight of market portfolio Wm = 140% or 1.4

Weight of risk free asset Wf = -40% or -0.4

So, expected return on the portfolio is weighted average return on its assets

=> Expected return E(r) = Wm*Rm + Wf*Rf = 1.4*13 - 0.4*5 = 16.20%

Standard deviation of this portfolio is Wm*SDm = 1.4*16 = 22.40%

Option D is correct.