You manage a risky portfolio with an expected rate of return of
20% and a standard deviation of 36%. The T-bill rate is 5%.
Your client chooses to invest 60% of a portfolio in your fund and
40% in an essentially risk-free money market fund. What are the
expected return and standard deviation of the rate of return on his
portfolio? (Do not round intermediate calculations. Round
"Standard deviation" to 2 decimal places.)
Expected return on the portfolio = w(x)*E(x) + w(y)*E(y)
Standard
deviation of portfolio =
where x and y are the securities
Expected return = 0.6*0.20+0.4*0.05 = 0.1400= 14.00%
Since, the risky asset has a standard deviation of 0, and the correlation between risky and risk-free portfolio is 0, the standard deviation of the portfolio is simply the the proportion of risky portfolio times the standard deviation of risky portfolio.
Standard deviation = 0.6*0.36
Standard deviation = 0.216 = 21.60%
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