# Portfolio Management question

An investor wants to achieve a portfolio risk (standard deviation) of 0.04. The expected return on the market portfolio is 0.12 with a standard deviation of 0.10. If the risk free rate is 0.04, the best expected return the investor can achieve is closest to: a) 0.048 b) 0.072 c) 0.088 d) 0.120 Show your calculation before I confrim the correct answer so I can see how you got that figure. Thanks

B Sigma§ = Wm * Sigma(m) Wm = 0.04 / 0.1 = 0.4, Wrf = 0.6 E(Rp) = 0.4 * 0.12 + 0.6 * 0.04 = 0.072

If he wants a 4 vol portfolio and market portfolio is 10 vol, assuming 2 asset portfolio and rf rate vol of zero, you want 40% market portfolio and 60% rf rate. .6 * 4% = 2.4% .4 * 12% = 4.8% Er§ = 7.2%

Thanks- B is indeed the correct answer.

Since the covariance between a risk-free asset and another asset is zero, and the standard deviation of a risk free asset is zero, the ordinarily cumbersome process of calculating portfolio standard deviation reduces to a simple weighted average.

How did you determine the 40% and 60% weightings?

.04 / 0.1 he need std of .04, has a asset with std dev of 0.1 and the other component is the risk free asset which has std dev of 0.

NICE

ah got it…thanks

I have a different solution. E = 4 % + 8 % * beta. To have highest expected return you need highest beta. beta = cov(p, mk)/ (std mk ^ 2). Correlation coefficient has to be 1 for beta to reach max. So max beta = 0.4; So max E = 7.2 %