Assume that an investor invests in one risky and one risk free asset. Let σ_m be the standard deviation of the risky asset and b the proportion of the portfolio invested in the risky asset. The standard deviation of the portfolio is then equal to: C) (1 - b) D) b

Question

Quizplus · Accepted Answer

The formula for the standard deviation of a two-asset portfolio is:

σP = √[(bσS)^2 + ((1-b)σF)^2 + 2b(1-b)ρσSσF]

where σS is the standard deviation of the risky asset, σF is the standard deviation of the risk-free asset (which is 0), ρ is the correlation coefficient between the two assets (which is also 0 for a risk-free asset), and b is the proportion of the portfolio invested in the risky asset.

Plugging in the values given in the question, we get:

σP = √[(bσS)^2 + ((1-b)0)^2 + 2b(1-b)(0)(σS)]
   = √[b^2σS^2]
   = bσS

So the standard deviation of the portfolio is equal to b times the standard deviation of the risky asset. Therefore, the correct answer is D.

Assume That an Investor Invests in One Risky and One