You invest $1000 in a complete portfolio. The complete portfolio is composed of a risky asset with an expected rate of return of 16% and a standard deviation of 20% and a Treasury bond with a rate of return of 6%. You should invest ________ of your complete portfolio in the risky portfolio if you want your complete portfolio to have a standard deviation of 9%.
A)100%
B)90%
C)45%
D)10%

Question

Quizplus · Accepted Answer

We need to use the formula for the standard deviation of a complete portfolio:
σp = wσr + (1-w)σf
where
σp = standard deviation of the complete portfolio (given as 9%)
w = weight of the risky portfolio (what we need to solve for)
σr = standard deviation of the risky portfolio (given as 20%)
σf = standard deviation of the risk-free asset (given as 0%, as a Treasury bond is considered risk-free)
Substitute the given values into the formula and solve for w:
9% = w(20%) + (1-w)(0%)
9% = 20w
w = 45%
Therefore, you should invest 45% of your complete portfolio in the risky portfolio.

You Invest $1000 in a Complete Portfolio