You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%.You put the rest of you money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%.The stock and bond portfolio have a correlation 0.55.The standard deviation of the resulting portfolio will be ________________.
A) more than 18% but less than 24%
B) equal to 18%
C) more than 12% but less than 18%
D) equal to 12%

Question

Quizplus · Accepted Answer

The standard deviation of the resulting portfolio is given by:
σp=(w1σ1)²+(w2σ2)²+2w1w2σ1σ2ρ
where, 
w1 and σ1 are the weight and standard deviation of the stock portfolio,
w2 and σ2 are the weight and standard deviation of the bond portfolio,
and ρ is the correlation between the two portfolios.
Substituting the given values, we get:
σp=(0.5×24)²+(0.5×12)²+2(0.5)(0.5)(24)(12)(0.55)
σp=299.52
Finally, taking the square root, we get:
σp=17.31, which means the standard deviation of the resulting portfolio is more than 12% but less than 18%. Therefore, the answer is C.

You Put Half of Your Money in a Stock Portfolio