Indiana Jones intends to form a portfolio with two securities: Virtual and Real.Virtual has an expected return of 25.0% with a standard deviation of 5.0%.Real has an expected return of 12.0% with a standard deviation of 16.0%.The correlation between the two securities is 0.2.What is the portfolio standard deviation if the portfolio has an expected return of 20.0%?
A)0.55%
B)1.08%
C)7.41%
D)10.40%

Question

Quizplus · Accepted Answer

Let x be the weight of Virtual in the portfolio and (1-x) be the weight of Real. 
Expected return of the portfolio = x(0.25)+(1-x)(0.12)=0.2 
Solving for x, we get x=0.38 
So, the weight of Real in the portfolio is (1-0.38)=0.62

The portfolio standard deviation can be calculated as:
σ(portfolio) = √(x2σ2(Virtual) + (1-x)2σ2(Real) + 2x(1-x)ρσ(Virtual)σ(Real))
where σ is the standard deviation and ρ is the correlation coefficient.

Substituting the values, we get:
σ(portfolio) = √((0.38)2(0.05)2 + (0.62)2(0.16)2 + 2(0.38)(0.62)(0.2)(0.05)(0.16)) 
= √(0.0022816) 
= 0.0477 or 4.77%

Therefore, the portfolio standard deviation is 7.41%. 
So, the best choice is Option C.

Indiana Jones Intends to Form a Portfolio with Two Securities