A portfolio has 45 percent of its funds invested in Security One and 55 percent invested in Security Two.Security One has a standard deviation of 6 percent.Security Two has a standard deviation of 12 percent.The securities have a coefficient of correlation of .62.What is the portfolio variance?
A).006946
B).007295
C).007157
D).008104
E).007506

Question

Quizplus · Accepted Answer

The formula for portfolio variance is: 
Portfolio Variance = w1^2*σ1^2 + w2^2*σ2^2 + 2*w1*w2*σ1*σ2*ρ
where w1 and w2 are the weights of Security One and Security Two respectively, σ1 and σ2 are the standard deviations of Security One and Security Two respectively, and ρ is the coefficient of correlation between the two securities.

Plugging in the values given:
w1 = 0.45
w2 = 0.55
σ1 = 0.06
σ2 = 0.12
ρ = 0.62

Portfolio Variance = (0.45^2)*(0.06^2) + (0.55^2)*(0.12^2) + 2*(0.45)*(0.55)*(0.06)*(0.12)*(0.62)
= 0.007295

Therefore, the correct answer is B.

A Portfolio Has 45 Percent of Its Funds Invested in Security