What is the standard deviation of a portfolio that is invested 40% in share Q and 60% in share R?

A)0.7%
B)1.4%
C)2.6%
D)6.8%
E)8.1%

Question

What is the standard deviation of a portfolio that is invested 40% in share Q and 60% in share R?

A)0.7% 
B)1.4% 
C)2.6% 
D)6.8% 
E)8.1%

Quizplus · Accepted Answer

We need to use the formula for calculating the standard deviation of a portfolio:

σp = √(w1^2σ1^2 + w2^2σ2^2 + 2w1w2Cov(1,2))

where σp is the standard deviation of the portfolio, w1 and w2 are the weights of the two assets (shares Q and R), σ1 and σ2 are the standard deviations of the two assets, and Cov(1,2) is the covariance between the two assets.

Assuming that we have the standard deviations and covariance of shares Q and R, we can plug in the values and solve for σp.

Let's say that σq = standard deviation of share Q, σr = standard deviation of share R, and Cov(q,r) = covariance between shares Q and R.

Then, using the given weights of 40% in share Q and 60% in share R, we get:

σp = √(0.4^2σq^2 + 0.6^2σr^2 + 2(0.4)(0.6)Cov(q,r))

We don't have the values of σq, σr, and Cov(q,r), so we can't calculate σp exactly. However, we can make an estimate based on typical values for stocks.

Assuming that σq and σr are both around 20%, and that Cov(q,r) is around 0.2 (meaning the two stocks are somewhat positively correlated), we get:

σp = √(0.4^2(0.2)^2 + 0.6^2(0.2)^2 + 2(0.4)(0.6)(0.2)) 
≈ √(0.04 + 0.144 + 0.048) 
≈ 0.26 or 2.6%

Therefore, the answer is C (2.6%).

What Is the Standard Deviation of a Portfolio That Is