Question

Consider the following data on returns (R), standard deviation (?), weights (W), and correlations (r) for two stocks:R1 = 10%, ?1 = 4%, R2 = 20%, ?2 = 6%, r12 = -1.0, W1=0.50, W2=0.50What is the standard deviation of a portfolio of stocks 1 and 2 with the above weights?1. 1.0%2. 1.10%3. 10%4. None of the given answers is correct.5. 0.20%

Answer 1

Answer: Option (4) is correct.

Explanation:

Given that,

Data on two stocks:

R1 = 10%

σ1 =  4%

R2 = 20%

σ2 = 6%

r12 = -1.0

W1 = 0.50

W2 = 0.50

Where,

σ - standard deviation

r - correlations

R - returns

Standard deviation of portfolio = $\sqrt{W1^{2}SD1^{2}+ W2^{2}SD2^{2} + 2(W1)(W2)(r12)(SD1)(SD2)}$

                                                    = $\sqrt{0.50^{2}0.04^{2}+ 0.50^{2}0.06^{2} + 2(0.50)(0.50)(-1.0)(0.04)(0.06)}$

                                                    = 0.01

                                                    = 1%