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.

Step-by-step 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%