Question

ou put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of your money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The stock and bond portfolios have a correlation of .55. What is the standard deviation of the resulting portfolio?

Answer 1

σ = 0.16099 = 16.099%

Explanation:

Data provided:

Amount put in portfolio 1, W₁ = 50% = 0.5

Expected return on portfolio 1 = 14%

Standard deviation of portfolio 1, σ₁ = 24%

Amount put in portfolio 2, W₂ = 50% = 0.5

Expected return on portfolio 2 = 6%

Standard deviation of portfolio 2, σ₂ = 12%

Correlation of stock and bond, σ₁₂ = 0.55

Now,

The standard deviation of the resulting portfolio is calculated using the formula

σ² = [(W₁σ₁)² + (W₂σ₂)² + 2(W₁σ₁)(W₂σ₂)σ₁₂]

on substituting the respective values, we get

σ² = [(0.5 × 0.24)² + (0.5 × 0.12)² + 2(0.5 × 0.24)(0.5 × 0.12)0.55]

or

σ = √0.02592

or

σ = 0.16099

or

σ = 0.16099 × 100% = 16.099%