Final answer:
The standard deviation of the portfolio with 60% invested in stock X and 40% in stock Y, with standard deviations of 10% and 20% respectively, and a correlation coefficient of 0.5, is 24.8%.
Step-by-step explanation:
To find the standard deviation of a portfolio consisting of two stocks, X and Y, with different weights, standard deviations, and a correlation coefficient, we must use the portfolio standard deviation formula:
Portfolio Standard Deviation = √(w₁²σ₁² + w₂²σ₂² + 2w₁w₂σ₁σ₂ρ)
Where:
- w₁ and w₂ are the weights of stocks X and Y in the portfolio, respectively.
- σ₁ and σ₂ are the standard deviations of stocks X and Y, respectively.
- ρ is the correlation coefficient between the two stocks.
Using the given values:
- w₁ = 60% or 0.6 for stock X
- w₂ = 40% or 0.4 for stock Y
- σ₁ = 10% or 0.1 for stock X
- σ₂ = 20% or 0.2 for stock Y
- ρ = 0.5, the correlation between stock X and Y
Substituting these values into the formula gives:
Portfolio Standard Deviation = √((0.6² x 0.1²) + (0.4² x 0.2²) + 2 x 0.6 x 0.4 x 0.1 x 0.2 x 0.5)
Portfolio Standard Deviation = √(0.036 + 0.016 + 0.0096)
Portfolio Standard Deviation = √(0.0616)
Portfolio Standard Deviation = 0.248 (or 24.8%)
Thus, the standard deviation of the portfolio is 24.8%.