Answer:
The volatility of the portfolio is 21.08%.
Explanation:
Portfolio Volatility Calculation
To calculate the volatility of a portfolio that consists of a long position of $10,000 in Karma Energy and a short position of $5,000 in Faust Corp, we can use the formula for the volatility of a portfolio:
Portfolio Volatility = (w1^2 * σ1^2 + w2^2 * σ2^2 + 2 * w1 * w2 * ρ1,2 * σ1 * σ2)^0.5
Where:
w1 = weight of Karma Energy in the portfolio (long position)
w2 = weight of Faust Corp in the portfolio (short position)
σ1 = volatility of Karma Energy
σ2 = volatility of Faust Corp
ρ1,2 = correlation between the returns of Karma Energy and Faust Corp
Given:
σ1 = 10%
σ2 = 22%
ρ1,2 = 0.5
w1 = $10,000 / ($10,000 - $5,000) = 2
w2 = -$5,000 / ($10,000 - $5,000) = -1
Substitute the values into the formula:
Portfolio Volatility = (2^2 * 10%^2 + (-1)^2 * 22%^2 + 2 * 2 * (-1) * 0.5 * 10% * 22%)^0.5
Portfolio Volatility = (4 * 100 + 1 * 484 - 2 * 0.5 * 10 * 22)^0.5
Portfolio Volatility = (400 + 484 - 220)^0.5
Portfolio Volatility = (664 - 220)^0.5
Portfolio Volatility = 444^0.5
Portfolio Volatility ≈ 21.08%
Therefore, the volatility of the portfolio is approximately 21.08%.