What is the standard deviation of the equally weighted two asset portfolio composed of asset X and asset Y based on the information given below? Variance of asset X=49% Variance of asset Y=81%, covariance of returns between the two assets is 0.0108 Question 39Answera.0.93%b.8.-96%c.5.74%
Question
What is the standard deviation of the equally weighted two asset portfolio composed of asset X and asset Y based on the information given below? Variance of asset X=49% Variance of asset Y=81%, covariance of returns between the two assets is 0.0108 Question 39Answera.0.93%b.8.-96%c.5.74%
Solution
The standard deviation of a two-asset portfolio can be calculated using the formula:
σp = sqrt[(w1^2 * σ1^2) + (w2^2 * σ2^2) + (2 * w1 * w2 * Cov(X,Y))]
where:
- w1 and w2 are the weights of the assets in the portfolio (for an equally weighted portfolio, w1 = w2 = 0.5),
- σ1^2 and σ2^2 are the variances of the assets (given as 49% and 81% respectively),
- Cov(X,Y) is the covariance of the returns of the two assets (given as 0.0108).
Substituting the given values into the formula, we get:
σp = sqrt[(0.5^2 * 0.49) + (0.5^2 * 0.81) + (2 * 0.5 * 0.5 * 0.0108)]
Solving this will give you the standard deviation of the portfolio.
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