An equally weighted portfolio comprises 10 assets which all have a standard deviation of 0.31. The average covariance between the assets is 0.04.The risk of this portfolio is _____%.
Question
An equally weighted portfolio comprises 10 assets which all have a standard deviation of 0.31. The average covariance between the assets is 0.04.The risk of this portfolio is _____%.
Solution
To calculate the risk of the portfolio, we use the formula for the standard deviation of an equally weighted portfolio:
σp = sqrt[(1/N) * σi^2 + (N-1/N) * Covij]
where:
- σp is the standard deviation of the portfolio
- N is the number of assets in the portfolio
- σi is the standard deviation of an individual asset
- Covij is the average covariance between the assets
Given that N=10, σi=0.31, and Covij=0.04, we can substitute these values into the formula:
σp = sqrt[(1/10) * (0.31)^2 + (10-1/10) * 0.04] σp = sqrt[0.00961 + 0.036] σp = sqrt[0.04561]
Therefore, the risk of the portfolio, expressed as a standard deviation, is sqrt[0.04561] = 0.21357 or 21.357%.
So, the risk of this portfolio is 21.357%.
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