Calculate Portfolio Risk: Equally Weighted Portfolio with 17 Assets

To calculate the risk of the portfolio, we need to find the portfolio's standard deviation.

The formula for the portfolio's standard deviation is:

σp = √(w1^2σ1^2 + w2^2σ2^2 + ... + wn^2σn^2 + 2w1w2Cov(1,2) + 2w1w3Cov(1,3) + ... + 2w(n-1)wnCov(n-1,n))

Where:

• σp is the portfolio's standard deviation
• wi is the weight of the ith asset in the portfolio
• σi is the standard deviation of the ith asset
• Cov(i,j) is the covariance between the ith and jth assets

Since the portfolio is equally weighted, each asset has a weight of 1/17.

Plugging in the given values:

σp = √((1/17)^2 * (0.28)^2 + (1/17)^2 * (0.28)^2 + ... + (1/17)^2 * (0.28)^2 + 2 * (1/17) * (1/17) * 0.07 + 2 * (1/17) * (1/17) * 0.07 + ... + 2 * (1/17) * (1/17) * 0.07)

Simplifying:

σp = √((17 * (1/17)^2 * (0.28)^2) + 2 * (17 * (1/17)^2 * 0.07))

σp = √((1/17) * (0.28)^2 + 2 * (1/17) * 0.07)

σp = √((0.28)^2/17 + 2 * 0.07/17)

σp = √(0.007840 + 0.008235)

σp = √0.016075

σp ≈ 0.1268

To express the risk as a percentage, we multiply the standard deviation by 100:

Risk of the portfolio = 0.1268 * 100 ≈ 12.68%

Therefore, the risk of this equally weighted portfolio is approximately 12.68%.