Consider a portfolio with a large number of uncorrelated assets, each carrying an equal weight in the portfolio. Which of the following statements accurately describes the volatility of the portfolio?
A.
The volatility of the portfolio will be equal to the weighted average of the volatility of the assets in the portfolio
B.
The volatility of the portfolio is the same as that of the market
C.
The volatility of the portfolio will be equal to the square root of the sum of the variances of the assets in the portfolio weighted by the square of their weights
D.
The volatility of the portfolio will be close to zero
When assets are uncorrelated, variances are additive. But volatility (which is standard deviation) is not. In the given situation, the total variance of the portfolio will be equal to the the square root of the sum of the variances of the assets in the portfolio weighted by the square of their weights. Its volatility will be the square root of this variance. Thus Choice 'c' is the correct answer.
(This is because V(cA + dB) = c^2 V(A) + d^2 V(B) - refer tutorial on combining variances.)
Choice 'a' is incorrect as it describes the calculation of variance, not volatility. Also, the presence of a large number of uncorrelated assets does not create a portfolio with volatility equal to zero or that of the market. The other choices are therefore incorrect.
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