Consider an equally weighted portfolio that contains 100 stocks.If the average volatility of these stocks is 50% and the average correlation between the stocks is .7,then the volatility of this equally weighted portfolio is closest to:
A).72.
B).63.
C).40.
D).50.

Question

Quizplus · Accepted Answer

The formula to calculate the volatility of a portfolio is:
Portfolio Volatility = √(∑(∑(wi*wj*σi*σj*ρij))))

where wi and wj are the weights of stock i and j in the portfolio, σi and σj are the standard deviations of stock i and j, and ρij is the correlation coefficient between stock i and j.

For an equally weighted portfolio with 100 stocks, wi = wj = 1/100 = 0.01 for all stocks. Using the given average volatility (σ) of 50% and average correlation (ρ) of 0.7, we can plug in the values to get:

Portfolio Volatility = √(∑(∑(0.01*0.01*0.5*0.5*0.7)))) = 0.63 or 63%

Therefore, the closest answer choice is B) 63%.

Consider an Equally Weighted Portfolio That Contains 100 Stocks