Question

# Q4. Suppose you develop a mutual fund that includes 500 NASDAQ stocks, all with equal weights...

Q4. Suppose you develop a mutual fund that includes 500 NASDAQ stocks, all with equal weights in the fund's portfolio. The average return standard deviation of the stocks is 44 percent, and the average pairwise correlation among the stocks is 0.30. What is your estimate of the standard deviation of the fund's portfolio?

 No. of stocks = 500 Weight of each stock = 1/500= 0.002 Standard deviaiton of each stock = 44% correlation between each stock = 0.3 no. of combination of standard portfolio calculation = 500^2 = 250000 Total no. of combination of (weight * std. dev.)^2 = 500 Total no. of other combination = 250000-500= 249500 Standard deviation of portfolio = (σp) √(500*(w s* σs )^ 2 )+ (249500 * (wS * σS * WS * σS * correlation)) (σp) = √(500*(0.002*44%)^2) + (249500*0.002*0.002*44%*44%*0.30) (σp) = √(0.05835104) (σp) = 0.2415595993 or 24.16% So, standard deviation of fund's portfolio is 24.16%

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