Question

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?

Answer 1

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%