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% |

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