Question

The return on a mutual fund has a normal distribution with expected value of 15% and standard deviation of 22%. The NAV of the mutual fund is $40. The fund is expected to distribute $2 in dividend to its shareholders one year from now. Calculate the probability that the NAV of the mutual fund a year from now (after the dividend distribution) will be between $50 and $60?

Answer #1

Since the return of MF is following Normal distribution curve ,

So the problem can be solved by use of Z score =

Required NAV before dividend distribution = $50+2 =$52 and $ 60+2 = $62 ,

Return % = 52-40/40 = 30% and 62-40/40 =55%

Assume , dividend distribution tax is ZERO( as not given in question )

Z -Score_{52} = 30 -15 /22 = 0.6818 and Z
-Score_{62} = 55 -15 /22 = 1.8182

After getting the value in Z-table

Z -Score_{52} = 0.7517 Z -Score_{62}
= 0.9649

Area in between = 0.9649 - 0.7517 = 0.2132

Probability for required NAV = 21.32%

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