Much is made of the fact that certain mutual funds outperform the market year af

Question

Much is made of the fact that certain mutual funds outperform the market year after year. For concreteness, consider a 10-year period and let the popu lation be the 4,170 mutual funds reported in The Wall Street Journal on Jan 1, 1995. By saying that performance relative to the market is random, we mean that each fund has a 50-50 chance of outperforming the market in any year and that performances is independent from year to year. 1. If performance relative to the market is truly random, what is the probability that any particular fund out performans the market in all 10 years? 2 Find the probability that at least one fund out of 4,170 funds outperforms the market in all 10 years.

Explanation / Answer

1) here probability of outperforming p=0.5

therefore probability that a fund outperform in all 10 years =(0.5)10 =0.000977 ~ 0.0010

2) probability that at least one fund out of 4170 funds outperform the market in 10 years =1-P( none of 4170 funds outperform the market) =1-(1-0.000977)4170 = 0.982995 ~ 0.9830

please revert if any clarification required,

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