Question

In a perfectly efficient market, an active strategy mutual fund that charges a 1% fee has about a 47% chance of beating the index net of fee. In a universe of 5,000 funds, how many funds would you expect to beat the index all but once out of the past 9 years? In other words, the fund would fail to beat the benchmark in one of the 9 years Enter answer accurate to two decimal places

Answer 1

Probability at bund beating the Index = 0.47 Probability for tailure = 1-0.47 = 0.53 Failure it bund is once out of 9 years Probability . F years of success in 8 = 60.47) 0.00238112866 Probability of bailure in 1 year = 0.53 probability of bailure in exartly 1 year This 9x0534 0.00238112866 = 0.013529 i Number of inder bunds in all that but would the beat out of the 9 years among 5000 bunds = 5ooo x 0.0113579 56.7895

The fund would fail to beat the benchmark in one out of 9 years = 56.7895