Question

QUESTION 16 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 5 years? In other words, the fund would fail to beat the benchmark in one of the 5 years. Enter answer accurate to two decimal places.

Answer 1

This can be solved using Binomial theorem of probability as

probability of success (beating the index)= 47%

so probability of failure= 53%

number of years (trials)= 5

required number of favourable outcomes, r= 4

Now using these in the binomial theorem formula

,п-r

= 5!/(4!*1! ) * (0.47)^4 * (0.53)^1

= 12.93%

Thus there is 12.93% chance that any given fund would beat the index all but once out of the past 5 years.

So in a universe of 5000 funds, we expect around 5000*12.93% = 646.56 funds to meet this criteria.

If any doubt in this, please let me know in comments