The point of this example is that if each mutual fund has a 50-50 chance of beating the market in any given week, it is very unlikely for a particular mutual fund to beat the market in at least 37 out of 52 weeks. However, if you have a lot of such mutual funds, then it is fairly likely that at least one of them will beat the market this often. You can see this from the data table. For example, if there are 600 mutual funds, the chance of at least one beating the market at least 37 out of 52 weeks is greater than 60%.
An analogy might help. If a person flips a coin 100 times, it's not very likely that she will get a streak of, say, 10 heads in a row. But if hundreds of people flip a coin 100 times, it's almost certain that at least one of them will get such a streak.
An Investment broker at Vizee Analytics claims that he has found a real winner. He has tracked a mutual fund that has beaten a standard market index in 37 of the past 52 weeks. Could this be due to chance, or has he really found a winner?
Objective: To determine the probability of a mutual fund outperforming a standard market index at least 37 out of 52 weeks.
=1-BINOM.DIST(B3-1,B4,0.5,TRUE)
To see whether any of the 400 funds beat the market at least 37 of 52 weeks , calculate P( Y > 1) = 1 -P (Y=0) in cell B9 with the formula:
=1-BINOM.DIST(0,B8,B6,TRUE)
The data shows beating the market 37 times out of 52 is no big deal with 400 funds, but beating it 40 times out of 52 even with 600 funds. The probability of this happening purely by chance is only 0.038 or less than 1 out of 25.
To see how the probability in cell B9 depends on the level of success on the reported fund (the value in cell B3) and the number of mutual funds being tracked 9ib cell B8), a two-way data table has been created in the range B13:G18. The formula in cell B13 is =B9, the row input cell is B3 and the column input cell is B8).
The Excel data for Tableau:
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