Question

An investment broker at a major investment company claims that she has found a mutual fund that is a true winner. This particular fund has outperformed the standard market index in 37 out of 52 weeks. Could this be purely due to chance (that is the probability that a particular fund does better than the market index is 50%) or did she really find a winning investment? Use the binomial distribution calculations to answer the question.

Answer 1

When we use the exact test using binomial distribution, the hypothesis and the test statistics looks lies as follow,

where, p₀ = 0.50

The distribution of random variable X is,

where, n = 52 and p = 0.50

The P-value is obtained using the formula,

Where, n = 52, k = 37 and p = 0.50

For the calculation purpose excel is used to calculate the probability using the function

=1-BINOM.DIST(37,52,0.5,TRUE)

Conclusion:

Since the p-value is 0.000598 less than 0.05 at 5% significance level, we can conclude that there is significant number of week that a particular fund is outperformed the standard market. Hence the probability is no due to chance.