22. “The strong-form of the efficient-market hypothesis is nonsense. Look at mutual fund X; it has had superior performance for each of the last 10 years.” Does the speaker have a point?

Suppose that there is a 50% probability that X will obtain superior performance in any year simply by chance.

a. If X is the only fund, calculate the probability that it will have achieved superior performance for each of the past 10 years.

b. Now recognize that there are over 10,000 mutual funds in the United States. What is the probability that by chance there is at least 1 out of 10,000 funds that obtained 10 successive years of superior performance?

Month (A)
Market Return (B)
Executive Cheese Return (C)
Paddington Beer Return May 07 2.7 ⫺3 1.6 Jun ⫺0.2 2.3 ⫺0.8 Jul ⫺3.8 ⫺5.1 0.3 Aug ⫺0.9 ⫺0.7 ⫺1.6 Sep 2.6 3.1 2.8 Oct 3.9 13 2.1 Nov ⫺4.3 ⫺2.1 ⫺6 Dec 0.4 6.2 ⫺1.7 Jan 08 ⫺8.9 ⫺4 ⫺5 Feb 0.1 0.4 ⫺0.4 Mar ⫺3.1 ⫺2.1 ⫺2 Apr 6.8 4.6 3.2 May ⫺0.6 ⫺0.3 0.4 Jun ⫺7.1 ⫺12.7 ⫺7.3 Jul ⫺3.8 1.1 ⫺4.1 Aug 4.2 7.2 2.3 Sep ⫺13.0 ⫺18.1 ⫺8.7 Oct ⫺10.7 ⫺6.2 ⫺12 Nov ⫺2.0 0.5 ⫺4.2 Dec 3.4 4.7 2.7 Jan 09 ⫺6.4 ⫺8.1 ⫺0.4 Feb ⫺7.7 ⫺2.1 ⫺9.4