Q1C.

Expert-verifiedFound in: Page 107

Book edition
9th

Author(s)
Zvi Bodie, Alex Kane, Alan Marcus, Alan J. Marcus

Pages
748 pages

ISBN
9780078034695

**Suppose you observe the investment performance of 350 portfolio managers for five years and rank them by investment returns during each year. After five years, you find that 11 of the funds have investment returns that place the fund in the top half of the sample in each and every year of your sample. Such consistency of performance indicates to you that these must be the funds whose managers are in fact skilled, and you invest your money in these funds. Is your conclusion warranted? **

The consistent performance after five years is not a proof of skill.

**The annual rate of return or average annual rate of return is used to calculate the investment performance.**** **

Suppose that finishing in the top half of all portfolio managers is purely luck, and that the probability of doing so in any year is exactly 1/2.

Then the probability that any particular manager would finish in the top half of the sample five years in a row is (½)5 = 1/32.

We would then expect to find that [350 x (1/32)] = 11 managers finish in the top half for each of the five consecutive years.

This is precisely what we found.

Thus, we should not conclude that the consistent performance after five years is proof of skill.

We would expect to find eleven managers exhibiting precisely this level of "consistency" even if performance is due purely due to luck.

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