The holy grail of investing, the ever-elusive alpha, is the additional return above and beyond what can be explained by the assumption of risk. IFA has long held that both individual and institutional investors should not waste their time or resources in seeking out managers who supposedly will deliver alpha. There are two primary reasons for this: First, it is costly, and it is a cost that is highly unlikely to provide a positive benefit, especially considering that the total amount of alpha that is available for capture in every asset class in negative. Second, the reach for alpha often causes investors to miss out on the returns associated with the risk factors of market, size, and value, all of which are there for the taking.

Despite all of this, we constantly see individual investors and 401k plan sponsors pick funds based on three or five years of hot returns. They are oblivious to the countless studies such as the S&P Persistence Scorecard which show that benchmark-beating returns appear no more often than we would expect to see from chance alone, and they cannot be relied upon to continue into the future. Perhaps these investors are not aware of the existence of a well-known statistical test which can determine if outperformance can be attributed to luck or skill, the t-test. It is based on the premise that the distribution of errors (or noise) is a bell-shaped curve, and we can thus calculate the probability of certain observations occurring under a given assumption.

When given a series of historical returns delivered by an active manager, the following steps may be taken to determine what the probability is that the performance is truly superior to a risk-appropriate benchmark.

- The returns of the manager are compared to the returns of the benchmark, and the difference is calculated for each calendar year.
- The average excess return and the standard deviation of the return differences are calculated.
- The t-statistic is calculated as the average excess return multiplied by the square root of the number of years divided by the standard deviation.
- If the t-statistic is greater than or equal to 2, then we are 95% confident that the manager has reliably delivered outperformance.

The question is often asked, “How many years of data do we need to have a t-statistic of 2 or greater?” The answer, of course, depends on the average excess return and the standard deviation of the return differences.

We can make a couple of assumptions such as the following:

The manager has an average excess return of 2% with a standard deviation of 6%. This implies the need for 36 years of data to get a t-statistic of 2. The assumption of 2% for the manager’s average excess return was chosen because the ability to deliver 2% above the benchmark after expenses is considered quite respectable in the investment profession, and a 6% standard deviation is approximately what IFA observed when measuring the alpha of over 600 actively managed funds.

Below is a table showing how the standard deviation of the return difference affects the number of required years:

Standard Deviation |
Number of Years Requiredto get a t-Statistic of 2 |

4% | 16 |

5% | 25 |

6% | 36 |

7% | 49 |

8% | 64 |

It is uncommon to have an excess return above the benchmark with a low standard deviation. In such cases, the manager is usually overwhelmed with new money and is no longer able to retain his advantage. According to Morningstar, the average mutual fund manager tenure for all domestic equity categories is 5 to 6 years. Clearly, this is not nearly enough time to establish the existence of stock-picking or bond-picking skill.

Once they develop an elementary understanding of statistics, the only sensible move for investors is to stop playing the mug’s game of manager-picking and instead accept the simple premise that risk is the only reliable source of returns, and with the help of a passively-oriented advisor, they can capture the returns available via exposure to the risk factors identified by the academics.

## About Index Fund Advisors

Index Fund Advisors, Inc. (IFA) is a fee-only advisory and wealth management firm that provides risk-appropriate, returns-optimized, globally-diversified and tax-managed investment strategies with a fiduciary standard of care.

Founded in 1999, IFA is a Registered Investment Adviser with the U.S. Securities and Exchange Commission that provides investment advice to individuals, trusts, corporations, non-profits, and public and private institutions. Based in Irvine, California, IFA manages individual and institutional accounts, including IRA, 401(k), 403(b), profit sharing, pensions, endowments and all other investment accounts. IFA also facilitates IRA rollovers from 401(k)s and 403(b)s.

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