(MoneyWatch) Having a working knowledge of math and statistics can play an important role in determining your success as an investor. Understanding concepts such as correlations, standard deviations, normal distributions, and skewness and kurtosis not only allows you to analyze the risks of various investments, but also is helpful in understanding how various assets mix with each other. Understanding how the risks of various assets work together allows you to choose the portfolio that will give you the greatest odds of achieving your financial goals. Having knowledge of statistics can also allow you to avoid one of the most common errors made by investors -- succumbing to the fallacy of the "hot streak."
It's well documented that both individual and institutional investors are what we can call "return chasers" -- pouring money into the latest hot funds. Investors attach great significance to market-beating performance records over three, five, and especially 10 years. The thinking goes, "Surely 10 years of beating the market can't be luck." One study found that an astounding 97 percent of fund flows went into mutual funds that carry Morningstar's four-star and five-star ratings -- ratings that are based heavily on recent performance.
Unfortunately, there's an overwhelming body of research that shows not only that past performance isn't prologue, but also that -- more to the point -- it has no predictive value whatsoever. Said another way, with so many funds trying to generate alpha, sheer randomness dictates that many will succeed. Without this knowledge, you'll succumb to the idea that past performance is predictive and fall prey to fallacy of the hot streak.
The Financial Times recently took a satirical look at this issue. The editorial noted:
Having long been famous for their memory, elephants may soon be hailed for their predictive skills. The future glory of the species rests on the massive shoulders of Citta, an Indian-born, but Polish-resident pachyderm chosen to predict with her trunk the correct results of all the 31 matches in the Euro 2012 football tournament. In a qualifying round she fended off powerful challenges by other aspiring tipsters, such as Jacko the parrot and Katherine the donkey.
The FT then suggested that Citta's "zoo in Krakow would become the destination of waves of headhunters, seeking to recruit her on behalf of the fund management industry. The belief that even animals can beat Wall Street experts has strengthened since 1988, when a portfolio created at random by a monkey outperformed more than 80 percent of U.S. fund managers."
As discussed in my book, "Investment Mistakes Even Smart Investors Make," the lack of knowledge of statistics leads to the mistake of failing to understand that streaks randomly occur far more frequently than we think. For example, the odds of flipping a coin 20 times and getting either four heads or four tails in a row are 50 percent. Because people underestimate the frequency of streaks, they tend to assign too much meaning to events that are likely to be random occurrences. One study even demonstrated that a "hot hand" in basketball was likely to be nothing more than a random event. A statistician following a basketball team around for an entire season found the odds of a career 50 percent shooter hitting the next shot were 50 percent, even if this player had just hit five shots in a row.
The lesson of Citta's tale is that an outcome that seems to be due to skill is often nothing more than luck. Consider the following tale, from 2003, that is one of my favorites.
Disappointed with the performance of its active manager, a multibillion dollar pension plan decides to fire the manager and initiates a search for a replacement. It performs a thorough screen of potential candidates. Among the screens are a record of superior performance over the prior 15-year period ending in 2002, a high persistency of superior performance, tenure of the manager, and turnover. The due diligence process has narrowed the final candidates to the following funds and a benchmark, the S&P 500 Index.
- Larry Swedroe Investment Trust -- 14.3 percent
- Legg Mason Value -- 14.1 percent
- Washington Mutual -- 12.4 percent
- Fidelity Magellan -- 12.3 percent
- S&P 500 Index Fund -- 11.5 percent
- Janus Fund -- 11.3 percent
Based on its track record, the winner of the performance derby is the Larry Swedroe Investment Trust. After being presented with the data, the investment committee votes to award the management of the plan to the Larry Swedroe Investment Trust. At the last moment, one member of the committee suggests that as one final bit of due diligence Larry Swedroe should be brought in to explain his winning strategy. Appearing before the committee, I'm asked to explain my strategy. I respond by stating that since my wife's name is Mona, my lucky letter is M. I therefore construct a value-weighted portfolio of all U.S. stocks that begin with the letter M and rebalance the portfolio annually. Skill, or the demon of luck?
You can avoid the mistake of following the "hot hand" by carefully considering whether the outcome might have been a random one. As investment manager Marty Whitman points out: "The gutters of Wall Street are strewn with the bodies of people who looked good for five years." The lesson is that when it comes to investing, driving forward while looking in the rear view mirror leads to crashes.
Image courtesy of Flickr user The U.S. Army