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Forever Elusive Alpha

By Salil Mehta, Statistical Ideas

Humans have been repeating this inefficient ritual for more than 700 years, with the first known origins were then in Europe. There sprung lenders and insurers who assessed the relative merits of individual commercial risk. The methods were somewhat more crude versus the resources available to people today, but none-the-less this is the humble birthplace from where modern investment speculation gets its origin. What should be the effective interest rate to lend an emerging company wanting to complete a construction project? What should an insurer charge to protect a ship setting sail into an stormy ocean, so that the premium pricing is profitable yet competitive?

Over time, more information was made available concerning those who needed capital market resources. And more ordinary people were able to invest in companies and products. Through the distribution of personal wealth and technological progress, society experienced episodic bouts of speculations and manias. Converting defined benefit plans in the U.S. to one where American workers invest their own contributions, made for even greater heterogeneity of outcomes in the individual pursuit of alpha. How can this progress be good, if there are a fewer portion of risk-adjusted beneficiaries? Let’s explore the outcomes and difficulties in the great inefficient search for exceptional alpha.

The true statistical test for outperformance relative to a highly liquid and investable benchmark takes into account how likely such performance could have been attained by luck alone. Afterall over any period of time, there will separation in the performance of individual stocks within a basket. Some lucky stock holders will own specific stocks that uniformly outperform the underlying index over this same period of time.

Nonetheless it is worth noting that the difficult statistical standard necessary to warrant the concept of skill over a long career, or life, has a smaller side effect. And that is that only minorities of those who speculate will actually have, through skill, statistically outperformed.

Let’s show how this works, using the time since the recent financial crisis as a baseline frame for the analysis. From there we’ll expand to a broader set of applications and timeframes. The market has gone through a large hockey-stick pattern since the height of the financial crisis, 5.5 years ago. Equity markets initially plummeted through early 2009, but have since rallied to new highs.

If you and your friends had all tried your hand at stock selection and market-timing along the way, then there is a good chance that you are now feeling pretty good right now. Making money is fun, and so is the emotional confidence that inflates disproportionately with one’s portfolio. But for more the vast majority of people, feeling too good is unwarranted. And hubris should be replaced with humility in the great amount of luck that explains their post-crisis performance.

How likely is it that an investor (or speculator) in U.S. equities over the past 5.5 years has demonstrated significant investment skills in this asset class? For our test we reduce the investable universe to a mapping of the current 30 Dow Jones Industrial Average (DJIA) stocks. And we ask what would be the performance of selecting a basket of any of the top quarter of these 30 stocks for each of the past 5.5 years. So the top 8 stocks had an outperformance of 1.2%, with a 0.5% standard deviation. This implies a significantly low, 1% chance of straying that far from the rest of the DJIA by chance alone.

Being satisfied with our critical threshold, we next solve the probability of continuously selecting a basket of the annual top quarter of DJIA stocks by chance alone. This is an elementary, compounded Bernoulli problem, and it comes to 0.1%.

We then use Bayesian probability (see equality below) to determine the portion of the population that has skill near the required 1.2% monthly outperformance, in order to compensate for the low 0.1% probability of attaining these results by luck alone. And this portion of the population comes to 21%.

p(outperform) = p(outperform|luck)*p(luck) + p(outperform|skill)*p(skill)

While there are empirical differences that would ensue from, not the beta of the 30 DJIA stocks, but rather from the component of the typical correlation and dispersion components of beta. For example, when the correlation is high and the dispersion is low, then more than typical portion of the investing population at that time would be able to outperform based on skill. And when the opposite parameters define the investment regime, then less than the typical portion of the investment population would be able to outperform based on skill.

Theoretically expanding this example to different time frames, we get the following results. Note that these examples work for the most common approach to equities speculation: market-timing with a discretionary allocation towards individual stocks. For 2 years, instead of 5.5 years, the portion of the population with skill increased to 36%. This is because it is significantlyless difficult to outperform monthly at the stated 1.2%, for less years. And hence not as easy to attribute a higher probability split to luck. On the other end of the time spectrum, for 25 years and 50 years of speculation, the portion of speculators who have statistical evidence of investment skills rapidly decreases to 0.76% and 0.02%, respectively. This is shown in blue, on the left axis of the chart below.

We can also skills-adjust these data, so that we can solve for the level of outperformance that a 2, 25, and 50 years investment career would need to equate to the 1.2% monthly outperformance from 5.5 years. This comes to 2.0%, 0.58%, and 0.4%, respectively. See the reddata below.


We also identify in green, the performance of an extraordinary investor, Warren Buffet. In 2001 Warren said in Berkshire Hathaway’s (BRK) Chairman’s Letter:

Investors should remember that excitement and expenses are their enemies. And if they insist on trying to time their participation in equities, they should try to be fearful when others are greedy and greedy when others are fearful.

This turned out to be advice more apt in 2008-2009, then it was in 2000-2001. Yet despite his extraordinarily favorable private placements, which he was able to negotiate during the depths of the financial crisis, on a market price he barely underperformed during the past 5.5 years. Market price was used since BRK’s recent months of valuation accounting data is not yet available. We also see in this chart that he has significantly outperformed over his 45-plus year history, and doesn’t really need the skills-adjusted handicap we show for those investing for such a long period of time.

To clarify this previous point, we see in that chart above that having only a third, of the recent 5.5-year skilled monthly outperformance, is needed to correct for the precipitous drop in the odds of outperforming at that level for over 25 to 50 years. Conversely, a spike higher in monthly outperformance is needed, during a more brief investment period, to statistically perform the same as the nearly 21% of people have been capable of outperform with skill during the past 5.5 years.

The confidence is tightest about the 5.5-year baseline analysis. And going forward in this analysis, we assume that there are roughly tens of millions of Americans who actively invest. Given this, the probability of investment skill would suggest roughly tens of thousands Americans in their 20s have this sort of investing experience any can feel comfortable that their recent gains may offer a chance for long-run continued outperformance. But otherwise nearly four out of every five of their peers, are already doomed in any pursuit of a 25 to 50 year statistical outperformance. Warren Buffet’s recent tumble is a poor counter-example of the possibilities of a miraculous, late-career revival.

Now on the other end of the age spectrum, nearly a only few thousand people with 20-30 years of investing experience have outperformed will skill. And finally of those in Warren’s age group (45-55 years of investing experience), just less than a hundred have also outperformed with skill.

Does this seem like a lot? Well to put this into some perspective, 99% of the top managing directors on Wall Street would have not outperformed with skill over this period.

With such daunting odds, what advice is there for people who dimly choose to speculate anyway, tying up large amounts of their human capital? There are five specific advice here to impart.

The first advice is that this age-old ritual is extraordinarily more transparent and fair then ever before. This makes things more difficult, and the fact that more people attempt to acquire alphadoesn’t advance the ease for you in actually achieving it. Just as the more people playing the lottery doesn’t increase your personal odds of having the winning ticket. The second advice is that simply learning the rules of finance or working in the industry hardly increases your chance of outperforming the market (see quote at bottom). This chance we showed in the note is fairly established in probability theory and super low. The advice here is akin to knowing how to throw a javelin or play chess doesn’t imply we should prepare for the Olympics or to play chess against a supercomputer. The third advice is that much more often it is better to simply buy an index fund, and know that human capital is better spent only entertaining other pursuits. The fourth advice is that the very small number of people are skilled investors share some rare talents. They are gifted with an unusual ability to seamlessly connect specific dots within an investment problem, well beyond the abilities of normal smart people. Just as important, they know the many areas where they do not personally excel at a world-class level, and nimbly have the sense to avoid those investment areas that trap others. And the fifth advice is that selecting world-class stocks or a world-class investment manager are both generally difficult, and anyway inefficient. If one can’t successfully select the former, then one can’t usually successfully select the latter. Simply selecting an investment manager for example, such as BRK (which has a proven long-term record), can often provide a false reading for the subsequent five years or so. Just see how the past 5.5 years of BRK were, as they were the most disastrous for the company, since 1965!

We leave with a 1998 quote from Warren Buffet. May the wisdom prove promising to those still toiling away, in pursuit of that extraordinarily elusive thing.

Success in investing doesn’t correlate with I.Q. once you’re above the level of 25. Once you have ordinary intelligence, what you need is the temperament to control the urges that get other people into trouble in investing.

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