My last post asked the question: “Are Quants the Chiropractors of Finance?” The analogy of a chiropractor was chosen to illustrate two potential risks:
- Over-reliance on a single model.
- The model becomes our guide to reality. Instead of merely describing what we see, it influences what we choose to pay attention to and thus changes our experience of the world.
I used the example of growth investing to illustrate the effects of these risks. In summary, growth happens in the future and there’s no data for the future because it hasn’t happened yet. My argument was that this pushes quants to do one of three things:
- Ignore it.
- Definite it in terms of what can be measured – e.g. assume that growth is “expensive” or the opposite of value.
- Try to proxy it using a third variable that shares a less-than-perfect relationship with growth and can be measured; such as historical earnings growth, price momentum or profitability
This post elaborates further on the second risk. The key point is this: using quantitative techniques changes the way that quants formulate research questions and that this might affect their results. Charlie Munger describes this risk in a speech presented at UCS Business School in 2003:
You’ve got a complex system and it spews out a lot of wonderful numbers that enable you to measure some factors. But there are other factors that are terribly important [yet] there’s no precise numbering that you can put on these factors. You know they’re important, but you don’t have the numbers. Well, practically (1) everybody overweighs the stuff that can be numbered, because it yields to the statistical techniques they’re taught in academia, and (2) doesn’t mix the hard-to-measure stuff that may be more important. That is a mistake I’ve tried all my life to avoid, and I have no regrets for having done that.
As always, it’s helpful to use an example: Breadth. Higher breadth, or a larger sample size is like oxygen to a quant for two reasons:
- A larger number of observations leads to a greater statistical power (i.e. a reduced risk of making Type 2 errors).
- Most of the factors identified by quants have a low signal-to-noise-ratio. They require lots of observations before clear evidence of an ‘edge’ emerges.
The need for breadth, or a sufficiently large number of observations, affects the way a research question is asked and the research design used by quants. For example, market timing. Most quantitative studies of market timing show that it is very difficult (if not impossible) to outperform the stock market, net of transaction costs and taxes.
The need for breadth, or a sufficiently large number of observations, affects the way a research question is asked and the research design used by quants.
The classic market timing study was performed by Professor William Sharpe, published in his paper Likely Gains from Market Timing (Financial Analyst’s Journal, 1975).
Professor Sharpe tested the effectiveness of market timing by first comparing the returns of a ‘perfect timing’ strategy, with a buy-and-hold investment in the Standard and Poor’s (S&P) Composite Index from 1934 through to 1972. At the beginning of each year, perfect timing strategy was 100 per cent invested in the highest returning asset class (either the S&P Composite or US Treasuries) over the next 12-months.
The perfect timing strategy yielded 14.86 per cent return per annum versus 10.64 per cent per annum for the buy-and-hold strategy. This was achieved with 14.58 per cent standard deviation for the perfect timing strategy versus 21.06 per cent standard deviation for the buy-and-hold strategy.
To test the potential gains based on imperfect market timing ability, various levels of prediction accuracy were tested using a binomial model, assuming that the market timer has equal prediction accuracy for both bull and bear market.
Professor Sharpe has found that benefits from market timing are only available to market timers with more than 74 per cent prediction accuracy on a risk-adjusted basis. He also indicated that there exists a bias when one assumes equal accuracy for predicting bull and bear markets, since there are more good years than bad years historically.
I don’t know about you, but I don’t know many investors that come up with a New Year’s resolution to invest 100 per cent of their savings into stocks or bonds for the next 12 months. For starters, most skilled investors know better than to take all-or-nothing, one-way bets. Most experienced investors know that fundamentals, such as valuation, only have predictive power over time horizons much longer than 12 months. And they are aware that fundamental indicators are only meaningful when they are at extreme-levels.
An experienced investor would know that, as an approximate rule-of-thumb, “the stock market moves up roughly a third of the time, sideways a third of the time and downward a third of the time” – Jesse Livermore. Consequently, moving out of stocks and into bonds is not a decision made lightly as it involves going against the odds. They would also be aware that fees and taxes make the odds even more unfavourable.
Putting all of this together its reasonable to believe that:
- Most experienced equity investors would stay fully invested unless there were good reasons to make a change.
- That these reasons wouldn’t come along very often, maybe once every few years.
- And they would be unlikely to take one-way, all-or-nothing bets.
So why did Professor Sharpe test the perfect timing strategy described above? My guess is that it has to do with breadth. The period from 1934- 1972 covers 38 years. Suppose that Sharpe tested a market timing rule that resulted in shifts every three years on average. He would have had only 14 observations instead of 38, reducing the statistical power of the study.
On the other hand, why didn’t he test rolling 12-month periods from 1934-1972? That would have produced 444 observations, significantly boosting the statistical power of the study. But this would have been very time-consuming. Remember, the paper was written in 1975 when computers were not as powerful as they are today.
Sharpe seems to have formulated the question in such a way as to have enough observations to obtain a statistically powerful result but not so many as to exceed the limitations of the computation tools that were available at the time.
In other words, the techniques probably determined the way the question was asked which, at least in part, determined the result. In so doing, he discovered that market timing, as defined by a strategy that no sane investor would probably ever contemplate, requires an almost-impossible level of accuracy to make it work. Sharpe also left the more relevant question of whether it’s ever appropriate to reduce a portfolio’s weight to equities largely unanswered.
My point is not to argue that market timing is possible or that investors should try it. Rather the point is that quantitative analysis isn’t suited to the analysis of infrequent events or ‘once in a lifetime’ opportunities or risks. Either there just isn’t enough data, or the data is so noisy that it takes a lot of it to be sure that something’s there.
The implication is that investors who rely solely on quantitative analysis are putting themselves at danger of ignoring opportunities and risks that seldom occur but can have enormous impact. Why is this a problem? Because it creates a blind spot where potentially life-changing decisions are missed. Charlie Munger explained why at the 1996 Wesco Financial Corporation’s annual meeting:
Experience tends to confirm a long-held notion that being prepared, on a few occasions in a lifetime, to act promptly in scale, in doing some simple and logical thing, will often dramatically improve the financial results of that lifetime. A few major opportunities, clearly recognizable as such, will usually come to one who continuously searches and waits, with a curious mind that loves diagnosis involving multiple variables. And then all that is required is a willingness to bet heavily when the odds are extremely favourable, using resources available as a result of prudence and patience in the past.
At the 2017 Daily Journal Annual Meeting, Munger gave a personal example of how 2 decisions in 50 years resulted in a $400-$500 million-dollar gain.
I read Barron’s for 50 years. In 50 years I found one investment opportunity in Barron’s out of which I made about $80 million with almost no risk. I took the $80 million and gave it to Li Lu who turned it into $400 or $500 million. So I have made $400 or $500 million reading Barron’s for 50 years and following one idea. Now that doesn’t help you very much does it? I’m sorry but that’s the way it really happened. If you can’t do it… I didn’t have a lot of ideas. I didn’t find them that easily, but I did pounce on one.
You’re probably thinking, how do we know that wasn’t just luck? Or how can someone else repeat Munger’s success? Even Munger was aware of this problem. He admitted that his answer wasn’t much help to others hoping to emulate his success.
Quantitative analysis is probably not the best way to analyse low- frequency, high-impact decisions.
Again, I’m not advocating that we all take out a subscription to Barron’s. Rather, the point is that quantitative analysis is probably not the best way to analyse low- frequency, high-impact decisions. Investors face these decisions, which is why its probably a good idea to use several different problem-solving approaches, including quantitative analysis.
Quantitative analysis is a powerful and useful tool. But like any tool it has its limits. It requires data, which means it may struggle in situations where the future is less than perfectly correlated with the past. It requires breadth, which means that it has difficulty answering questions about events that occur infrequently. And its effectiveness relative to other forms of analysis also depends on the ratio of signal to noise. But that’s a topic for another post.