Poll forecasting, Kelly criterion and mean reversionNovember 13, 2020 2023-05-11 8:30
Poll forecasting, Kelly criterion and mean reversion
Poll forecasting, Kelly criterion and mean reversion
If you are even half interested in electoral politics, you have been in for a treat over the past fortnight. India’s third-most populous state’s election of Chief Minister (by casting c42m votes) and the United States’ election of President (c150m votes) (1) had a common thread: the eventual outcome was hugely different from the polled outcome. While Biden’s pre-election lead of 8.0ppt (2) turned out much higher than actual lead of 3.3ppt, NDA’s final seat tally was 29% higher than exit poll estimates.
The fact that they got it wrong is NOT of too much interest to us; that happens all the time when working with small sample sizes. What’s interesting, however, is how the small changes in initial assumptions drove large changes in the outcome. India Today – Axis poll (one that we rate highly, both on analysis and integrity) had pencilled-in 80 off 243 for the ruling coalition, whereas the actual seat count was 125 (56% higher). In a refreshing admission of mistake (3), Axis conjectured that it missed the mark, inter alia, as overall female turnout was 5% more than male, which swung the election. Reiterating for the sake of emphasis–a 5% swing in roughly half the voters led to 56% higher seats for one side!
One might think that’s outlandish, but we had written about this phenomenon in our August 2020 letter (link here) while describing Ed Lorenz’s Chaos Theory and how tiny changes in the initial condition lead to dramatically different outcomes. Today, we argue that when dealing with chaos theory (for e.g., investments in the banking sector), a mean reversion model often serves as a better guide than a probability-based model.
Kelly criterion: Remember the 2008 hit film 21 in which hotshot MIT grads bring Las Vegas casinos down on their knees? That was a real-life story, the inspiration of which lay with Ed. Oakley Thorp, a mathematics professor and blackjack player, who developed the concept around counting cards in the late 1950s.
Ed’s technique, in turn, was based on what is called the Kelly criterion, which provides a mathematical way to determine the optimal size of: (a) bets if you are gambling; or (b) asset allocation if running a portfolio. It is expressed as ‘2p – 1 = x’ or 2x the probability of winning minus 1 equals the percentage of one’s bankroll that should be bet (probability of winning is 55%, bet 10%; probability increases to 70%, bet 40% and so on). Ed used this technique to great effect in blackjack, estimating the probability based on whether high cards were dealt to players or they were in the hand with the dealer, sufficiently altering his betting positions.
Mean reversion: Many authors argue that the skills required to excel at investments and poker/blackjack are similar. Robert G Hagstorm writes in his book, Investing: The last liberal art, that over the years, the Kelly criterion has become a part of the mainstream investment theory. Some believe Warren Buffett as well as Bill Gross use Kelly methods in managing their portfolios. Another author William Poundstone wrote a book, Fortune’s Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street, arguing how both are inter-related.
For us, there is a subtle, but important, difference. Outcomes are finite in gambling. For example, let’s imagine you enter into a wager with a friend that with one roll of dice you will get 6. Straight odds are one in 6 or a 16% probability. But then, suppose your friend rolls the dice again, quickly covers with hand, peeks and says, I can tell you it’s an even number. With this new information, you can recalculate the odds to 33%. While you were considering placing the bet, your friend says, “and it is not a 4,” and you can bump the probability up to 50%!
Assessing that probability in equity investment framework is quite another thing. Consider this NBFC which predominantly finances used commercial vehicles. In a conversation with us last week, they mentioned that their collection efficiency for October was 95% plus. This high number was surprising, given that their book comprises customers which have been severely impacted by the pandemic (6% are taxi operators, plus not all freight movement is back to normal). We couldn’t help but ask the reasons behind their book behaving so well.
One reason that stood out was that their current book had seasoned rather unexpectedly. The ILFS crisis in 2018 meant exceedingly small addition to the number of customers over the past two years. And, as old customers kept paying their EMIs, their loan to value fell to a level that it didn’t make sense for them to default. Obviously, 75% customers are owner-drivers (who will want to retain their livelihood and hence will not default) also helped.
Now, this is the same stock that fell 66% in less than a month in March 2020 and has risen 36% over the past month. How easy do you think it is to correctly calculate the probability of loss in this NBFC’s book at the peak of the pandemic? If calculating probability is reasonably difficult, Kelly criterion is of little help for equity investing. Instead, we find ourselves seldomly relying on mean reversion. In another one such letter (link here), we were baffled by the highest underperformance of the banking sector on record yet, and had noted the following: Now that we are in the midst of the highest relative under performance ever seen in the banking sector, only time will tell whether it is the case of another ‘myopic loss aversion’ by investors or ‘this time, it’s really different!’
As half of that underperformance got reversed over just a few months, we are getting increasingly convinced that a mean reversion model works as a better guide than a probabilistic model, especially in dealing with sectors where small changes in assumptions trigger large changes in outcomes.
(1) US election of next President is subject to the outcome of the pending legal cases