Ulysses and the Sirens of Skewness
Or why you should tie your CIO the mast
Burn the Ships!
Hernan Cortes landed in Vera Cruz in 1519 and almost immediately preceded to burn his ships on his way to conquering an empire. What could be crazier than eliminating your escape route when in an unknown land with possibly hostile inhabitants? As we shall see, human emotions fall into this category, and many times need a gentle (or not so gentle) push in the direction of rationality.
Hedonic Treadmill
A common results in behavioral psychology is the hedonic treadmill, which posits that happiness follows a mean-reverting process, after a shock (either good or bad) it returns to a genetically determined set point. A 1978 study compared happiness levels between paraplegics and lottery winners. Shortly after the event, subject happiness deviated from that of a control group in the direction you would expect (can’t really do a before and after as that would mean you can either predict lottery winners, or university psychology departments are significantly overfunded). Some time after each event, subject happiness was remeasured and now matched that of the control group. In other words, paraplegics and lottery winners felt equally happy. With the recent replication crisis in psychology, it is worth stating that this is a robust result that can be traced as far back as the writings of Seneca and St. Augustine. This has significant implications for investor behavior, especially when combined with Kahneman and Tversky’s Prospect Theory.
Prospect Theory
Habituation is one of the important results of Prospect Theory. As Nassim Taleb explains in the paper from which this post is inspired, habituation implies that the change in utility per dollar (delta) from a gain or loss, drops as you get away from the set point (i.e. a loss/gain of 2 has less than twice the effect than that of 1). This contrasts with classic utility theory which posits that the pain of each marginal dollar of loss is higher than the previous one (i.e. a loss of 2 has more than twice the impact than that of 1).
The below charts show the empirically estimated utility function from Tverksy and Kahneman (1992) for Prospect Theory. The first chart shows the utility of an investor at different levels of gains and losses. The second chart shows the impact of each marginal dollar at different levels. From both charts we can see that small losses and gains have a much higher proportional impact (delta) on utility than large ones. In addition, losses have a larger impact than gains.
Framework
We combine the Hedonic Treadmill and Prospect Theory in the following framework.
- Through the Hedonic Treadmill, investor utility (relative to their PnL) gets reset to the setpoint every certain amount of time; which we will refer to as the portfolio evaluation period.
- Given habituation and for the same risk/return level (an admittedly vacuous concept), investors prefer strategies that make a small amount of money each evaluation period (maximizing deltas per dollar of gain) and lose a large amount rarely (minimizing deltas per dollar of loss) to the reverse. That is, they prefer strategies that blowup rather than bleed.
- Given this, assets and strategies that follow a bleed payoff (small consistent losses with rare large gains) should have a greater risk premium than those that follow a blowup payoff in order to compensate investors for the painful return sequencing.
Important to note: This framework does not imply investor irrationality, rather logical responses to biologically determined utility curves. Irrationality would be comparing homo sapiens behavior to a homo economicus and being surprised when behavior differs from the model.
The Sirens of Investing
Given the above framework it might seem investors are doomed to invest in blowup strategies with lower expected returns given their utility curves and the pain of following bleed strategies. In fact there is significant evidence of this happening in the market. The rise of hedge funds over the last few decades can mostly be explained by investors accepting lower expected returns in exchange for a payoff transformation. Hedge Funds give investors higher Sharpe Ratios in exchange for commensurately higher skewness (see chart below). Not necessarily increasing investors’ risk/return profile but increasing their experienced utility.
Alas, there is good news. Somewhat buried in the framework is the concept of the portfolio evaluation period, the other important variable in how an investor experiences a sequence of returns (in addition to the utility function). Interpreted for an individual, it might be literally how often he checks the value of his portfolio. For an institution it might be the regularity over which the investment staff (the group making decisions) is evaluated.
Benartzi and Thaler explore this concept in their 1995 article on Myopic Loss Aversion and the Equity Premium Puzzle. Their hypothesis is that the shorter the evaluation period of investors the higher the equity risk premium due to the pain of short term loss (similar to our framework). They find that the equity risk premium over bonds can be explained by an investor evaluation period of one year. A time-frame suspiciously matching that over which most market-participant bonuses are calculated.
A more recent paper by Larson, List and Metcalfe reached similar results through an experiment with professional traders. It randomized traders into two groups, and gave the first group market-data in one second intervals, and the second in four hour intervals. The traders in the long interval group invested 33% more in riskier assets and realized 53% higher profits relative to the short interval group.
Outside of the academic world, venture capital and private equity are the most noticeable examples of extended evaluation periods and bleed payoffs (and not accidentally the highest returns). VC funds particularly know ahead of time that they will lose money quarter to quarter as the majority of their investments burn cash and lose value, but their scarce home-runs (I am told this is a technical term) more than make up for this over the lung run (i.e. the J curve). There are three major reasons why they can invest in this way.
- VC and PE funds generally have a 10 year life cycle, which approximates the fund evaluation period (particularly for European waterfall structures where incentive fees get paid based on whole fund performance instead of deal by deal).
- Fund managers control cash-flows (instead of investors) and thus do not fear that short-term under-performance will lead to redemptions, nor are forced to invest when opportunities are poor.
- Given the private nature of the investments, they do not bear the market volatility that sends the managers of other fund structures running for the hills, and away from high expected returns but poor experienced utility profiles.
These examples show the importance of the evaluation period and most importantly, that it is not fixed (unlike our utility function). Given this, investors would be wise to lengthen their evaluation periods in order to obtain the higher returns available to bleed strategies without feeling the pain of short-term under-performance.
One way to do this is simply by extending the frequency at which they look at their portfolio’s PnL. While this might be possible for individual investors with a simple asset allocation between index funds or certain low maintenance strategies (Warren Buffett style), it is not viable for many institutional investors. They generally have more complicated strategies, or regulatory imposed reporting timelines (for example investment firms that comply with CFA Institute GIPS Standards, must value portfolios at least monthly).
How to Tie a Knot
Investors who cannot easily alter their evaluation periods, would be wise to do some introspection and develop precommitment mechanisms in the areas they know they are likely to falter.
If there is one over-arching lesson from Jack Schwager’s excellent Market Wizards series, it is that to be a successful trader you don’t have to be perfect (even Homer nods). The most important thing is to “know thyself” and develop a system that emphasizes your strengths and minimizes your weaknesses. For example, one trader upon getting interested in a stock, would immediately take a small position. In this way he felt that if the position rallied while he performed further diligence, he would not feel he had “missed out” and become hesitant to invest until a drop that might never happen.
Recent research has shown that people are significantly more likely to stick with tough decisions by precommitting rather than exerting willpower. Although precommitment mechanisms tend to be very personal, there are certain general categories that can be explored.
Change the Frame of Reference:
The only widespread bleed payoff most people own are insurance contracts. Home insurance can be thought of as a narrowly defined out of the money put option on the value of the house. Yet, owning insurance doesn’t seem as painful as holding a bleeding investment strategy. One reason for this is that we don’t “mark to market” our insurance contract, we just consider it an expense. We don’t fret over our put having lost value from our house not burning to the ground.
Certain strategies, (such as tail-hedges) should be approached in the same way. If you believed strongly enough to invest in the strategy, then you should protect yourself from bailing once the strategy starts behaving exactly as you knew it would. In fact Nassim Taleb writes in his books that Empirica LLC (his hedge fund) started reporting to its clients in this way (as a cost instead of percentage return), as it alleviated the emotional strain of sticking with the investment.
Another example can be seen in Berkshire Hathaway’s letters to shareholders. In them Buffett choses as his measuring stick for BH’s short-term performance not their volatile stock price (which shareholders generally focus on with) but rather their book value.
Commitment Contracts:
Famous for their ability to spur virtuous habits, commitment contracts establish a penalty if they are not fulfilled over a specified time period. Typical (and successful) uses include exercising a certain number of times a week and quitting smoking.
In the investment field they are more generally known as Lockup Periods (time-span over which investors cannot redeems their funds) or Early Redemption Fees. These terms are generally thought to be detrimental to investors and to the benefit of fund managers as they reduce investor’s liquidity. Indeed sometimes they are, but if used appropriately, they can immensely benefit investors. The tragicomedy of comparing dollar weighted versus time weighted returns for mutual funds (not to mention index fund returns!) shows how awful investors are at timing flows; lockups could help defuse this behavior.
The key point, is that they are structured correctly. Many times investment agreements have discretionary liquidity terms (such as gates) that managers will generally use for their benefit instead of investors. If instead of this, they had automatic terms, they could help investors greatly. For example, fund terms could state that if the market falls by over 20%, then withdrawals are automatically suspended for 3–6 months or something similar.
Conclusion
There are generally two ways to outperform the market:
- Knowing More
- Being More Rational
Given the way market prices work, the more people use a technique the harder to successfully apply it becomes. It should come as no surprise then that knowing more than the market is almost impossible, as this is what most investors, pundits, analysts, etc. focus on. For the second way though, there is less competition. There are no rationality analysts out there, just research analysts.
Most investors should thus focus on the second way in managing their portfolios. Although we cannot control our sometimes irrational emotional reactions we can plan ahead for them. This is the point of tying ourselves to the mast. Investors will be well rewarded for conducting introspection and figuring out which knots work best for their wrists. Simple precommitments can lead to great returns. As Ben Graham taught “In investing it is not necessary to do extraordinary thins to get extraordinary results”.
