Bootvis asks in a comment on my previous post:

"Financial theory says that rational investors should prefer positive skewness. This is proven under some weak assumptions in “On The Direction of Preference for Moments of Higher Order Than The Variance” by Scott and Horvath (1980) (I can only find it on jstor, behind a wall ).What’s your view on this discrepancy?"

I have not read the above paper and do not have access to JSTOR either. So the below response is just my broad view on the topic.

Agents prefer Negative Skewness

My emphasis so far has been on the preference for maximising negative skewness from an agent's perspective in a principal-agent relationship. This preference is exacerbated by the moral hazard subsidy. I conclude that the combination of the moral hazard subsidy and the principal-agent problem allows agents to simultaneously maximise negative skewness and improve the risk-return trade-off for owners by increasing leverage.

Whether investors who are not agents would prefer negative skewness is a trickier question. Taleb in this paper clearly concludes that investors prefer negatively skewed bets. But as Bootvis mentions, this contradicts the consensus opinion of financial theory that investors prefer positive skewness. An obvious example of the preference for positive skewness is the phenomenon of "longshot bias" or the popularity of lotteries.

Kahneman-Tversky on Longshots and Black Swans

Kahneman and Tversky offer one way to reconcile these two viewpoints in this paper where they argue that "impossible" events, i.e. black swans, are neglected whereas "possible" but low probability events, i.e. longshots, are overweighted. Preference for negative skewness is not operative for mildly skewed payoffs. It is operative for severely skewed payoffs. As expressed by Kahneman and Tversky: "A change from impossibility to possibility or from possibility to certainty has a bigger impact than a comparable change in the middle of the scale." In other words, there is a "category-boundary effect" when an event deemed impossible becomes possible. The event is significantly underweighted when deemed impossible and overweighted when it is suddenly deemed possible i.e. the lottery effect only kicks in when the event is deemed possible.

This phenomenon also explains the violence of market reaction and the dramatic move in market prices around this boundary. In fact, it can be argued that the change in market prices itself can cause a move in investor views across this category-boundary in a positive feedback process. For example, if market prices suggest that a tail risk is not improbable, this alone may incentivise economic actors to purchase insurance against the event.

Any behavioural explanation that invokes Kahneman and Tversky does not apply to "rational" investors as defined in modern financial theory. For example, the underweighting of tail events can be explained as a result of investors utilising the "Availability Heuristic" and inducing the probability distribution from past experience. As Andrew Haldane notes: "The longer the period since an event occurred, the lower the subjective probability attached to it by agents (the so-called “availability heuristic”). And below a certain bound, this subjective probability will effectively be set at zero (the “threshold heuristic”)."

Is a Preference for Severe Negative Skewness Irrational?

I would argue that using such heuristics may even be rational when not judged against the unrealistic standards of homo economicus. Inducing probabilities from past experience may be entirely "rational" given bounded rationality and an uncertain environment. As WB Arthur puts it: "Agents “learn” which of their hypotheses work, and from time to time they may discard poorly performing hypotheses and generate new “ideas” to put in their place. A belief model is clung to not because it is “correct”—there is no way to know this—but rather because it has worked in the past, and must cumulate a record of failure before it is worth discarding."

It can be extremely difficult to ascertain the true distribution of an extremely negatively skewed bet from historical data. A long run without an observed loss makes us less confident about any initial negative thesis. This is also the primary explanation for why we prefer longshots in horse races or play the lottery. Both are fundamentally less uncertain than financial markets. At least we know the full set of outcomes that are possible in a horse race ! Real life markets are nothing like betting markets. They are dominated by true uncertainty and practitioners derive shaky conclusions from historical data and experience. Statistically, it can be extremely difficult to differentiate between alpha and extreme negative skew.

A More Profound "Moral Hazard"

Severely negatively skewed bets usually blow up under conditions of severe distress in the economy when the government is likely to intervene strongly to prevent systemic collapse. As David Merkel mentions in this note, the Great Moderation has been characterised by a Fed that is willing to cut interest rates at the smallest hint of trouble, even in situations where systemic risk was far from severe.

The current "no more Lehmans" policy is practise means that the Fed and the Treasury will do anything to prevent negative tail scenarios. In the face of such an explicit insurance policy, selling tail events may be entirely rational.

Negative Skewness and Fixed Income Markets

Taleb essentially denies that even longshots are overpriced in financial markets. I am not convinced that moderate negative skewness is at all "preferred". Moreover, most of the empirical evidence he presents pertains to severely skewed payoffs. But there is one point he raises in a reply to Tyler Cowen's review that deserves more analysis. The vast majority of blowups that Taleb recounts are in the fixed income markets.

Indeed, I think the preference for negative skewness is most relevant in fixed income markets. The original fixed income instrument i.e. the bond has an extremely negatively skewed payoff by construction as does the original "alpha" strategy, the carry trade. Secondly, fixed income markets are dominated to a much larger extent by banks and other agents who are compromised by the moral hazard and/or principal-agent problem. Third, the nature of structured product markets in fixed income are dominated by new methods to construct negatively skewed payoffs. To give a few examples, callable range accruals in interest rate products, the PRDC in currency products and almost any credit structured product that aims to achieve a AAA rating like the leveraged super-senior.

This is not to deny the popularity of severely negatively skewed payoffs in equities (for e.g. the reverse convertible note). But they are nowhere near as predominant.


The moral hazard subsidy, the principal-agent problem and investor "irrationality" each incentivise economic actors to take on considerably negatively skewed bets. Assessing the relative contributions of each from historical market data is extremely difficult given that there is no plausible way to separate the effect of the three causes. The problem is exacerbated by the difficulty in drawing any conclusions about tail events from a study of historical data. However, the concentration of historical blowups in fixed income markets leads me to suspect that the combination of moral hazard and the principal-agent problem had a more prominent role in fuelling the crisis than genuine "irrationality".


David Merkel

Good article. Having been a corporate bond manager, and a mortgage bond manager, and designed many insurance contracts, I can say that people like positive skewness and do not like negative skewness. The great question is what they do when offered more yield in exchange for more negative or less positive skewness. Yield illusion is a significant factor in almost all debt, preferred, and equity markets. The stream of cash befuddles and deludes. Even professionals, unless they have their emotions under control, are inclined to trades that increase yield and take more risk, rather than those that decrease yield and reduce risk. Yes, people like positive convexity -- but when push comes to shove, they tend to sell options cheaply in exchange for a little more yield. PS -- the worst of it is that Wall Street deliberately designs retail products to take advantage of this behavioral flaw. Offer more yield by selling options that an average person can't evaluate. It is so slimy, but it happens all the time; even some institutional buyers get snared.


Thanks for the comment David. My aim was just to reconcile these two apparently contradictory preferences, desire for positive convexity and "increased yield". And the fact that institutional buyers get snared so often seems to indicate that they may even be aware of the tail risk but their role as agents reporting to less aware principals is the stronger driver.

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Clicking my name will take you to the article. I should have done this earlier :(


Thank you Bootvis - without either invoking Kahneman-Tversky or Knightian uncertainty, a preference for negative skewness cannot be justified. And even then, it is accurately described as a preference only for severely negatively skewed bets. I have another post in the works which will flesh out the Knightian uncertainty argument in more detail.

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