Salience theory suggests that decision makers exaggerate the probability of extreme events if they are aware of their possibility. This gives rise to subjective probability distributions and undermines conventional rationality. In particular, salience theory explains skewness preference, i.e. the overpricing of assets with a positive skew and the under-pricing of contracts with a negative skew. There is ample evidence of skewness preference, most obviously the overpayment for insurance contracts and lottery tickets. In financial markets, growth stocks with positively-skewed expected returns have historically been overpriced relative to value stocks. This is important for macro trading. For example, a specific publicly discussed disaster risk should pay an excessive premium, and short-volatility strategies in times of fear of large drawdowns for the underlying should have positive expected value.

This post ties in with SRSV’s summary lecture on implicit subsidies.

The below are excerpts from the paper. Emphasis and cursive text have been added.

### What is salience theory?

“Salience theory of choice under risk provides an intuitive account for why people like skewness, both in absolute and relative terms. Accordingly, __attention is automatically directed toward outcomes that stand out in the choice context while less attention-grabbing outcomes tend to be neglected__.”

“According to salience theory…a decision-maker [*assigns*] a subjective probability to each state of the world that depends on the state’s objective probability and on its salience. __A state is the more salient the more the payoffs in this state differ__…Decision makers focus their attention on those states of the world where the attainable outcomes differ a lot.”

“Whether a salient thinker appears to be risk seeking or risk averse depends on the skewness of the risk at hand. Put differently, __for a fixed expected value and variance, a binary lottery is chosen over its expected value if and only if it is sufficiently skewed [ to the upside]__…An increase in the lottery’s skewness is equivalent to an increase in both of the lottery’s payoffs and in the probability that the lower payoff is realized. Since the lottery’s expected value is fixed, the difference between the lower payoff and the expected value decreases in the lottery’s skewness, while the difference between the expected value and the higher payoff increases in the lottery’s skewness. “

“__Probabilities of outstanding outcomes are inflated, while probabilities of less salient outcomes are underweighted__. In a typical lottery game, for instance, the large jackpot stands out relative to the rather low price of the lottery ticket, thereby attracting a great deal of attention. As a consequence, the agent overweighs the probability of winning the salient jackpot and behaves as if she was risk-seeking. In contrast, an agent typically demands insurance against unlikely, but potentially large losses. Compared to the rather small insurance premium the large loss stands out, its probability is inflated, and the agent behaves as if she was risk-averse. As a consequence, __the salience mechanism yields both a preference for right- and an aversion toward left-skewed risks__.”

The __salience model predicts skewness preferences__; that is, whether a salient thinker opts for a risky instead of a safe option depends in a systematic way on the skewness of the risk at hand…The channel…through which salience theory predicts skewness preferences…[*is called*] the contrast effect. The **contrast effect** means that __when comparing a risky and a safe option, a certain outcome of the risky option receives the more attention the more it differs from the safe option’s payoff__… The contrast effect induces a focus on the large, but unlikely upside of right-skewed risks, and a focus on the large potential loss in the case of left-skewed risks.”

“Diminishing sensitivity reflects **Weber’s law of perception** and it implies that __the salience of a state decreases if the outcomes in this state uniformly increase in absolute terms__. Hence, diminishing sensitivity can be described as a level effect according to which a given contrast in outcomes is more salient for lower outcome level.”

### The importance of skewness for market prices

“Most puzzles in choice under risk can be attributed to the skewness…The __conventional wisdom that in general people prefer risks with a higher expected value and/or a lower variance can be overturned by preferences over the skewness of a risk__. Many individuals, for instance, overpay for insurance with low deductibles against left-skewed risks that yield a rather large loss with a small probability. But at the same time, these individuals often seek right-skewed risks such as casino gambles that realize a large gain with a tiny probability…The __fact that people seek right-skewed and avoid left-skewed risks is often referred to as skewness preferences__.”

“Skewness preferences are not only relevant for insurance and gambling decisions, but they also have important implications for other economic and financial decision situations. In asset markets, for instance, __investors pay a premium for positive skewness__…This may help us to understand the well-known growth puzzle according to which value stocks, that are under-priced relative to financial indicators, yield higher average returns than (overpriced) growth stocks. [*Academic research*] suggests that this discrepancy arises as value stocks are typically left-skewed while growth stocks are usually right-skewed.”

### The importance of relative skewness

“We show that not only a lottery’s absolute skewness matters but also how skewed it is relative to the other options. To capture this, __we propose a novel measure of relative skewness that depends on the correlation structure of the available lotteries__. Since the correlation of the lotteries determines the set of feasible payoff combinations, it also affects how skewed a given lottery appears to be relative to alternative options. As a consequence, a salient thinker’s behavior varies with changes in the correlation structure even if this does not convey any relevant information.“

### The findings of laboratory experiments

“We conducted two laboratory experiments in order to test for our predictions…

- As predicted by salience, we find that
__the more skewed the risky option is, the more likely it is that subjects will choose a risky option over the safe option__that pays its expected value…The share of risk-takers strictly increases in the lottery’s skewness. - Also in line with the salience model, this
__preference for positive skewness becomes stronger for lotteries with a larger expected value__.”

“Our experimental results confirm that relative skewness indeed plays an important role, which is consistent with salience.”