Blog

Short-selling in the Tails

Short selling is defined as the sale of a security that is not owned by the seller. Although the practice is fairly straightforward yielding payoffs that are linear in the price of the underlying asset, short sellers are usually sophisticated agents whose aggregate behavior can have potentially complex outcomes. In fact, short selling an asset should put downward pressure on its price helping demand meet supply. However, there is reason to believe that large and simultaneous short positions can have nonlinear effects and propel price plummets.

Short selling has been amply studied in recent years by academics who have converged around the consensus that this market practice has mostly positive effects, by providing liquidity, increasing market efficiency, and aiding price discovery. Nonetheless, regulators around the world decided to prohibit it during the 2008 financial crisis motivating their decision by remarking that during exceptional circumstances of heavy market bear, prices are more vulnerable to (potentially predatory) short selling that can exacerbate downfalls, and even lead to crashes.

This policy behaviour presupposes there are nonlinear effects in the relationship between short selling and stock prices that trigger during extreme scenarios. Most studies have assessed the average impact of short selling and have evidenced no particular tendency for it to bring down prices. However, in order to understand if SEC’s decision to ban short selling were justified, it would be interesting to understand how the relationship between short selling and stock prices changes during extraordinary scenarios, i.e. tail events.

Short selling and the occurrence of extreme events

On purely theoretical grounds, “predatory” short selling can induce institutions that are close to their capital constraints to initiate fire sales causing prices to plummet (see Brunnermeier and Oehmke, 2013 for the mathematical formulation of this problem). The effect is worsen if short sellers are able to coordinate, enlarging the so-called “doomed” region, thus requiring a smaller initial drop in returns to trigger complete liquidation of the firm’s assets.

However, empirical evidence of this phenomena from the literature is somewhat mixed. A strand of papers opts for examining stock returns during different short selling regimes. Bris, Goetzmann and Zhu (2007) find that in markets where short selling is either prohibited or not practiced stocks tend to have less negative returns. According to Saffi and Sigurdsson (2011) however, this is actually due to more overpricing occurring and not to less extreme negative returns.

Other studies have exploited actual trade data but have not been any more elucidating of the effect of short selling. Shkilko, Van Ness and Van Ness (2012) study intraday price reversals and find that short sellers exacerbate declines but to a lesser extent than long sellers. Quite to the contrary, Beohmer and Wu (2013) find that short sellers act as liquidity providers during transient price turnarounds, buying when prices drop and selling when prices jump unusually high. This is evidence that short sellers trade on the basis of superior information rather than speculation. These contrasting results might be influenced by the selection criteria of price reversal episodes.

Debunking Tail Correlation in short selling and stock price

In a new joint work with Tomas Garbaravičius (Banks of Lithuania) and David Veredas (ECARES, Université Libre de Bruxelles), we employ a methodology that accounts for all observations to estimate the association between short selling activity and stock prices during extreme (tail) events.

The study makes use of a commercially available dataset on securities lending that provides a daily proxy for short interest: the percentage of shares outstanding that are sold short. While most prior studies employed monthly or bi-monthly short interest information (that cannot capture fine grain changes in short sellers’ positions), we use the daily number of shares on loan to track changes in covered short sales.

The empirical investigation is conducted for over 6 years of data on banks and insurance companies that are the constituents of the STOXX Europe 600 and STOXX North America 600 indices. A first look at the linear correlations given in Figure 1 confirms the strikingly low association between short selling and stock prices on average.

fig1

Figure 1: Linear correlation between short interest on the stocks of financial institutions and the returns on those very same stocks

However, a descriptive analysis of the conditional tail frequencies indicates that a strong relationship is more likely when the two variables, stock price and short interest, take on extreme values.

Figure 2 shows the median conditional tail frequencies of short interest changes (ΔSI) and returns (r). These are the empirical probabilities of observing one variable in its tail given that the other variable is also in its tail.

fig2

Figure 2: Conditional tail frequencies between stock returns and the change in short interest

Days with extremely high short selling on stocks (i.e., short interest movements larger than two standard deviations from the mean) of European banks, had a probability of witnessing extremely low returns of 7.8%. This was found to be substantially higher than the probability of observing extremely high returns on days of extremely high short selling (only 2.7%). Moreover, this is also much higher than the corresponding conditional probability for two normal random variables with the same correlation as that observed in the data (shown in lighter colour). The latter means that fat tails and asymmetry characterize the relationship between short selling and stock prices. The same patterns were found for the stocks of North American banks and, to a lesser extent for those of European insurance companies.

In order to quantify and differentiate the relation that occurs during exceptional circumstances from the relation during average days, we make use of a novel measure of tail correlation. The TailCoR, developed by Ricci and Veredas (2012), can uncover a relationship between short selling and stock price changes when both variables are at the extremes of their distribution. Moreover, the TailCoR can be implemented under general and mild assumptions, as it does not depend on specific distributional assumptions, and does not require any optimisations.

fig3

Figure 3: Southeast TailCoR measures the association between extreme positive movements in short interest and extreme contemporaneous negative returns.

We adopted a variant of TailCoR called Southeast TailCoR to measure the association between extreme negative price movements and extreme positive changes in short interest (that can be linked to aggressive changes in short positions). It was found that southeast TailCoR was larger than any other variant of TailCoR (e.g. that associated with negative returns and negative short selling) evidencing that large short selling movements are associated with large downward falls in stock prices.

Among the different sectors analysed, European insurers were found to have the largest southeast TailCoR followed by North American and European banks. We find two reasons for this. First, as can be noticed in Figure 3, larger firms tend to have a smaller tail correlation between short interest and returns. As explained in Beber and Pagano (2013) and in Glosten and Harris (1988), small-cap stocks have generally lower stock liquidity, which can induce larger price effects of short selling. Since European insurers represent the smallest firms in our sample, this effect is particularly pronounced for this group. Secondly, most insurance companies were not included in bans that were introduced in 2008 because regulators in Europe mainly targeted the banking sector. Thus, smaller market capitalisation and weaker regulatory attention might therefore explain the stronger tail association observed for European insurance firms.

Conclusions and policy implications

In conclusion, we provide novel evidence of a strong negative relation at the tails of short selling and stock prices implying that large short positions are related to extreme downfalls in prices. Moreover, a more in depth analysis reveals that the association is even stronger for small cap firms.

Further results in the paper show that the relation has varied through time. In particular, short selling bans did not decrease the vicious relationship uncovered. Rather, a lower level of tail association has been witnessed during the last few years when policies aimed at curbing abusive short selling have been applied in the US and in Europe.

References

Beber, Alessandro, and Marco Pagano. "Short‐Selling Bans Around the World: Evidence from the 2007–09 Crisis." The Journal of Finance 68.1 (2013): 343-381.

Boehmer, Ekkehart, and Juan Julie Wu. "Short selling and the price discovery process." Review of Financial Studies 26.2 (2013): 287-322.

Bris, Arturo, William N. Goetzmann, and Ning Zhu. "Efficiency and the bear: Short sales and markets around the world." The Journal of Finance 62.3 (2007): 1029-1079.

Brunnermeier, Markus K., and Martin Oehmke. "Predatory Short selling*." Review of Finance (2013): rft043.

Glosten, Lawrence R., and Lawrence E. Harris. "Estimating the components of the bid/ask spread." Journal of financial Economics 21.1 (1988): 123-142.

Saffi, Pedro AC, and Kari Sigurdsson. "Price efficiency and short selling." Review of Financial Studies 24.3 (2011): 821-852.

Shkilko, Andriy, Bonnie Van Ness, and Robert Van Ness. "Short selling and intraday price pressures." Financial Management 41.2 (2012): 345-370.

Complex systems and agent-based modelling

A new paradigm for understanding macroeconomic phenomena

The great discovery of the nineteenth century was that the equations of Nature are linear, and the great discovery of the twentieth century is that they are not.  - Körner, T.W. (1988)

The concept of reductionism relies on the simple idea that any system can be broken down into its basic components, thereby allowing for a more ‘fundamental’ understanding of its whole. Over the past century, the reductionist framework has gained significant ground in the natural sciences with, to paraphrase the Nobel laureate in Physics, Stephen Weinberg ‘the explanatory arrows always pointing downwards’, from the macroscopic to the microscopic level, genes to DNA, thermodynamics to statistical mechanics etc. However, the great limitation of reductionism is that it fails to consider the emergent properties that can arise at each hierarchical level or, as P.W Anderson, another Nobel laureate in Physics put it:  "At each stage, entirely new laws, concepts and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one” (Anderson, 1972). This key characteristic is at core of “complex systems”, i.e. systems in which large collections of components interact in nonlinear waysand seems to characterize numerous phenomena in biology, physics, epidemiology or social sciences. As Körner (1988) mentions, to study such a system where the outputs are not directly proportional to its inputs, we need to go beyond traditional linear analysis where individual components can be treated independently from the whole system since the “whole is more than the sum of its part” to paraphrase Aristotle in his Metaphysics.

Of course, the reductionist mindset is hardly new to economics. In macroeconomics, the approach is at core of its research agenda on its microfoundations which arose in response to the now-famous Lucas critique. In a nutshell, this states that any macroeconomic model that does not allow individual agents to adjust their behaviour could not be used for policy since, when applying such models, said agents would simply alter their behaviour until the model no longer worked. Spearheaded by the Real-Business Cycle (RBC) model of (Kydland and Prescott, 1982), researchers combined the microfounded approach with Lucas’s ‘Rational Expectations Hypothesis’ to create the class of macromodels now referred to as DSGE (Dynamic Stochastic General Equilibrium).

This begs the question, just how reductionist (i.e. microfounded) can a model be if it writes off the notion of agent heterogeneity by assuming a representative agent who makes all production/consumption decisions in the model economy? The answer is, not a whole lot. Not only does it preclude the notion of emergent behaviour at the agent-level (since agent interactions are ignored), it assumes that agents possess a level of knowledge of the market (thereby allowing them to make optimal plans) that is inconsistent with real-world observations.

A truly reductionist approach would model agents individually and see what phenomena emerge endogenously at the macro level due to their interactions. This ‘bottoms-up’ approach is known as agent-based modelling and has recently been proposed as an alternative to mainstream DSGE models by Farmer and Foley (2009), who advocate that such models are inherently equipped to handle nonlinear behaviours due to their purely computational (as opposed to analytical, as in DSGE models) nature. The use of heuristics at the agent-level rather than optimization mechanisms as drivers of macroeconomic fluctuations is a central theme in De Grauwe (2012) who attributes ‘limited cognitive capabilities’ to agents in order to show how macroeconomic booms and busts can be attributed to self-fulfilling waves of agents optimism and pessimism.

Interestingly, considering behavioural heuristics based on ‘psychology experiments’ (as Farmer and Foley suggest) ends up leading us further down the reductionist rabbit-hole into the realm of prospect theory, developed by Kahnemann and Tversky (1979) who advocate the important role of human psychology in determining economic behaviour. By zooming in on the psychology of agents, the theory is able to explain why ‘We have an irrational tendency to be less willing to gamble with profits than with losses.’

Proponents of the agent-based modeling paradigm claim that current ‘microfounded’ macromodels do not truly reduce the system to the agent-level and moreover, over-rely on the rational expectations assumption (leading to the representative agent framework), which does not allow for the presence of endogenous emergent phenomena. Economist Kevin Hoover has humorously referred to such models as ‘nothing else but an aggregate in microeconomic drag’ (Hoover, 2006). However, this does not spell the end for locating the fundamentals of economics. Agent-based models and behavioural economics show that, by using computational models combined with simple heuristics, one can produce aggregate variables that emerge endogenously due to the repeated interactions of the agents comprising the system. The challenge is now to provide an understanding of what macroeconomic conditions (i.e individual characteristics coupled to the structure of interactions between them) can generate (in)stability of the system in order to guide policy-makers to formulate regulatory framework and monitor it accurately.

References

 Anderson, P. W. (1972). More is different. Science177(4047), 393-396.

De Grauwe, P.. Lectures on Behavioral Macroeconomics. Princeton University Press, 2012.

Farmer, J.D, and D. Foley. "The economy needs agent-based modelling." Nature 460.7256 (2009): 685-686.

Hoover, K. D. "A Neowicksellian in a new classical world: The methodology of michael woodford's Interest and Prices." Journal of the History of Economic Thought 28.2 (2006): 143-149.

Kahneman, D., & Tversky, A. (1979). Prospect theory: An analysis of decision under risk. Econometrica: Journal of the Econometric Society, 263-291.

Körner, T.W. (1988), Nonlinear oscillator, in ‘Fourier Analysis’, Cambridge University Press.

Kydland, F. E., & Prescott, E. C. (1982). Time to build and aggregate fluctuations. Econometrica: Journal of the Econometric Society, 1345-1370.

Weinberg, S., "18 Newtonianism, Reductionism and the Art of Congressional Testimony." Emergence: contemporary readings in philosophy and science (2008): 345.