**Harnessing Neuroscientific Insights to Generate Alpha (2022)***Elise Payzan-LeNestour, James Doran, Lionnel Pradier, Tālis J. Putniņš*

Financial Analysts Journal, 78(2), 79-95, URL

The human brain is insanely powerful but it also has some interesting (and funny) flaws. We are all prone to psychological biases that are very hard to control. This week’s AGNOSTIC Paper examines the *after-effect*, one particular example for this. The authors show the impact of this bias in the US stock market and design a systematic trading strategy to exploit it.

The paper contains a lot of information about modeling of realized- and expected volatility. That’s not my primary area of expertise but I like how the authors apply the psychological after-effect to this setting. So I decided to include this paper in the series. I believe that the after-effect is relevant for practically all types of regime-shifts, but more on that below. The post follows the usual structure and the list is there to navigate.

Everything that follows is only my summary of the original paper. So unless indicated otherwise, all tables and charts belong to the authors of the paper and I am just quoting them. The authors deserve full credit for creating this material, so please always cite the original source.

## Setup and Idea

The after-effect is a well-researched psychological phenomenon and the idea is quite simple. If you are long enough exposed to a certain stimulus, you will have the illusion of the exact opposite stimulus after the first one disappears. That’s the scientific definition. Let’s have some real-world example to see how it works. The most common illustration of the after-effect is the *waterfall-illusion*. If you focus on the downward flow of a waterfall for some time, whatever you will look at afterwards will slightly move upwards. You can test this for yourself with the video below. If it doesn’t work for you? Either you did it wrong or your brain is more advanced than mine (in this case, congratulations!).

The authors argue that the after-effect is also relevant and observable in financial markets. Specifically, they look at the expected- and realized volatility of the S&P 500 Index. The idea is again straight forward. If investors suffer from the after-effect, we should find the following pattern. After longer periods of high volatility (first stimulus), investors should perceive moderate levels of volatility as lower than they actually are (illusion of opposite stimulus). As a consequence, short-term expectations for the stock market and its volatility could be distorted. The authors show both theoretically and empirically, that this seems to be indeed the case for the US stock market.

## Data and Methodology

The following chart once again summarizes the core idea of the paper. If investors experience high volatility for some time (in this case 4 days), they tend to subsequently underestimate moderate levels of volatility and vice versa. I think this is reasonable and I know it from myself. At the time of writing this, the VIX Index^{[1]}The VIX Index measures the expected volatility of the S&P 500 Index over the next 30 days. More information about it here. stands at 33.7%. This is not a doomsday-level but it’s substantially higher than “normal”. Higher values for the VIX Index indicate more uncertainty and suggest negative sentiment among investors. When it hopefully reverts back to something around 20%, most investors are probably more relaxed than they should be. A VIX of 20% feels much better after a week with 30% than it does after a week with 22%. That’s the after-effect.

To examine their idea empirically, the authors need two methodological parts. First, a definition for volatility regimes to identify the after effect. Second, they need some testable hypothesis how the after-effect impacts volatility perceptions and expectations of investors.

For the first part, they calculate the volatility of the S&P 500 Index over a rolling three month window at each day. To determine the volatility regime on a particular day, they compare the current value to the rolling volatilities over the last three months (63 days). It sounds complicated but essentially, they just compare the volatility today with the recent past. The following chart illustrates this. The authors define volatilities within *y* standard deviations of the 3-month-mean as *moderate*. Volatilities that are more than *x* standard deviations above or below the mean are *high* and *low*, respectively.

Of course, they need to set the parameters *x* and *y*. Those are discretionary inputs of the model and there is a trade-off. The higher *x* and the lower *y*, the larger the difference between *moderate* and *high/low* volatility. This leads to more pronounced after-effects which is good for the analysis. But this comes at the cost of fewer after-effects in the sample. There just aren’t enough periods of extremely high volatility to make statisticians happy.^{[2]}That’s the old problem of stock market history and we cannot do something about it. Therefore, the authors propose values for *x* and *y* between 1 and 1.75. They also show that their results are robust across those values.

According to the authors, there is a potential after-effect when volatility shifts to *moderate* after investors experienced extreme volatility for at least 3 days. Mathematically, that’s either the sequence *{VH, VH, VH, M}* or *{VL, VL, VL, M}*.

The second part of the methodology is more difficult. The authors derive a theoretical model that explains daily changes of the VIX Index by the preceding realized volatility and other control variables. Most importantly, distortions from the after-effect also impact VIX changes in this framework. As mentioned above, I don’t know much about such modeling. So I will not go into the details. However, the key takeaway of this model is a testable regression equation that reveals some interesting results.

## Important Results and Takeaways

### The after-effect distorted the VIX Index

The data supports the hypothesis. The authors indeed find that the indicator for after-effects is significantly related to daily changes of the VIX Index. The VIX captures investors’ expectation about future stock market volatility and is one of the most important indices of the world. The results therefore suggest that the after-effect has a meaningful impact on the US stock market. Depending on the specification, the magnitude of this impact is comparable to a 1% change of the S&P 500 Index. Although that’s within the normal daily fluctuations of stocks, it is pretty sizable for a behavioral bias. And in absolute market values, 1% is of course a lot of money.

The authors further show that the impact of the after-effect is asymmetric. Transitions from *high* to *moderate* volatility are much for important than transitions from *low* to *moderate*. In fact, the effect on the VIX Index is not statistically significant for the latter. The authors argue that volatility probably cannot get low enough to trigger a serious after-effect from this side. Therefore, they limit their remaining analysis to after-effects after shifts from *high* to *moderate* volatility.^{[3]}”after-effects after” – stylistically brilliant… Notably, the impact of the after-effect on the VIX Index is even stronger at this end.

In my opinion, this is an impressive result. The S&P 500- and VIX Index are two of the most liquid and most important indices of the world. Such a strong impact of one psychological bias is counter-intuitive because those indices should be efficiently priced. Again the disclaimer, I am not an expert for volatility markets. But the model of the authors seems reasonable and the after-effect follows a clear economic and psychological logic. The results are also robust across several specifications. So I am tempted to believe the results.

However, the authors could have easily included additional out-of-sample tests. The only required data are stock- and volatility indices. That’s easily available for international stock markets like Europe or Germany. Until I have seen the same pattern in other markets, I remain somewhat skeptical. But who knows, maybe someone will do a follow-up on that.

### Exploiting the after-effect yielded significant alpha

The psychological bias of one investor is the profit opportunity for the other. If investors indeed systematically suffer from the after-effect, it should be possible to exploit this with a rules-based trading strategy. The authors propose three strategies that use an ETF on the S&P 500 Index, futures on the VIX Index, and a combination of both. The following chart summarizes the trading rules.

The tables contain a lot of details but the general theme for the S&P 500 ETF is actually quite simple (Tables 1-2). First, the strategy attempts to move out of equities during periods of high volatility. This is based on the (typically) negative correlation of stock returns and the VIX Index.^{[4]}As mentioned before, the VIX tends to spike during crises when stock returns are negative. Second, the strategy goes long equities after after-effects.^{[5]}”after after-effects” – stylistically brilliant once again… Why? Because investors tend to underestimate volatility in this case. This may translate into higher returns and the strategy attempts to earn them.^{[6]}Interestingly, the strategy doesn’t correct the mispricing but attempts to exploit it as long as it is there.

The trading rules for the VIX futures are of course the other way around. Higher volatility increases the VIX, so the strategy goes long after periods of high volatility. The idea (and hope) is that regimes of higher volatility are persistent over some time. At the other extreme, the strategy goes short the VIX when investors underestimate the actual volatility after after-effects.^{[7]}This is the last “after after”. Promised! Except for those two cases, the strategy just holds cash.

For the combined portfolio, the authors allocate 97% of the hypothetical portfolio to the respective position in the S&P 500 ETF and 3% to the VIX futures. They don’t comment on the reasons for this allocation and I don’t know why they use those particular weights. Due to the low correlation of the two assets and strategies, the combined portfolio offers substantial diversification benefits.

The table shows performance measures for the trading strategies from 2004 to 2020 and different values of *x* and *y*. The results look promising. For example, the timing strategy of the S&P 500 ETF yields statistically significant alphas of up to 8.06% per year. For the more diversified *combined* portfolio, this number is even larger. Overall, the timing model of the authors seems to add considerable value compared to a simple buy-and-hold strategy.

However, I am again somewhat skeptical. The authors follow the common academic approach and test their hypothetical strategy for all model parameters *x* and *y*. This is completely fine to show evidence for your hypothesis. But in practice, you need to make choices. Nevertheless, we could add the strategy to a multi-strategy portfolio^{[8]}Multi-strategy portfolios combine different, at best uncorrelated, investment strategies in one portfolio. The idea is to provide additional diversification, less volatility, and more consistent returns. or use it together with other timing signals. But as already mentioned, I wouldn’t do any of this without international out-of-sample tests. Especially because the data is so easily available for this strategy.

## Conclusions and Further Ideas

The primary reason I selected this paper is not the trading strategy but the after-effect itself. Although I studied quite a lot of behavioral finance, I didn’t knew the after-effect in this form. But I think it is highly relevant. Not only for volatility, but for all kind of regime-shifts. If you think about it, there are many things in financial markets to which we are exposed over a long period. For example, interest rates. Over the last decade, we had very low interest rates (first stimulus). Now, central banks around the globe start to increase them and we have trouble to navigate the new environment. I don’t know if investor currently overreact to the shift in interest rates but the pattern could qualify for the after-effect.

Okay, we now know that our brain is occasionally flawed. The interesting question is of course how to deal with that and ultimately, how to avoid such biases. Unfortunately, this is not easy. Knowing that psychological biases exist is the important first step but it is not sufficient. The best advice to avoid them is to systematize as much as possible. Checklists, clearly defined processes, and precise documentations of decisions are all helpful tools for this purpose. For example, it is truly amazing how systematic checklists improve outcomes in virtually all disciplines. I believe everyone should have a list of psychological biases to go over before making important decisions. The after-effect certainly qualifies for that.

- AgPa #56: The Equity Risk Premium of Small Businesses
- AgPa #55: Backtests in the Age of Machine Learning
- AgPa #54: Transitory Inflation
- AgPa #53: Investing in Interesting Times

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