Exploiting Behavioural Bias with a Quantitative Model

By Todd Kennedy, Senior Portfolio Manager, SSgA - Australia

(Observer's note: I happen to find this interesting article on behavior finance while searching information on quantitative modelling. The biases mentioned in this article are commonly found among inexperienced individual investors, and therefore worth of being recorded here.)

Markets are not fully efficient, and investors are not always rational. In recent times the body of evidence supporting behavioural finance models that attempt to explain market inefficiency and the nature of investor irrationality has been mounting. If we understand the behavioural biases at work in equity investing, we can not only avoid making the same mistakes ourselves, we can profit from the mistakes of others.

Following on from the recent essay by Arlene Rockefeller1, this essay discusses the SSgA active Australian equity model, and explains the underlying behavioural biases that we attempt to systematically exploit using our quantitative approach.

We use growth factors to exploit the fact that in the short-term, stocks under react to market information. We use value factors to exploit the fact that in the long-term, stock prices over react, and we use a quality factor to avoid value traps.

Behavioural Biases that Lead to Mis-Pricing
There are numerous behavioural biases that are displayed by people generally. Some of these lead to poor investment decision-making and, collectively, these biases work to cause mis-pricing in equities. A brief description of the biases that affect stock prices follows.

Anchoring Bias
Anchoring is the bias whereby people irrationally cling on to some fact or information that should not affect decision-making. Experiments have demonstrated that when people are shown a number they know to be meaningless, that number still has influence over their decisions2. If this is true, then it is particularly hard to ignore such powerful anchors such as daily share prices when they are so readily observable. If a stock rises or falls significantly in one day, the stock is viewed as more expensive or cheap relative to the previous day, ignoring or discounting any new information that has become available. This leads to short- term under reaction to new information as stocks price in the new information gradually rather than instantly.

Herding Bias
We know that people in society tend to conform to the behavior of others even when the behavior is irrational, forsaking their own judgment in preference for following the actions of others. History supplies numerous examples of extraordinary group behaviour such that the power of herding can not be ignored. We may think that the madness of the tulip bubble in the mid 17th century, when people risked their life savings to speculate on the price of tulips3, would never be repeated in modern times. However, aspects of the recent technology bubble present uncomfortable parallels. Herding perpetuates stock price momentum and leads to long-term overshooting of share prices on both the upside and downside.

Belief Perseverance/Confirmation Bias
Once momentum has set in from the above biases, it feeds upon confirmation biases. When a person buys a stock and the stock's price subsequently rises, they don't look for reasons to contradict their belief in its value, but rather they tend to seek confirming information only to reinforce their existing belief.

Prospect Theory
Prospect theory deals with how investors behave when faced with the prospect of a gain or a loss. Investors are generally more conservative with gains, and more reckless with losses than they should be. This leads to selling winners too soon to lock in gains, and holding onto losers too long to avoid losses. This is understandable as locking in a gain creates a feeling of joy, and removes the possibility of the position becoming a loss. With losses, a paper loss is often viewed as only a “potential” loss, but once the loss is crystallized, it becomes real and leads to feelings of regret. These natural human emotions work against us in an investment setting when being rational and dispassionate is required.

Mental Accounting
People tend to put gains and losses into separate mental accounts and treat them as individual positions, ignoring any offsetting positions within a portfolio. An undue emphasis is placed on the current gain/loss when making an investment decision instead of looking at the future prospects of the investment on its own merit.

Disposition Effect
The disposition effect is the effect that prospect theory and mental accounting has on asset prices. This behaviour generates short-term under reaction to news in the market4. Positive news for a stock generates excess irrational selling pressure as the stock rises, slowing its ascent to a new equilibrium as investors lock in gains and sell out too early. The slow march to the new value rather than a sudden jump to a new level is observed as positive momentum. Negative news has a similar effect. The reluctance to sell losers slows the stock price from reaching equilibrium. The additional marginal selling remaining creates negative momentum.

Hot Hand Fallacy/Law of Small Numbers Representativeness
People have a natural tendency to rely on recent observations more so than past events. They extrapolate this information too far into the future, when in fact more reliable longer-term averages are appropriate. In sport, this is known as the hot hand fallacy. A player is often selected for a crucial task on the basis of a good recent performance rather than a player with good long run statistics5. This is true in investing as well. People mistakenly believe that if a stock has gone up ten days running, it is hot and will continue to rise.

When only small numbers of observations are available, people form a belief that these observations are representative of a larger population of events. In reality, statistically random clustering of events occurs which can mistakenly be identified as a trend. Chance plays a larger role in investment returns than people tend to believe. At the portfolio level, this is known as idiosyncratic risk. The only defense against this is diversification.

Overconfidence Bias
Forecasting with skill is a very difficult thing to do. The error in a forecast, no matter how well made, is generally quite large. It has been shown experimentally that as people try to improve forecasts with a greater volume of information analysed, they often end up only increasing their confidence in the forecast rather than increasing the accuracy of the forecast itself6. Once a stock has been recommended or bought, a rising share price supports overconfidence as people generally discount the possibility that they are wrong. People tend to stay overconfident because they attribute success to skill, and failure to other external events that can be blamed.

Overestimation of Skill
It is common for people to overestimate their own skill. Studies have shown that 90% of car drivers think that they have above average skill7. In investments, 75% of fund managers think they are better than their peers8. Analysts and investors usually miscalculate the probability of their forecasts being wrong, and also underestimate the degree to which they can be wrong. As a result, inappropriately large portfolio bets may be taken based on a misguided belief of one's own skill.

SSgA Australian Quantitative Model: Growth, Value and Quality
The SSgA Australian quantitative model has two growth factors, two value factors, and a quality factor. The relationship between each factor and the behavioural biases that drive their success as investment tools will now be explained.

Growth Factor 1 - Momentum
Momentum is the observed phenomenon where rising stocks tend to continue to rise, and falling stocks continue to fall. It is a well researched effect, but many investment professionals struggle with understanding why it exists. Behavioural finance supplies the answers.

We have seen that Anchoring Bias, Prospect Theory, Mental Accounting and the Disposition Effect all act to create short-term under reaction to market information. The residual trading that is left to occur, as investors capitulate to accept the re-rated stock valuation, acts as a pressure on the stock price. This gradual rather than sudden price adjustment is how momentum is initiated. Once momentum has developed in a stock price, it is perpetuated by the actions of investors displaying Herding, Belief Perseverance, Confirmation and Representativeness biases. This leads to long-term over reaction to market information.

The collective action of investors following these natural human behavioural biases support the hypothesis that momentum will persist for the foreseeable future.

Momentum is exploited by buying stocks that are rising, and selling stocks that are falling. There are many variations available on the exact manner in which to do this, but all essentially work by picking short-term trends and following them. However, it is wise to look at other factors when engaged in momentum investing. We need to keep an eye on the deviation from fundamental value when deciding on how far to pursue stocks on a short-term basis.

Growth Factor 2 - Earnings Outlook
Our earnings outlook factor is used to monitor changes in analyst forecasts for a company. In some markets we monitor changes in analyst recommendations. In Australia we monitor the changes in forecast future earnings as we find that these have better explanatory power over future stock returns in the local market. However analyst forecasts are susceptible to Overconfidence and Overestimation of Skill biases.

Since we know that these biases act to create short-term under reaction to new information, we can incorporate new information into our model instantly with a factor that targets the changes in analyst estimates. Targeting the changes in the forecasts rather than the actual forecast also helps to avoid systematic behavioural biases in analyst forecasts.

Value
Whilst momentum makes trend following work in the short-term, it also has the characteristic of overshooting fair value, which in turn makes value investing work over the longer run. When people have succumbed to behavioural biases and pushed prices too far from fair value, it's time for rational investors to step in and force prices to revert to reasonable levels.

The trigger for mispriced assets to mean revert can be either dramatic news which impacts broad sentiment, it could be the combined action of value investors, or it could come from the listed company itself. A company's board is in the best position to assess their own future earnings potential. When they observe their share price being driven unreasonably high, they may issue additional shares. When their share price is unreasonably low, they may buy shares back.

Our value model has two components. They are Forward Earnings Yield and Dividend Yield. Our value factors attempt to profit from the mistakes of others by identifying these mispriced securities and trading in the opposite direction.

Value Factor 1 - Forwards Earnings Yield
One method of identifying stocks at extremes of valuations is to analyse the forward earnings yield a company is on. More conventionally, this is similar to looking at a company's Price to Earnings (PE) ratio. Low yielding (high PE) stocks tend to under perform high yield (low PE) stocks in the longer run. We collect forecast future earnings from a broad range of brokers to diversify the opinion base, and convert this information into yields. We then reduce the influence of behavioural biases by normalising the data so that all forecasts are forced into a standard normal distribution. This helps protect against anchoring biases in the data. The normalization process debases the anchors by forcing a mean zero value for estimates. We can then assess what is relatively expensive against what is relatively cheap.

Value Factor 2 - Dividend Yield
Dividend yield is a value factor that acts as a positive anchor for stock selection. If we expect a certain minimum yield to be paid for a company, we won't be drawn into paying too much for its stock. It is insurance against overvaluation as high stock prices would need to be supported by high dividend payments to be justified.

Quality Factor
One problem with value investing is identifying when a stock is getting cheaper for a good reason. These types of stocks are known as “Value Traps”. They appear to be good value on stock selection screens, but are actually investments that should be avoided. For example, high yielding stocks may be high yielding because they are about to stop paying dividends and their price has fallen already in anticipation of this expectation. Or as this factor seeks to identify, the quality of a company's earnings may be deteriorating and that deterioration is being concealed in the balance sheet. Our quality factor acts as a defense against earnings deterioration lead value traps.

Avoiding Biases with Quantitative Processes
Investors are influenced by behavioural biases. Some of these biases lead to predictable outcomes. Stocks are observed to under react to new information in the short-term, and over react in the longer-term.

We systematically capture these inefficiencies in the market by producing models that exploit these biases whilst using disciplined risk control and optimisation techniques to construct portfolios objectively and dispassionately. As long as the market continues to be influenced by behavioural biases, our models which are built to exploit them should continue to work. Consider the following.

Anchoring can not occur in a quantitative process if you do not supply anchors.
Overconfidence can be avoided by applying strict and systematic risk controls in the portfolio construction process.

Overestimation of Skill can be avoided by statistically calculating it. With a good estimate of the skill a process has, we can build portfolios that exploit the actual level of skill we have rather than the level of skill we think we have.
Prospect Theory will not be followed by a quantitative process that does not reference past gains or losses of individual positions.

Hot Hand Fallacies, Law of Small Numbers and Representativeness Biases can be replaced with back-testing of investment factors over significant time periods, and the predictive power of the model factors can be measured. Another way of avoiding the Law of Small Numbers problem is to keep an out of sample period which avoids overfitting.

Quantitative processes also remove the human constraint of the limit of brain power. People can only focus on a limited amount of information at any one time. This is why portfolios built by bottom up stock pickers are often concentrated portfolios.

The power of quantitative processes lies is in the rationale that if you can get the input data for every stock you can invest in, you can apply the process to all stocks simultaneously and build the best portfolio possible given forecasts of risk and return.

Summary
Markets are influenced by the behavioural biases of investors. It is possible to identify and measure the extent to which these biases are present in the market. It is also possible to construct quantitative processes that are not susceptible to these biases, and can systematically exploit the inefficiencies which irrational investment produces, whilst simultaneously controlling for risk.


--------------------------------------------------------------------------------

1 Rockefeller, A., (2006). “SSgA's Approach to Quantitative Active Equity Management,” State Street Global Advisors, 2006.
2 Tversky, A. and Kahneman, D. (1974). “Judgement under Uncertainty: Heuristics and Biases”, Science, 185, 1124-1130.
3 Mackay, C., (1841). “Extraordinary Popular Delusions and the Madness of Crowds”, Chapter 3, Tulipomania.
4 Grinblatt, M. and Han, B., (2005). “Prospect Theory, Mental Accounting and Momentum”, Journal of Financial Economics, 78, 311-339.
5 Gilovich, T., Vallone, R., and Tversky, A., (1987). “The Hot Hand in Basketball: On the Misperception of Random Sequences”, Cognitive Psychology, 295-314.
6 Oskamp, S. (1965). “Overconfidence in Case Study Judgements”, Journal of Consulting Psychology, 29, 261-265.
7 Kahneman, D. and Riepe, M., (1998). “Aspects of Investor Psychology”, Journal of Portfolio Management, Vol. 24, No. 4.
8 Montier, J., (2005). “Seven Sins of Funds Management” Dresdner Kleinwort Wasserstein, 16.

Note: This essay is based on the SSgA active Australian model. SSgA is constantly producing and updating active models around the globe that function in similar ways, but specialised for the individual markets in which they operate.

This material is for your private information. The views expressed are the views of Todd Kennedy only through the period ended August 23, 2006 and are subject to change based on market and other conditions. The opinions expressed may differ from those with different investment philosophies. The information we provide does not constitute investment advice and it should not be relied on as such. It should not be considered a solicitation to buy or an offer to sell a security. It does not take into account any investor's particular investment objectives, strategies, tax status or investment horizon. We encourage you to consult your tax or financial advisor. All material has been obtained from sources believed to be reliable, but its accuracy is not guaranteed. There is no representation nor warranty as to the current accuracy of, nor liability for, decisions based on such information. Past performance is no guarantee of future results.

This is No Longer Funny

By Paul Wilmott

I’ve been critical of much of quant modelling for many years. I don’t like the assumptions, the models, the implementations. I’ve backed this up with sound reasons and wherever possible tried to find alternative approaches that I think are better. I don’t honestly expect to change the world, much, but, hey, I do what I can. Human nature is such that very often things have to go from bad to worse to bloody awful before the necessary paradigm shift happens. I hope we are close to that point now.

Who am I kidding? As another hedge fund disappears thanks to mishandling of complex derivatives, I predict that things are going to get even worse.

When it was just a few hundred million dollars here and there that banks were losing we could all have a good laugh at the those who had forgotten about convexity or whatever. But now the man in the street has been affected by these fancy financial instruments. It’s no longer a laughing matter.

Part of the problem is that many of the people who produce mathematical models and write books know nothing about finance. You can see this in the abstractness of their writing, you can hear it in their voices when they lecture. Sometimes they are incapable of understanding the markets, mathematicians are not exactly famous for their interpersonal skills. And understanding human nature is very important in this business. It’s not enough to say "all these interacting humans lead to Brownian Motion and efficient markets." Baloney. Sometimes they don't want to understand the markets, somehow they believe that pure mathematics for its own sake is better than mathematics that can actually be used. Sometimes they don't know they don't understand.

Banks and hedge funds employ mathematicians with no financial-market experience to build models that no one is testing scientifically for use in situations where they were not intended by traders who don’t understand them. And people are surprised by the losses!

I realized recently that I’ve been making a big mistake. I’ve been too subtle. Whenever I lecture I will talk calmly about where models go wrong and where they can be dangerous. I’ve said CDO models are bad because of assumptions about correlation. I’ve pointed out what you can do to improve the models. I’ve talked about hidden risks in all sorts of instruments and how sensible use of mathematics will unveil them. I’ve explained why some numerical methods are bad, and what the good methods are. But, yes, I’ve been too subtle. I now realise that one has to shout to be heard above the noise of finance professors and their theorems. Pointing people in the right direction is not enough. Screaming and shouting is needed.

So here, big and bold, gloves off, in capital letters (for this seems to help), are some fears and predictions for the future.

THERE WILL BE MORE ROGUE TRADERS: While people are compensated as they are, while management look the other way to let the ‘talent’ do whatever they like, while people mistake luck for ability, there will be people of weak character who take advantage of the system. The bar is currently at €5 billion. There will be many happy to stay under that bar, it gives them some degree of anonymity when things go wrong. But that record will be broken.

GOOD SALESMEN WILL HOODWINK SMART PEOPLE: No matter what you or regulatory bodies or governments do we are all a pushover for the slick salesman.

CONVEXITY WILL BE MISSED: One of the more common reasons for losing money is assuming something to be known when it isn’t. Option theory tells us that convexity plus randomness equals value.

CORRELATION PRODUCTS WILL BLOW UP DRAMATICALLY: This means anything with more than one underlying, including CDOs. Stop trading these contracts in quantity this very minute. These contracts are lethal. If you must trade correlation then do it small and with a big margin for error. If you ignore this then I hope you don’t hurt anyone but yourself. (I am sometimes asked to do expert-witness work. If you blow up and hurt others, I am very happy to be against you in court.)

RISK MANAGEMENT WILL FAIL: Risk managers have no incentive to limit risk. If the traders don’t take risks and make money, the risk managers won’t make money.

VOLATILITY WILL INCREASE ENORMOUSLY AT TIMES FOR NO ECONOMIC REASON: Banks and hedge funds are in control of a ridiculous amount of the world’s wealth. They also trade irresponsibly large quantities of complex derivatives. They slavishly and unimaginatively copy each other, all holding similar positions. These contracts are then dynamically hedged by buying and selling shares according to mathematical formulae. This can and does exacerbate the volatility of the underlying. So from time to time expect to see wild market fluctuations for no economic reason other than people are blindly obeying some formula.

TOO MUCH MONEY WILL GO INTO TOO FEW PRODUCTS: If you want the biggest house in the neighbourhood, and today not tomorrow, you can only do it by betting OPM (other people’s money) big and undiversified. There are no incentives for spreading the money around responsibly.

MORE HEDGE FUNDS WILL COLLAPSE: You can always start a new one. Hell, start two at the same time, one buys, the other sells!

POLITICIANS AND GOVERNMENTS WILL REMAIN COMPLETELY IN THE DARK: Do you want to earn £50k p.a. working for the public sector, or £500k p.a. working for Goldman Sachs? Governments, who are supposed to set the rules, do not even know what the game is. They do not have the slightest clue about what happens in banks and hedge funds. Possibly, for the same reason, London will lose out to New York as a world financial centre.