Small numbers, larger mistakes: How number bias affects investor information

Advice and information provided by stock analysts, such as target prices and recommendations, have a powerful influence on investor decisions. However, new research shows that the way the human mind processes numbers means that analyst forecasts are frequently inaccurate when compared with eventual outcomes.

Information and opinion moves markets. While much information is news based and prompted by external events, certain individuals such as policymakers, economists, and analysts, for example, exert a disproportionate influence over the valuations of firms and, in doing so, the fortunes of industries and economies more generally. Much of the information these individuals provide draws on evidence-based research. But what if there were inherent undetected biases in the way such research is processed, interpreted and portrayed, that increase the chances of any information and opinion based on that research being incorrect?

This is an issue investigated by Alain Schatt (HEC Lausanne, University of Lausanne) and his colleagues Tristan Roger (Université Paris-Dauphine) and Patrick Roger (EM Strasbourg Business School) in their paper “Behavioural Bias in Number Processing: Evidence from Analysts’ Expectations”. The authors looked at the work of sell-side analysts. The role of the sell-side analyst is to produce unbiased opinions based on proprietary research about companies. The research results are often published in reports focusing on the financial and operational performance of specific companies (and sometimes industries as a whole) and reflected in investment recommendations, usually expressed as ‘buy’ ‘hold’, or ‘sell’ as well as in stock price targets . As such, the opinions of sell-side analysts are often highly influential in determining investment decisions and stock price movements.

The small numbers effect

 As the authors note it is well-documented that financial analysts tend to be optimistic in their forecasting. This is borne out by research that shows that, over a period of several years, the average returns suggested by target prices issued by analysts greatly exceed the actual market returns. What is less clear is the explanation for such excessive optimism. Here the authors make a novel contribution to the discussion by showing that all individuals, and in this case analysts specifically, process small numbers differently from large numbers and this is reflected in the handling of stock price data. This specific behavioural bias, which the authors term ‘small price bias’, is evident when analysts issue target prices and make other recommendations relating to company stocks.

Small price bias stems from neuropsychology and the way the human brain deals with large and small numbers when making calculations. Essentially, we tend not to be able to instinctively appreciate the distance between two small numbers in the same way that we do the distance between larger numbers. In other words, if we think in terms of price rises, instinctively we feel it is easier to move from 1 to 1.5 than from 100 to 150, even though the relative variation is the same. This suggests that if a stock analyst takes an optimistic view of a company’s prospects, and is thinking about returns (i.e. relative variation), that perspective is more likely to be exaggerated for stocks with a lower market price than for those with a higher market price.

This is borne out in the data that the authors used to investigate this phenomenon. A sample of 814,117 target prices on 6423 US stocks issued by 9141 analysts over a 14 year period from 2000 to 2013 was used. The authors compared target prices with actual prices at the time (the implied return), and with future realized prices. The results show that analysts issue bolder target prices for lower priced stocks compared with higher price stocks. Across all stocks for the sample period the average implied return for stocks with a nominal price below $10 was some 39%, compared with 19% for stocks with prices above $40. And when target prices issued by analysts were compared with actual prices realized in the market, small price stock targets were 26.88% more optimistic than large price stock targets. These findings remain true when controlled for a number of factors, such as the market capitalization of the firm, that might also, in part at least, account for the findings.

Implications of small price bias

The findings have a number of implications. For investors, for example, it is important to be aware that target prices for stocks with a low price are likely to be exaggerated. And they are likely to be more exaggerated than target price recommendations for higher price stocks.

For boards and senior managers the findings may have implications for the composition of remuneration and reward packages. When remuneration committees set compensation packages for senior executives they often base part of that remuneration on stocks reaching a specified target price (as a triggering event for rewards, for example). For those individuals who set or provide oversight on such compensation packages it is important to factor in small price bias to decision making over target prices.

There is also message for stakeholders engaged in listing private companies. Using small price bias it is possible to manipulate the perceptions of investors before an IPO. Imagine a successful start-up about to publically list with 1000 stocks at CHF 100 each. If it does a stock split prior to the IPO and divides the issued stock by 1000 (and the price accordingly) small price bias means that it should be easier to negotiate a higher offer price and attract more optimistic target price predictions.

Overall the lesson is that, as the authors show, it would be a big mistake to ignore small price bias.

Related research paper: Behavioral bias in number processing: Evidence from analysts, Journal of Economic Behavior and Organization 149 (2018) 315–331. Tristan Roger, Patrick Roger & Alain Schatt.

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