Behavioral Economics and the The Livermore Loss Table

 

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Jesse Livermore was a stock trader who made and lost multiple fortunes. Stating his life was tumultuous is an understatement. His stock trading method was discussed in the book “How to Trade in Stocks” (1). His method appears to have primarily been price trend following. There is also a brief reference to analysis of a business’s competitive advantage. The book is an interesting read, providing a glimpse of his life and stock trading.

One mathematical concept discussed in the book is the Livermore Loss Table. Livermore points out that a loss of 10% in stock price requires only slightly more than a 10% gain in order to return to break-even. However, losses greater than 10% require increasingly asymmetrically gains to return to break-even. Livermore’s strategy was to exit a long position if the stock fell by 10% to avoid the difficulty of the large gains to return to break-even. As discussed earlier, Livermore traded primarily based on price trends. If a stock price wasn’t following the trend he predicted, his view was that the market was telling him his trend prediction was incorrect.

The Loss Table concept is illustrated in the following table. We use a hypothetical stock with an initial price of 1 dollar. Losses are shown as a percentage and absolute dollar amount. The new stock price and percentage gain required to return to break-even are presented.

Initial Price ($)    Loss (%)     Loss ($)     New Price ($)     Gain required for $1 price(%)

        1.00                1.00              0.01                0.99                                1.01

        1.00                5.00              0.05                0.95                                5.26

        1.00               10.00             0.10                0.90                               11.11

        1.00               20.00             0.20                0.80                               25.00

        1.00               30.00             0.30                0.70                               42.86

        1.00               40.00             0.40                0.60                               66.67

        1.00               50.00             0.50                0.50                              100.00

The table illustrates that at 10% losses and below, a relatively equal gain in stock price is required to return to break-even. Required gains to reach break-even increase quickly once the 10% level is surpassed. For a 20% loss, a 25% gain is needed. For a 50% loss, the stock price needs to increase by 100% just to return to break-even!

We aren’t endorsing or denigrating Livermore’s method of training in this article. Rather, it is the mathematical principle underlying the Loss Table that is important to discuss. It is often the case that people have difficulty interpreting ratios.

Behavioral economics provides several possible reasons for this difficulty. Three of these are:

1. Cognitive Load (2,3): Ratios require more effort to process than absolute numbers. When people are cognitively taxed, they may default to simple explanations. In this example, people could take a mental shortcut and erroneously think “if something falls 50%, it just needs to rise 50% to get back to the starting point”.

2. Denominator Neglect (4,5): People often focus on the numerator and neglect the denominator. In this example, the denominator is the stock price. The stock price is lower after the loss. A smaller denominator means a larger percentage gain is needed than the initial percentage loss:

Initial stock price = $1

Stock price after 50% loss = $1 x 50% = $0.50

Absolute dollar gain to return to $1= Desired Price – Current Price = $1 - $0.50 = $0.50

Percentage increase needed to return to $1 = (Dollar amount required / Current Price) x 100%

Percentage increase needed to return to $1 = ($0.50 / $0.50 x 100%) = 1 x 100% = 100%

The math isn’t complicated. It’s just easy to forget that the denominator has changed because the stock price has changed.

3. Gist-Based Reasoning (Fuzzy-Trace Theory)(6,7): This theory suggests that people sometimes process information by simple generalizations rather than using exact details or calculations. This theory has some similarity to the Cognitive Load Theory. In fact, the use of Gist-Based Reasoning may increase when there is high cognitive load since people may look for shortcuts when the difficulty of the task increases.

In this example, someone might quickly estimate that losing half of something means you just need to get that half back to make yourself whole. The gist of this is correct. However, since daily moves in stock prices are often shown in percentages, the half you need to retrieve is actually a 100% gain after the new, lower, stock price becomes the denominator.

Conclusion: Depending on the investing strategy you follow, you may be pleased or dismayed when a stock price falls. If you follow a fundamental strategy, you could be pleased that the stock has gone on sale, provided the business fundamentals are unchanged. If you are following a trend strategy, and were expecting the stock price to increase, you could be unhappy because the market failed to agree with your hypothesis. Regardless of the approach you follow, keeping the Loss Table principles in mind will help you make well-reasoned, and rational, decisions.

References:

1. Livermore J.L. How to Trade in Stocks: The Classic Formula for Understanding Timing, Money Management, and Emotional Control. Edited and introduced by Richard Smitten. McGraw-Hill, NY: 2001.

2. Sweller J. Cognitive load during problem solving: Effects on learning. Cognitive Science, 1988; 12:257–285.

3. Shah P. & Hoeffner J. Review of graph comprehension research: Implications for instruction. Educational Psychology Review, 2002; 14:47–69.

4. Yamagishi K. When a 12.86% mortality is more dangerous than 24.14%: Implications for risk communication. Applied Cognitive Psychology, 1997; 11:495–506.

5. Reyna V. F., Nelson W. L., Han P. K. & Dieckmann, N. F. How numeracy influences risk comprehension and medical decision making. Psychological Bulletin, 2009; 135:943–973.

6. Reyna V. F. & Brainerd C. J. Fuzzy-trace theory: An interim synthesis. Learning and Individual Differences, 1995; 7:1–75.

7. Reyna V. F. A new intuitionism: Meaning, memory, and development in Fuzzy-Trace Theory. Judgment and Decision Making, 2012; 7:332–359.

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