When Following the Crowd Works: Trend-Following in Markets Explained Using Game Theory
In financial markets, traders aim to profit by predicting what the majority of investors will do and taking these actions before others do. Many traders rely on the analysis of fundamental data to find insights that they believe other investors have not yet found, but will eventually find and act on. Others however, make their decisions on the assumption that investors will continue their current behavior. The latter method is called trend-following.
In the past century the use of trend-following in markets has garnered praise from the likes of Jesse Livermore1, Nicholas Darvas2 and more recently Richard Dennis. Richard Dennis began his career trading commodities at the MidAmerica Commodities Exchange with a $400 stake. Within ten years he was able to make over $100 million and has credited his success to trend-following 3. Dennis’ strategy mainly consisted of opening a position when the price of a commodity moved significantly in a particular direction and betting that the price would continue in that direction. If the price failed to maintain its momentum and had more than a moderate move in the opposite direction, the position would be closed. Using this strategy, if a trend continues after the trader opens their position, the trader is likely to profit, however if the trend quickly reverses, then the trader suffers a small loss. Therefore, the efficacy of this strategy rests on whether or not a trader is able to make more money on trends that continue than they lose on trends that do not continue.
Let the profit, p of a trend-following trader be defined by the formula:
p=n|W|-n’|L|
where:
n= number of trades where trend continues after position is opened
n’= number of trades where trend reverses soon after position is opened
W= average profit for winning trades
L= average loss for losing trades
For this example we will assume that trading fees are negligible.
As stated above, when using trend-following, since traders will exit before markets go too far against them, individual losses tend to be small, so it can be assumed that in general L<W.
In order to for a trader to make a significant amount of money over time therefore, one of two things must be true:
- The number of trades where the trend continues is greater than or equal to the number of trades where the trend reverses
- The number of trades where the trend continues is smaller than the number where the trend reverses, but the profit gained from the few trends that do continue outweighs losses.
Using game theory we can assess how likely either of the above conditions is to be met. Consider the payoff matrix below.
| Me/ Majority of Investors | Buy(Majority) | Sell(Majority) |
| Buy(Me) | 10,10 | -1, 10 |
| Sell(Me) | -1, 10 | 10, 10 |
In this game, the Nash Equilibria are (Buy, Buy) and (Sell, Sell). In either condition, neither side can increase their payoff by changing strategies (assuming the other side continues with their current strategy). As stated above, traders aim to predict what the majority of investors will do and do it before them. If the majority of investors make their decisions using the matrix above, then it is obvious that in an environment where the majority are buying, an investor trying to make a decision is likely to buy, since they believe that subsequent investors will also make the same decision since subsequent investors will be looking at a similar payoff matrix when making their decision. This is the rationale behind bubbles, people buy assets that they believe will increase in value, they believe that there will be an increase in value because they think that subsequent investors will have the same belief. The same logic can be applied to panic-induced selling.
Therefore, once a strong trend has been established, it is likely to continue until something disrupts it. This disruption can be caused by new information that changes investors’ beliefs about the future value of an asset, or when too few buyers (or sellers) remain to continue driving the price in a particular direction. This means that while significant trends may not be numerous, when they do occur, the positive feedback mechanism described above will tend to drive them long enough for those who joined the trend early to make a significant profit. This allows trend-following to satisfy condition 2 above and makes it a potentially profitable trading strategy.
The strategy’s greatest pitfall is if a trader is unable to find enough significantly profitable trades to create a large enough n|W| in the equation above. To remedy this, profits can be increased be minimizing n’|L|. This would be done by finding a way to reliably distinguish between trends that will continue and will not continue. It would therefore be useful for potential traders to explore such methods.
- https://www.investopedia.com/articles/trading/09/legendary-trader-jesse-livermore.asp
- https://www.investopedia.com/articles/trading/07/darvas-box.asp
3. https://www.investopedia.com/articles/trading/08/turtle-trading.asp
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