October 01, 2010

Selling Winners and Holding Losers

Extracted from the book: Quantitative Trading Strategies,  Lars Kestner
Studies of human bias in economic situations shed light on how the mind affects trading
decisions. In one such study conducted in 1998, Terrance Odean, professor of finance at the University of California, examined 10,000 accounts at a large discount brokerage firm to determine if individuals’ trading styles differed between winning trades and losing trades made from 1987 and 1993. He found a significant tendency for investors to sell winning stocks too early and hold losing stocks too long. Over his test period, investors sold approximately 50 percent more of paper profits on winning trades than they sold of paper losses in losing trades.
Based on the data, Odean concluded that winning stocks were sold quicker and more frequently than losing stocks. Although the results were a bit surprising, this behavior by investors could make sense. When we buy stocks, we’re placing a bet that a company is undervalued. Stocks that increase in value are logically
becoming less undervalued as they rise, while stocks that decrease in value are logically becoming more undervalued. Winning stocks that have increased in value could be considered not as cheap as when they were purchased. Losing stocks that have declined in value could be considered cheaper than when purchased. In this case, it makes sense to sell the winning stocks that have become less cheap and
hold losing stocks that have become cheaper.
Although the logic is sound, Odean’s results show that the opposite actually occurs. Winning stocks that were sold continued to rise, while losing stocks that were held continued to fall in value. In the year following sales, stocks sold with gains by individual investors outperformed the market by an average 2.35 percent. At the same time, losing stocks that were held underperformed the market by an average of 1.06 percent. Odean discovered, on average, that investors underperform the market by selling their winners too early and holding on to their losers too long. Based on purely economic terms, it’s unclear why they behaved in this manner; psychology may provide the missing link. Clearly, the more profitable course of action suggested by the study is to buy winning stocks and sell losing ones. Two theoretical underpinnings dominate the tendency to sell winners and ride losers: prospect theory and mean reversion theory.

Prospect Theory. Prospect theory adapts psychologists’ Daniel Kahneman and Amos Tversky’s theories to financial markets. It suggests that investors are more risk averse when dealing with profitable investments and more risk seeking in investments with losses. We all enjoy winning and take pain in losing. As a result, investors and traders take winners very quickly (to placate our psyche) and hold on to losers (to hold on to hope that the losers may eventually become winners).

To demonstrate, give people the following choice:

Game 1
75 percent chance of making $1000
25 percent chance of making $0
100 percent chance of making $750

We can calculate the expected value of each game by summing the product of each outcome’s probability by its payout:
Expected payout of risky choice = 75% * $1000 + 25% * $0 = $750

While the expected value of both options is the same in Game 1, individuals tend to be very risk averse with gains. Most people will take the certain $750 rather than take the risk for a higher payout.

Now consider Game 2, which presents the exact same choice, only among losses:

Game 2
75 percent chance of losing $1000
25 percent chance of losing $0
100 percent chance of losing $750
Expected payout of risky choice = 75% * –$1000 + 25% * $0 = –$750

In Game 2, most people will choose to risk the chance to come out even and take the first option. While both options have the same expected value, the possibility of coming out without a loss is often too much to pass up. Basically, the tendencies revealed in both games show that individuals are risk averse with their winnings and risk seeking with their losses.

This, of course, jibes with Terrence Odean’s research. From practical experience, I can add that I’ve often caught myself holding on to losing trades while thinking, “If I can only get out even on this trade,” or taking it so far as to calculate breakeven points in hopes of avoiding the disappointment of closing out a losing trade. If prospect theory is alive and well in the financial markets, we may be able to take advantage of human nature by designing trading strategies that are not susceptible to the inconsistent thinking embedded in human nature.

Mean Reversion Theory. The second theory explaining why investors sell winners and hold losers is that investors buy and sell stocks as if they expect mean reversion in prices. Mean reversion occurs when a series of numbers eventually reverts back to a long-term average. A good example is interest rates. As measured
by the yield on the 10-year Treasury bond, interest rates have traded in a range mostly between 5 and 8 percent over the past 10 years (see Figure 1.13).

More often than not, when interest rates are low, they are met by supply from issuers looking to borrow money. This leads to an increase in rates. Conversely, when rates are high, they are met by demand from investors looking to lock in the abnormally high interest rates. This causes interest rates to decline to more normal levels. If investors believe that stock prices move in a similar path, they will be willing to sell stocks that rally and hold stocks that decline—believing that each will eventually return to its more normal level.

For example, consider stock XYZ, as seen in Figure 1.14. It trades between $50 and $55 for many months before breaking below this range to $45. When looking at the graph of the stock, the mean reversion associated with human nature would lead us to believe that the move was abnormal and that it should be bought. A similar example is stock ABC in Figure 1.15. When ABC breaks above $50 per share after also trading between $45 and $50, we might believe that the stock should be sold on the basis that it too will reenter its previously established $45 to $50 range again.

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