If you buy a stock for $50 and it reaches an all time high of $100, but you sell at $75, why do you feel that you’ve made a loss?
Minds and Markets
In most people’s minds finance and economics are the domains of clear, quantitative thinking. Economists merely uncover financial truth one after another as they develop new mathematical tools for modeling capital and how wealth is created. Markets, likewise, are ethereal natural forces tapped into rather than created. In truth, the assumptions that underly the pricing models used for the past three decades are based on two basic principles:
People make rational decisions
People are unbiased towards new information
Meanwhile, down the hall on university campuses, researchers in cognitive science have uncovered evidence that humans are not quite the rational decision makers expected. Humans make decisions with limited information and rather than treat new information with independent probabilities, context and history are critical to our decision making.
Humans often make predictable cognitive errors. As George Soros states in his classic “The Alchemy of Finance”, it was when he moved from stock analyst to fund manager that he found that what he thought and how he made decisions suddenly became of paramount importance, as his fund depended on his sound decision making in arenas not limited to picking stocks.
These biases affect novices and expert traders alike. The value of a particular financial instrument depends heavily on the perception of its value. How is value determined? Again, we feel this is simply a matter of relying on objective mathematics. Numbers are not enough to describe investor decision making.
Take a simple coin toss. Ellen Langer showed that people are more willing to bet on the outcome before the coin is flipped than after. People behave as if their involvement makes a difference in value. You’re thinking, “How foolish, I’d never make that mistake”. If you’re like most college students, you think you are above average. As a matter of fact, 82% of them do, according to a classic study by Ola Svenson. Overconfidence is a consistent bias humans show, and it shows up in the markets.
Overconfident traders trade too much. Overconfident traders believe their information and ability to act on it is superior to most and they will profit from their actions. This leads to excessive trading, which hurts profitability. Overconfidence also leads to higher risk taking. As John Nofsinger points out, this is partially due to the illusion of knowledge, the notion that more information improves decision making.
If I ask you what the odds of a dice rolling a 4 are, you would likely conclude 1 in 6. If I then tell you the die previously rolled a 4 six times in a row, you might be assign a greater likelihood on the dice rolling a 4, or the contrarians might say less. Although the dice has no memory, people do, and it affects their decision making. As we saw in Langer’s research, the very act of participation changes one’s sense of value. Thus the novice trader’s new tools and research may act to instill excessive confidence in the decision making process.
In considering the past, investors often rely on what Novel Prize winner Richard Thaler dubs “mental accounting”. Sums of money are categorized as “losses” or gains” and then treated differently, counter to what the rational model of economics would predict. One experiment that demonstrates this by Hal Arkes and Catherine Blumer showing how the labels we assign costs affect our decision making. They asked subjects to consider this scenario:
“A family has tickets to a basketball game, which they have been anticipating for some time. The tickets are worth $40. On the day of the game there is a big snowstorm. Although they can still go to the game, the snowstorm will cause a hassle that reduces the pleasure of watching the game. Is the family more likely to go to the game if they purchased the ticket for $40 or if the tickets were given to them for free?”
The typical response was that the family was more likely to attend if they purchased the tickets. The cost is the same in either scenario. But the decision to attend affects the outcome people choose. By purchasing the ticket, the mental account of a cost for attending the show is created. To “close this with a loss” is aversive, and people believe that the goal must be attained by purchasing another ticket.
Not only was the basis of the decision factored, but it was shown that timing mattered as well:
“A family has long anticipated going to the basketball game, which will take place next week. On the day of the game there is a snowstorm. Is the family more likely to go to the game if they purchased the $40 tickets 1 year ago or yesterday?”
In this scenario, subjects thought the family would be more likely to attend if they just purchased the tickets. Although the time value of the money spent would be greater from a purchase a year ago, the psychological cost has diminished over time, and people are less likely to be hurt by the cost.
Mental accounting also accounts for the risk behavior traders exhibit. Richard Thaler also showed that people are more likely to accept a wager on a coin toss if they had just been rewarded money than if they had not. This “windfall” profit is classified as a bonus, and thus risk capital. The percentage of economics students willing to accept a bet of $4.50 in a coin toss went from 41% when they were not given any money to 77% when they were given $15.
Thaler also showed that experiencing a small loss produces risk aversion to a fair bet, but if they lost significant money and offered the chance to “break even” a majority of students accepted, even if the bet was not fair. Losses can exacerbate losses.
One common phenomenon many traders know all to well is selling winning trading and holding losing trades. Hersh Shefrin attributes these to the desire for pride and avoidance of loss. If you record a trade with a profit and a trade with a loss, you may realize the profit to attribute a successful trade to your sound decision making, but avoid realizing a loss that speaks otherwise. Although this seems simple, capital gains tax incentivizes holding winners to avoid realizing capital gains and selling losers to reduce taxes owed – the opposite strategy that most traders pursue.
Terrence Odean examined 10,000 trading accounts from 1987 to 1993 from a national discount brokerage to see the percentage of winners and losers closed in proportion to the number of paper winners and losers held. He found sales represented 23% of the number of total gains and losers represented about 16% of total losses. In other words, investors are twice as likely to close winners than losers.
Anchoring and Adjustment
What counts as a gain or a loss is also relative to prior prices, not considered as independent of an investor’s attention. A stock acquired at $50 and and achieves a year-end value of $100. A few months into the new year it is sold at $75. While this is objectively a $25 gain, the investor likely feels as if there was a loss. One classic decision-making bias Nobel Laureate Daniel Kahneman and Amos Tversky identified is this effect, called anchoring and adjustment. Meir Statman asked subjects this question:
“In 1896 the Dow Jones Industrial Average (DJIA) was at 40. At the end of 1998, the DJIA was at 9,181. The DJIA is a price-weighted average. Dividends are omitted from the index. What would the DJIA be at the end of 1998 if the dividends were reinvested every year?”
The correct answer is 652,230. Surprised? You may have been subject to the anchoring and adjustment effect. By starting at 9,181 and computing change from there, you are statistically more likely to guess a number close to that reference point.
Buying by the pack
The tenets of behavioral economics have profound implications for biases traders exhibit that have not predicted by mainstream models of valuation and pricing. Over the coming years these concepts will become better known and produce not only better predictive financial models but allow individuals to become better investors. Cognitive illusions and biases cannot be erased, just as one can’t help but imagine the lights dancing on a movie screen as real people. Traders seeking to avoid these mistakes would do well to identify these biases in their own trading and create incentives for avoiding them. Just as smokers are willing to pay more by the pack to limit their smoking, developing trading programs that discipline at a small cost (for instance, liquidating trades with a certain loss that perhaps have a potential for future profit) can prove useful.
“Trading Futures and Options on Futures involves substantial risk of loss and may not be suitable for all investors. Each investor must consider whether this is a suitable investment.”