Disposition Effect: Problem of Small Profits and Large Losses

One of the major concern bothering traders and investors alike is the tendency of selling winners too early and holding on to losers too late. Put it differently, market participants book their gains too early but holding on to their losses much longer.

Let us understand this phenomenon by taking three different types of traders.

Trader X believes in churning money from one trade to other very quickly and therefore intends to earn series of small profits, however, he follows the same discipline when booking his losses by following strict stop losses and does not allow losses to mount and eat into number of small profits.

Trader Y believes in spending his energy into identifying big opportunities and therefore eying at large profit from his position, he may have deep stop loss and therefor potentially facing large loss. Both the traders are perfectly fitting into the definition of rational traders as they don’t behave differently while facing gains and losses.

Trader Z tends to close his profit making positions too early but fails to exhibit the discipline when it comes to closing his loss making transactions. The impact is devastating. While he may have the same success ratio as trader one and two, his small number of large losses may outweigh his large number of small gains and he may end up underperforming both trader one and two by a big margin. Even worse, he may end up facing net losses.

If you feel that you also face similar problem to trader (investor) Z, following section of this article can be a potential game changer for you. So let us try to analyze why trader Z behaves differently when he faces gains and faces losses. Following could be the possible explanation for his irrational behavior.

  • Prospect Theory

The prospect theory of Kahneman-Tversky explains how decision makers actually behave when facing choice under uncertainty. They used S shaped value function (Figure 1) to explain the value of utility attached to specific gains or losses with respect to a fixed reference point. It is interesting to note that the value function is concave in the gains region and convex in the loss region. It shows risk aversion in the domain of gains and risk seeking nature in the cases of losses. Even investors, who are considered to be risk averse, behave differently when facing losses. Value assigned to the losses is approximately 2.25 times to gains with respect to the reference point.

Figure 1

ProspectTheory

Let us try to understand how an investor develops a tendency to sell winners and riding onto losers using prospect theory framework by taking a simple example. Our trader Z purchased a stock at Rs. 50 a month ago and since then it has fallen to current level of Rs. 40. Now he faces two equi-probable outcomes.

  1. Sell the stock now and book loss of Rs. 10, which is only a ‘paper loss’ as of now.
  2. Holding the stock for one more month with 50:50 chance of facing additional loss of Rs.10 or ‘breaking even’.

Since the Trader Z is facing this choice in the loss domain of value function, going by prospect theory he would show strong preference for option 2 and hold on to his stock for one more month. Such risk seeking tendency or loss aversion behavior is so prominent in the loss domain that he may prefer holding on to stock for one more month even if the chances of his breaking even in next month is less than 50%! No wonders why many investors tend to marry their loss making stocks for years!

  • Mental Accounting

While explaining trader Z behavior in loss domain we ignored the effect of taxes especially short term capital gains tax in the Indian context faced by an investor.

In India, if one holds his stock for a period of more than one year, entire gain on the sale of such investment is treated as long term gains and it is exempted from the tax. However, if the stock is held for less than one year and sold at profit it is subject to a short term capital gains tax of 15%. This is self is disincentive enough for not to sell your winners early and avoid disposition effect.

For a while, think about an investor who is sitting on short term profit in the month of March of a given year. He also has some stocks in his portfolios with less than one year holding period and is currently trading at a price below his purchase price. However, he wants to hold on to these stocks as he purchased it from a long term perspective and that is perfectly fine. Under such circumstances ideally one should go for the tax swap. He should sell stocks with short term losses and simultaneously buying substitutes. This helps setting of short term gains against short term losses by incurring small transaction cost and help avoiding significant amount of tax. However, practicing this is easier said than done for an investor. Investors view each stock purchased separately, they create separate mental accounts for each and do accounting for each in their respective account. They tend to evaluate each stock with a reference point which is its purchase price. Which means booking loss in to one stock and buying its substitute in order to save tax is not a simple choice as if forces them to close one account at loss. And even if tax savings could be substantial feeling of loss or selling below breakeven price overpower such saving and force investors to make suboptimal decision.

  • Seeking pride and Avoiding Regret

Both traders and investors feel the same when it comes to selling stocks at profit and closing transaction at loss. While closing position at profit gives a feeling of pride, closing position at loss induces regret. The feeling of regret is much stronger than the feeling of pride.

  • Framing effects

Let us go back to S shaped value function in figure 1. People tend to assign different values to same payoffs if presented differently under the influence of S shaped value function.

Twelve transactions with small gains of Rs. 1000 each is preferable and provides more value than a single transaction with a gain of Rs. 12,000 due to concave nature of value function in gain zone. On the other hand, twelve transactions with loss of Rs. 1000 each feels worse than and single large loss of Rs. 10,000 due to convex nature of value function in loss zone. Such framing leads to a tendency of booking small profits but allowing losses to mount big.

It is quite surprising that not only naïve traders and investors but professional traders and investors including fund managers succumb to disposition effect. To conclude, if you are falling prey to such irrational behavior, keep your emotions away and follow discipline of executing transactions with strict stop losses in order to gain most out of your investments.

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