Decision Making In Prisoner’s Dilemma

4.1 Applications: prospect theory (and heuristics) in behavioral finance

Some people think of financial markets as the most effective way of allocating resources and of traders as rational profit-maximizers. There is some skepticism, though, coming from the realization that only part of investments is driven by fundamental values of equity, while another part is driven by unpredictability, and a substantial part is driven by speculation.

Classical economists’ theoretical rendering of the behavior of financial markets and the actual behavior of traders significantly differ. Theoretical economists talk about the strict unpredictability of the future prices of stocks, for which there is a term “random walk”. Traders, however, know that “sentiment” of other investors is what counts, and they adjust their investments to these sentiments. It is not always (or usually) clear what inputs are the investors sensitive to. Urbánek (2003, p. 215) mentions a study of above-chance successful bookmakers (who are not traders in the strict sense, of course), who were often not able to express what helps them to decide in the way they do.
Then there is further skepticism coming from the field of behavioral finance (influenced by Kahneman and Tversky’s work), concerned with unpredictability and speculation aspects of trading, as well as with heuristics and biases, probability over/underestimations, failure to aggregate losses, and the convexity of utility function for losses (and ensuing loss aversion). Behavioral finance demonstrates that traders and markets show decision anomalies and fail to maximize profit.
One example, already mentioned, is the equity puzzle that was explained by Benartzi and Thaler by investors’ myopic loss aversion and failure to aggregate risk. Some other anomalies are not so clearly explicable and sometimes the best explanation of traders’ and trades’ behavior is so called noise trading (see Black, 1986; De Long et al., 1990). Trading is partially based on information (outcomes) and partially on heterogeneous group of inputs and influences that is called “noise”. Noise probably includes various heuristics, probability-distortions, loss-aversive distortions, and even “fads” (Shiller, 1984). Fads mean buying assets primarily not because they promise high gains, but because they are popular. Trading on fads can sometimes secondarily bring gains to individual traders, since lot of noise-traders buy the popular assets (price goes up), but not to noise-traders as a group, because the sentiments (fads) change unpredictably (“noisily”) and noise traders are not smart enough to leave investment bubbles (fads) in time.
If there was no noise trading, it would be possible to use event studies to predict the price of assets (Black, 1986). Event studies are studies of events that can reasonably influence prices, such as changes in dividend yield, political events, comments of influential economists or bankers, expected harvest, expected consumption, etc., see Shiller, 1981; Cutler et al., 1989; French & Roll, 1986.
Event studies show that most of the changes of prices (for example of stocks) can not be accounted for on basis of available new information. Similarly Shiller, 1979, 1981 shows that the fluctuation of interest rates and stock prices can not be explained using publicly available new information. The explanation of this phenomena is still in a preliminary stage. It can be possibly explained by differences in the subtleness of investors: less sophisticated investors do not base the price they are willing to pay properly on expected returns of the asset (in other words on available relevant information), this in turn reduces the capacity of smart investors to base their investments on rationally expected returns, because they must take into consideration noise trading of less sophisticated investors, and this further lowers rational predictability of prices, which increases loss aversion of all investors, which again lowers the proportion of rationally placed investments. The prices are no doubt excessively volatile and our understanding of their movements is at best rudimentary. We also know there is systematic over- and undervaluation of certain types of stocks (De Bondt and Thaler, 1986), and over- and underreactions to earnings announcements (Chopra et al., 1992; Bernard, 1993), but we do not know exactly why.
Only in a few cases there exists a more or less clear sense of the anomaly at hand and its psychological explanation is available:
(1) The explanation of differential pricing of closed-end funds and open-end funds with the same composition of stocks is proposed by Lee et al., 1991. (The difference between an open end-fund and a closed-end fund resides in the fact that to liquidate a holding in a closed-end fund investors must sell their shares to other investors rather than redeem them with the fund itself for the net asset value per share, as is possible with an open-end fund (Lee et al., 1991, p. 59).) The three parts of the puzzle are: a) volatility of prices, b) discounted prices, and c) initial premium (and they can be accounted for by noise-trading, risk aversion, and optimism, respectively, see below).
a) Closed-end funds are on average priced with a discount. The discount shows high volatility: it typically ranges between 10%-20%. The authors assume that higher volatility of closed-end funds’ prices (compared to the prices of the underlying securities or open-end funds of the same stock composition) may reflect differential moves of sentiments of the closed-end funds’ shareholders (as compared to open-end funds’ shareholders). Closed-end funds are owned and traded primarily by individual investors, who are known to trade more on noise than institutional investors (according to research, institutions hold only around 5% of closed-end funds shares, whereas institutional ownership of stocks ranges between cca 20-55%).
b) The second part of the puzzle, namely that closed-end funds sell at discount, is caused by the volatility of its prices that enhances the risk of investing into these funds. Risk aversion must be compensated by lower prices of the assets.
c) Another part of the puzzle is why are the closed-funds started at all and why investors buy into closed-end funds initially at a premium. Noise-traders are typically optimistic about closed-end funds, so for the fund founders it is profitable to put stocks together into a fund and sell them to naive investors. To be more exact, the closed-end funds get started when noise-traders are optimistic, that is when existing funds sell at a premium or at only a small discount.
(2) The concepts of loss aversion and mental accounting (Thaler, 1999) can explain why people hold losing stocks too long (Shefrin & Statman, 1985).
Mental accounting is a way in which we account gains and losses (a way in which we perceive them). If, for example, a large loss is mentally divided into several smaller losses (of the same summary magnitude as the large one), they will psychologically hurt the loser more than if the large loss was not divided (and vice versa for aggregation of losses) – see Kahneman & Tversky, 1979. “The main idea underlying mental accounting is that decision makers tend to segregate the different types of gambles faced into separate accounts, and then apply prospect theoretic decision rules to each account by ignoring possible interaction” (Shefrin & Statman, 1985, p. 511; see also Kahneman & Lovallo, 1993; Rabin, 2000).
If I mentally subtract a given loss L from a bigger gain G (i. e., G > L), the resultant perceived utility of this account would be greater than if I mentally accounted (perceived) L and G separately (because in this way I eliminated the steeply negative perceived value of L). For a general discussion of this topic see Shefrin & Statman, 1984, pp. 401-408. Mental accounting together with prospect theory can also explain why shareholders like dividends (Shefrin & Statman, 1984). They will rather get a lot of small gains than one large gain of the same summary amount (the perceived utility function is steeper for smaller gains).
Now, mental accounting can take a form of not “carrying out” the losses. If there is hope that the losses will be eliminated in the future, decision makers have tendency to defer them – even if empirical evidence predicts the losses will get worse. This tendency to defer losses if there is but a slight chance of their elimination in the future is why investors ride losing assets too long (see Shefrin & Statman, 1985). Professional traders often follow some simple rules that enable them to prevent (or control) the negative emotional reaction to taking a loss. This negative emotions come from loss aversion – see Thaler, 1980; Kahneman & Tversky, 1982. Professional traders for example sell any asset if it lost 5% or 10% of its purchase price.