In a great book “Behavioural Finance for Private Banking”, the authors, Thorsten Hens and Kremena Bachmann, write on decision biases.

“Sub-optimal decisions may result not only from biased information processing but also as a consequence of other heuristics, which are not particularly related to the assessment of probabilities. The most prominent examples are summarized hereafter.

Ø       Mental accounting

If problems are analyzed in an isolated fashion, individuals' decisions may be biased by narrow framing. An example for this effect is using mental accounting as a heuristic used to organize, evaluate and keep track" of decisions (Thaler, 1999). For example, many people divide their household budget into expenses for food and expenses for entertainment. At home, where the food budget is applied, they eat fish instead of lobster because it is less costly. In a restaurant, however, they order a lobster, even though the costs are higher. If they ate lobster at home and fish in the restaurant, they would save money. Nevertheless, people choose to limit the food expenses at home, because they are thinking separately about food in a restaurant and at home.

As in the food example, individuals think differently about the way income is generated (work, gambling, bonus, etc.). They do not integrate all sources of income into one account. Similarly, they do not integrate all assets in one portfolio. Instead, individuals use layers in a pyramid format, each of them addressing different investment goals. The idea is illustrated in Figure 1.

The problem with this investment approach is that investors make decisions within the layers. Neglecting the correlations between the returns of assets belonging to different layers may create sub-optimal inefficiencies.

Figure 1: Portfolio pyramid (Courtesy of Ginita Wall CPA CEPR)

Ø       Disposition effect

Mental accounting may also explain the "disposition effect". It describes the investors' tendency to hold losing assets too long and sell winning stocks too early, given that these assets belong to different accounts. Empirical evidence for this effect is provided, for example, by Odean (1998). He finds that individual investors are more likely to sell stocks that have gone up in value, rather than stocks that have lost. This can be seen in Figure 2, where PGR is the number of realized gains divided by the number of total gains (realized and "paper" gains) and PLR is the number of realized losses divided by the number of total losses (realized and "paper" losses).

Figure 2: Disposition effect (Source: Odean (1998))

One explanation for this observation is that investors make two mistakes at once: they build two mental accounts - one for the realized gains (or losses) and another one for "paper" gains (or losses) - and they take investment decisions that make their previous investment decision (to buy an asset) look better (see Hens and Vlcek, 2005 and Barberis and Xiong, 2008). If a loss occurs, investors would keep it as a "paper" loss (investors do not sell the asset) because this is associated with a lower utility loss than selling the asset and realizing the loss. If a gain occurs, the investor is better off if he realizes it (sell the asset) than to keep the gain as a "paper" gain.

Note that this sort of mental accounting is clearly irrational since it hinders the client in facing the real economic situation of his assets. Moreover, note that the disposition effect occurs because the client does not plan his investments ahead, but backwards. Assets that made a loss with respect to the buying price are kept in the "paper" account, while gains with respect to the buying price are realized. This is like justifying the actions one has already taken and not like looking ahead for the best continuity of the investments.

Ø       House money effect

The mental accounting bias can be also used to explain the house money effect - a greater willingness to gamble with money that was recently won (see Thaler and Johnson, 1990). The reason is that the utility loss associated with a loss is diluted if the loss is aggregated with an earlier gain and the investor is ready to take more risks.

Ø       Home bias

One of the more prominent asset allocation puzzles is the degree to which investments are focused in home country equity as opposed to foreign investments. This phenomenon is called home bias. French and Poterba (1991) for example find that investors in the United States, Japan and United Kingdom allocate 94 % respectively 98 % and 82 % of their wealth in domestic equities (see figure 3). The home bias can be associated with the notion that people prefer familiar situations. They feel that they are in a better position than others to evaluate particular decision problems. However, one should be aware that the feeling of being better informed may be deceptive and lead to the illusory feeling of being on secure ground.

Figure 3: Equity portfolio weights of U.S., Japanese and British investors (Based on French and Poterba (1991))

The home bias can be also linked to ambiguity aversion; when faced with a choice between two lotteries with, say, a 50:50 chance of getting $100 or not getting anything, versus a lottery with the same outcome but with unknown probabilities, those people who never have invested in foreign stocks choose the lottery with known probabilities. In an experimental study, Ackert et al. (2004) show that providing participants with information about a firm's name and home base motivate them to increase their investments. The firm's name alone is not sufficient to change investment behaviour.

Note that ambiguity aversion may well be compatible with rational choice since markets will typically be incomplete for those states that give rise to ambiguity. However, given the current degree of globalization of financial markets, a strong home bias seems hard to justify.

Ø       Endowment bias

Although decision-makers are aware that their choice to take an action or not should depend only on the expected pay-offs, in many situations they cannot avoid taking into account previous decisions. Such behaviour may result from the endowment effect or the sunk costs effect. The endowment bias describes the reluctance of people to part from assets that belong to their endowments. If it is more painful to give up an asset than it is pleasurable to obtain it, then buying prices will be significantly lower than selling prices. In other words, the highest price an individual pays to acquire an asset will be smaller than the minimal compensation that would motivate the same person to give up that asset once acquired. To illustrate the point, consider once again the following example (see Kahneman, Knetsch and Thaler, 1990).

Example: Endowment bias

Suppose that you can choose between a mug and a chocolate bar, both with the same market value. Which one would you choose?

A) a mug       B) a chocolate bar

You own the good now.

Suppose that you can exchange what you have for the other good. Are you going to trade?

A) yes           B) no

The experiment shows that roughly half of the people prefer each good. After the goods were handed out, people are allowed to trade: those who had wanted mugs but got chocolate (or vice versa) could swap. Barely 10 % of students decided to trade. In contrast, given that the gifts were randomly allocated, one would expect 50 % to swap. Even after a short time with things of little value, ownership had overwhelmed the individuals' prior tastes.

In other words, if one must pay for goods and these goods are not in one's reference endowment, one values it as a gain. But if one has the right to get compensation for giving them up, the reference endowment now includes these goods and, consequently, one values the goods as a loss. Therefore, loss aversion necessarily implies a divergence between the amount one is willing to pay for goods and the amount one is willing to accept as compensation for giving up the same goods.

The endowment bias may cause several investment mistakes. In particular, investors biased by their endowments may hold on to securities that they have inherited or have purchased regardless of whether it is wise to do so. As a result, investors caught by the endowment bias may feel compelled to continue holding a stock even if its economic prospects are not encouraging.

Ø       Sunk costs

The next bias that affects implementing decisions is the bias originating from past investments that are now irrevocable, i.e. the sunk costs. We know rationally that these costs are irrelevant to decision-making. Only incremental costs and benefits should influence future choices. Yet research shows that the more we invest in something (financially, emotionally, or otherwise), the harder it is to give up that investment. For example, in a telephone call, being on hold and hearing the recording "Please stay on the line" often means that it will probably take longer to get connected. Nevertheless, it's hard to hang up and call again later. Similarly, one may find it harder to terminate a project that is not profitable if the project has already required large investments. One reason why it is so difficult to free oneself from sunk cost reasoning is that people are unwilling to admit to a mistake. For example, by selling a poorly performing asset that was previously regarded as a great investment, one may feel that this is making a public admission of earlier poor judgment. This was also the reason for the disposition effect.”