Rational Models Versus Behavioural Models

Rational Models Versus Behavioural Models

Questions:

6.1 Rational Models versus Behavioural Models
(a)(i)We have so far considered rational models for an asset’s expected return. By ‘model’ I mean a mathematical expression for expected return. By saying that a model is ‘rational,’ I have assumed that some or all investors in the model make the best possible decision given all relevant information.
(a)(ii) In CAPM, rational investors solved a portfolio allocation problem. They (1) had a utility function characterized by risk aversion, (2) knew the means, variances, covariances of all assets that they able to invest it, and (3) chose the best combination of portfolio weights for their risk aversion levels. A one-factor model for asset returns emerged from these assumptions.
(a)(ii) The APT does not explicitly model investors making portfolio allocation decisions. Instead, it assumes that asset returns follow a factor structure, sufficient securities exist to form well-diversified portfolios, and there exist investors that are always looking for arbitrage opportunities. The activity of such ‘arbitrageurs’ eliminates compensation for idiosyncratic risk, giving rise to the multi-factor APT model for asset returns. In APT, the arbitrageurs play the role of the rational investor: They make the best possible decision given all relevant information. 
(a)(iii) Given the existence of rational investors, market prices are believed to more or less incorporate all relevant information that is public, that is, price are ‘semi-strong efficient.’
(b) Behavioural Finance says that investors do not always make the ‘best possible decision.’ This can be due to (1) limits on how investors process information (e.g., investors tend to focus on recent information), and (2) behavioural biases (e.g., investors may behave differently towards the same decision depending on how the decision is ‘framed’).
 
6.2 Limits on Information Processing
(a) The information that is relevant to stock prices includes such things as recent and historical returns, financial performance, and earnings announcements. This information influences investor beliefs about how stocks are expected to perform. I refer to the process of updating beliefs as information processing, and the inability to correctly update beliefs as limits on information processing. If investors have limits on how they process information, then the trading decisions based on these beliefs will not be fully rational. I state four limits on information processing below: (i) forecasting errors due to overweighting recent information, (ii) overconfidence, (iii) conservatism or under reaction, (iv) representativeness or neglecting the size of the sample.
(b)(i) Forecasting errors due to overweighting recent information People give too much weight to recent experience in comparison to previously available information when forecasting asset performance. For example, due to recent good performance, people may predict a firm to have higher future earnings that what the data objectively indicates.
(b)(ii) Overconfidence People tend to overestimate the accuracy of their beliefs, resulting in poorer investment decisions. Psychology research has documented that men tend to be more overconfident than women. Consistent with this, a study found that men trade far more than women, and it also found that, on average, greater trading resulted in poorer performance.
(b)(iii) Conservatism or under reaction Investors tend to be slow in incorporating new information into their beliefs about how good or bad a firm is doing. This means that stock prices might initially underreact to news about a firm, so that prices do not reflect new information immediately, as the Efficient Market Hypothesis would predict, but only after some time has elapsed. Such a bias would give rise to momentum in stock market returns.
(b)(iv) Representativeness or neglecting the size of the sample People incorrectly generalize the results of a small sample. For example, they may look at recent trends and without sufficient evidence use that as a basis for long-term performance. This is consistent with observing near-term overreaction and long-term correction in stock prices. A study has shown that after earnings announcements stocks with the best recent performance suffer reversals after a few days.
 
6.3 Behavioural Biases
(a) In addition to beliefs about stock prices, investor decisions about what stocks to trade may also depend on how investors act in different situations, that is, they may depend on ‘behavioural’ factors. Three such behavioural factors that give rise to decisions that appear to be inconsistent with ‘rational behaviour’ are (i) framing, (ii) time inconsistent preferences, and (iii) Prospect theory.
(b)(i) Framing Framing refers to the manner in which investors think about a decision, that is, how they “frame” a decision. A fully rational investor ought to focus on just the facts, not how the facts are presented, but an investor who is not fully rational is affected by the presentation. For example, an individual may reject a bet which is framed as a risk associated with possible gains, but may accept the same bet when it is framed as a risk associated with possible losses. 
Example (from Investments, Bodie et al.): Consider a coin toss with a payoff of $50 for tails. Now consider a gift of $50 that is bundled with a bet that imposes a loss of $50 if that coin toss comes up heads. Both cases have the same outcome for heads and tails, but the differences in framing can lead to different attitudes towards the bet. Which of the two cases “feels better” to you?
(b)(ii) Time inconsistent preferences You might decide that you will not eat dessert tomorrow, but when tomorrow comes around, you change your mind and have a large slice of chocolate cake. This is called time inconsistency. Your “optimal” decision regarding what to eat changed based on when you made your decision.
 
We can think of the decision of not eating dessert tomorrow as your “rational” choice, and the decision of eating dessert after seeing a delicious piece of cake as being your “behavioural” choice. We can think of similar examples when it comes to investing: An individual may choose that next week he will only engage in a certain number of trades, but when next week comes around he finds that the thrill of trading pushes him to trade more aggressively.
(b)(iii) Prospect theory Prospect theory says that we possess non-standard preferences. A standard preference is one where individuals are risk averse, and this is represented by a concave utility. For example, consider a utility function with utility on the y-axis and income on the x-axis:
 
The function’s shape indicates two important things: (i) diminishing marginal utility of income, (ii) risk aversion. Marginal utility refers to how much my utility increases for an increase in income. The function’s concave shape indicates that when I am poor, I am more happy with an increase in income than when I’m rich. We see this below. The utility associated with a $40k income is 90. Increasing my income by $10k gives me 10 additional units of utility (from 90 to 100). Now my income is $50k. Increasing my income by an additional $10k gives me 5 additional units of utility (from 100 to 105). Hence, I value an increase in income more when I’m poorer.
 
Risk aversion says that I would rather have a given income with certainty than with uncertainty. To see this, suppose first that my compensation package is fixed at $50k. My utility in this scenario is 100. Now assume that my compensation package is variable, such that if my performance is “bad,” I earn $40k, and if it is “good,” I earn $60k. Assuming the probability of performing “bad” and “good” is the same, that is 0.5, my expected income in this scenario is also $50k (=0.5×40+0.5×60) , however, my expected utility is
Expected utility=P(b)U(b)+P(g)U(g)
=0.5(90)+0.5(105)
=97.5.
Since the utility of a fixed compensation of $50k is higher than the utility of earning a variable compensation whose expected value is $50k (utility of 100 versus 97.5), I prefer certainty to uncertainty. Hence, a concave utility function indicates that I am risk averse. On the other hand, a convex utility function would indicate that I was risk-loving (show this). What about a risk-neutral investor?
Prospect Theory states that people care about income relative to a reference point. For increases in income relative to that reference point, I exhibit the usual risk-averse behaviour. For decreases in income relative to that reference point, I behave differently, that is, I exhibit risk-loving behaviour. The Prospect Theory utility function is shown below. 
    
We say that an investor who exhibits Prospect Theory preferences is “risk averse over gains” and “risk loving over losses.” We can infer this from the curve above by noting that the curve is concave when income gains are positive, and convex when income gains are negative, which is the same thing as saying that the curve is convex when there are losses.
Prospect Theory helps explains such behaviours as why investors hold onto “losers,” that is, stocks that are earning negative returns relative to their benchmarks (negative abnormal returns). Such stocks can be represented by points on the lower part of the curve that is convex. On this part of the curve, investors are risk-loving, and are more satisfied with the uncertain losses associated with holding onto losers than they are with the certain loss associated with selling off a loser. What about “winners”? Which part of the curve would they be represented on and would Prospect Theory predict that investors hold onto winners or sell them off?
 
6.4 Evaluation of the Behavioural Critique
The behavioural critique that investors are not fully rational is well taken. It is difficult to imagine any investor capable of instantaneously processing vast amounts of information. The behavioural approach offers some explanations for the anomalies we observe in Finance, however, behavioural Finance does not offer a unified theory such as the CAPM that is able to simultaneously explain and predict a number of phenomena. This is a substantial shortcoming.

1) When are markets considered to be efficient?

2) What are the three types of market efficiency, and how much information do they assume prices to contain?

3) What are abnormal returns?

4) Write down an example of a predictive regression of the next period’s market return.

5) If we wish to understand the relationship between firm size and abnormal returns, why would we look at the abnormal returns associated with a portfolio of firms rather than individual firms?

6) What is short-term momentum and long-term reversal?

7) Does the fact that smaller firms and higher book-to-market firms exhibit higher risk adjusted returns necessarily mean that the efficient market hypothesis is incorrect?

8) What makes a model rational?

9) What are the characteristics of the standard utility function?

10) What kind of risk appetite is demonstrated by a utility function that is (i) convex, (ii) concave, and (iii) a straight line?

11) How is Prospect Theory different from the standard risk-averse utility?

12) Why is a theory based on fully rational investors unrealistic?

13) Why are many Finance scholars skeptical of behavioural explanations?

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