On having multiple discount functions

Another interesting development in the world of Behavioural Finance is the idea that individuals have multiple discount functions. For example, researchers such as Prof David Laibson argue that we have at least 2 discount functions, one for the very short term say minutes, hours, days, and then another for the longer term. The tension the investor faces is the tradeoff between these two. For example, simple exponential discount functions argue that the change in  discount rate is more or less constant over time. Yet consider this thought experiment - imagine you were given two sets of choices 1) a) $100 now or b) $101 in 60 mins from now and 2) a) $100 in 1 week or b) $101 in 1 week and 60 mins. Almost everyone will choose 1a and 2b but this is not consistent with a simple discount function. The attraction of the immediate is overwhelming for most people, percieved as far more beneficial than any delayed extra value. Yet beyond the immediate people switch to a more rational process incorporating the extra delayed benefit. Its as if they have two discount functions, one that kicks in for the near term, emphasizing short term benefits and the second which is used to evaluate longer term costs and benefits. Even more fascinating some researchers are arguing that these discount functions actually correspond to different more or less developed parts of the cerebral cortex, associated with high level reasoning and more emotional animalistic instincts. But these discount functions are not merely quantitatively different, they seem to be qualitatively different too. For example, when you change the reward, say to ice cream or a candy bar, the short term benefits even more massively outweigh longer term benefits.

Of course, marketing people instinctively know these things we suspect, the offer of the free ipod when you sign up for a new credit card, peoples tendancy to spend hours negotiating on physical aspects of a car purchase, and then only a moment to decide whether to get auto financing (which is where most of the profits are made).

So what is the punchline - real physical things obtained immediately are valued much MUCH more than abstract non physical things delayed.

What do probabilities mean to people? The Cost of Certainty

One of the most interesting notions in Prospect Theory, is the idea that individuals really don't understand probabilities. That is they make little distinction between similar probabilities (say the difference between 0.25 and 0.3) and treat them essentially the same. However that is not true at the extremes, we seem to have a cognitive bias in favor of zero and 1 as absolute certainties. Yet ironically, absolute certainties are never the case. Mathematically this is described as a weighting function that converts quantitative probabilities into qualitative weights - using a function like the following:

So basically we underestimate probabilities when they are slightly less than 1 and overestimate them if they are slightly more than zero. What does this mean for finance? Well, people will pay more to receive contingent cashflows which are very unlikely because they will overstate the actual probability. This is part of the attraction of lotteries - although the probability is small, there is a small probability of success and that makes all the difference. Similarly investors will heavily discount cashflows that are not absolutely certain.

Prospect Theory and what it means for economics

Traditional Economics is based on the notion of a utility function which increases as a concave function) with increasing levels of wealth. Our decisions as economic actors therefore boil down to selecting the option that generates the highest expected utility. But ask yourself this, faced with a fair one off gamble in which you might make 2000 dollars or you might lose 1000 dollars, what would you do? Most people would choose not to gamble even though the expected utility will be positive. Why? Note that this is not true if we were able to play the game say a thousand times - in which case almost everyone will take the bet.
Behavioral theorists suggest this unwillingness to take the single bet is because we care about losses more than gains, counter to the principles of traditional utility theory, and so have posited a prospect theory that charges a greater value loss for losses in current wealth that for gains. If you like, the utility function is "kinked" around the current level of wealth.

Most of financial markets are based on a zero sum game. Consider a structured product. If I win, you must lose and vice versa. Financial engineering can only add value to such transactions by exploiting the differences in the preferences of the transactors. For example by emphasing the elements of the transaction that most appeal to the other side, say high returns, or delayed payment, or low risk. Being a zero sum game, these elements are paid for by subtracting from aspects of the transaction that the counterparty does not care so much about, like operational complexity, or like risk.  Value is created from the transaction (but not utility however) if the structure reflects the differences in the counterparties wants and needs. Prospect theory  acknowledges that value is inherently client specific (it depends on their reference point for example), and that financial product design is really about understanding behavioral biases in order to better align. So is Prospect theory purely descriptive while Utility theory is normative? Should we give up structured products because they pander to our cognitive weaknesses? Although Prospect theory is partly descriptive, it is also normative. Other counterparties have cognitive biases too, and we must interact with them, so it behooves us to understand and acknowledge these biases/limitations/constraints in our transactions with them.

Models and Overconfidence

Whether a scientist, or a financial engineer, when we invest in an idea, a model, a way of thinking, by definition, we believe it to be an accurate representation of the world, and so interpret new information in terms of this model. New information that is consistent with this model makes us more confident in its use, while new conflicting information is often regarded as spurious, exceptional or irrelevant. The model provides us with an anchor, and biases us away from alternatives.  We protect our models from the world of evidence, in the same way we protect ourselves, no surprise here, as in some sense these models constitute ourselves. The models change only with crisis, some overwhelming surge of evidence that cannot be ignored. Ironically, financial models, (unlike models of physics) when broadly and consistently acted upon, will often build up arbitrage and economic pressures in the market to break the models. So no one can see the breakdown coming, everyone is shocked when it does happen, and yet everyone can rationalize after the fact why the crisis occured.
Perhaps the truth is that reality is more complex than we can ever know, and like a good buddhist, all we can do is acknowledge and respect the complexity that we face, realizing like the quantum physicist, that the act of understanding the world, also changes it into something else.

The Curse of Overconfidence and some revealing party tricks...

Irving Fisher, probably the greatest american economist of his generation (most known for his theory of interest rates), remarked famously just before the great crash of 1929 that "Stock prices have reached what looks like a permanently high plateau". To be fair, he put his money where he mouth was, and invested much of his assets in the stock market. Soon after he was broke, and had to sell his home in NewHaven Connecticut to pay his debts (fortunately his university bought his house and let him live there, or he would have been destitute!). Even after his experience, he continued to argue that he had been right.
The curse of overconfidence is not unique to economists, indeed one of the major trends in new economic thought is behavioral finance, applying all of social science theory to finance, not just economics. And one the cornerstones of this theory is that people are overconfident, inconsistent, lazy, and simply stupid at times. In short, not the "homo economicus" of classical theory. Consider one's own overconfidence - ask yourself or your friends to define a 90% [lower,upper] range for answers to the following questions (no cheating!), and find out if you indeed tend to get 9 out of 10 them right.

1. What is the population of Turkey?
2. What is the weight of the Empire State Building? (tons)
3. What is the GDP of Australia?
4. How many cells in the human brain?
5. How likely is it that you will be struck by lightening this year?
6. How many bibles are there in the world?
7. How many children will die of malnourishment in the world in the next day?
8. How likely is it that you will be in a plane crash this year?
9. What is the likelihood of a asteroid hitting the earth in the next year and destroying all life on the planet?
10. What is the likelihood of a AAA bond defaulting in the next year?

 Answers (no peeking)

1. 72,561,312 as of 1st January 2010
2. 365,000 tons
3. $1 trillion USD
4. 100 billion
5. 1/750,000
6.  6,000,000,000
7. 3000
8. 1/675,638
9. 0.00000002
10. 0.1

Most people (assuming they play fair) get significantly fewer than 9 out of 10 of these questions right. They believe the world is less complex and better understood than it actually is, and this influences their behaviour. Unfortunately sometimes with disasterous results - i am reminded of the quote from Larry Kersten, an american sociologist that "before you attempt to beat the odds, be sure you could survive the odds beating you.”