Less Wrong is a community blog devoted to refining the art of human rationality. Please visit our About page for more information.

Shane Legg on prospect theory and computational finance

13 [deleted] 21 June 2009 05:57PM

People are not rational expected utility maximisers.  When we have to make decisions, all sorts of cognitive biases and distortions come into play.  Seminal work in this area was done by Kahneman and Tversky.  They produced a model of human decision making known as prospect theory, work that Kahneman later won a Noble prize ...

... I looked at these investors and thought, “Hey, they’re just like reinforcement learning agents. No big deal. If I want to know what investors with probability weighting and a curved value function do, I can just brute force compute their optimal policy by writing down their Bellman equation and using dynamic programming. Easy!” It was a mystery to me why, seemingly, nobody else was doing that. So off I went to build software to do just this, starting with a simple Merton model…

... When we fired up my simulator and gave this distribution to an investor that had probability weighting: the investor took one look at that scary negative tail and didn’t want to invest in the stock. This is exactly what the model should predict.  In short, we took realistic stock returns, and presented this to an investor with a realistic decision making process complete with a bunch of parameters that have been empirically estimated by others in previous work, and what we got out the other end was realistic investor behaviour!

Read the whole article here at Vetta Project.

Comments (6)

Comment author: Psychohistorian 22 June 2009 02:58:44AM 3 points [-]

This is interesting, but (as far as I know) a much better explanation as to why most people don't own stock is that they don't actually bother researching how to invest or spend much cognitive effort on investing.

Perhaps Napoleon's old statement needs a corollary: "Never attribute to a complicated model of behaviour contingent on the interconnection of numerous noisy empirical estimates that which is adequately explained by incompetence."

Comment author: mathemajician 22 June 2009 08:29:22AM *  5 points [-]

Sure, there will be a great many factors at work here in the real world that our model does not include. The challenge is to come up with a manageable collection of principles that can be observed and measured across a wide range of situations and that appears to explain the observed behaviour. For this purpose "can't be bothered" isn't a very useful principle. What we really want to know is why they can't be bothered.

For example, I know people who can be bothered going to a specific shop and queueing in line every week to get a lottery ticket, and then scheduling time to watch the draw on television. It would be a lot less total effort over the years if they went into their internet banking and transfered a few thousand dollars into an investment fund that their bank offers. Plus their expected return would be positive rather than negative. Even if you point this out to them, they probably still won't do it. Why is it then that they can't be bothered doing this, but they can be bothered buying lottery tickets? One potential explanation provided by prospect theory is probability weighting: the negative tail on stock returns gets over weighted, as does the chance of winning the lottery. No doubt you can come up with other hypotheses about what is going on.

I'll also add, that while this work is a bit different to things usually covered here, it is perhaps interesting for some people to see an attempt to incorporate some of these ideas of cognitive biases into a formal mathematical model of behaviour -- in this case the behaviour of investors.

Comment author: roland 22 June 2009 03:38:53AM 0 points [-]

I was thinking about the same. The question is, how much research must you do in order for stock investing to become profitable comparing to other ways of investing? There is also the question of fees to pay, the less you invest, the more the fees weigh in.

Comment deleted 22 June 2009 01:38:50PM [-]
Comment deleted 23 June 2009 05:30:58AM *  [-]
Comment author: SoullessAutomaton 23 June 2009 09:33:49AM *  0 points [-]

I invested £500 in the stock market on 2003, and 9 months ago I withdrew £850.

Wouldn't that be 2003-2008, i.e., five years?

That's about 11.2% annual return, if I'm mathing correctly this early in the morning.

Comment deleted 23 June 2009 03:19:07PM *  [-]
Comment author: andrewc 29 June 2009 11:57:26AM 0 points [-]

Depends on what you bought. More than a few stocks had the last few years of growth wiped off them last year, and that includes many well hedged managed funds. Your youthful assessment of the risks was perhaps better than you give it credit for.

What would the original investment be worth right now had you not cashed it in?

Comment author: Unnamed 23 June 2009 11:30:10PM 0 points [-]

I think that Bernatzi & Thaler (1995) were the first to do an analysis of this sort (using the results of behavioral decision making research to explain why people didn't buy stocks), although this new paper seems to include more of the features of prospect theory. Bernatzi & Thaler's abstract:

The equity premium puzzle refers to the empirical fact that stocks have outperformed bonds over the last century by a surprisingly large margin. We offer a new explanation based on two behavioral concepts. First, investors are assumed to be "loss averse," meaning that they are distinctly more sensitive to losses than to gains. Second, even long-term investors are assumed to evaluate their portfolios frequently. We dub this combination "myopic loss aversion." Using simulations, we find that the size of the equity premium is consistent with the previously estimated parameters of prospect theory if investors evaluate their portfolios annually.