Wall Street Interview Tactics & Monty Hall Economics
God and the Economists
Apparently the Monty Hall test is one that Wall Street firms commonly use to see if potential applicants are suitable material for the madness that is a trading desk in the heartlands of financeland. In so using the test these corporations are, knowingly or not, addressing some of the most hard to overcome behavioural biases that often defeat legions of unprepared investors.
In fact, this particular test has been a source of delight for grant seeking academics of all persuasions. The thing is that the Monty Hall test can be explained in many different ways, most of them simultaneously contradictory. However, it does increasingly look like this blatantly irrational behaviour is hard-wired into our neurons. It seems God really doesn't like economists.
Stick or Twist?
For those who don't know – and it's hard to believe that there are many people left in that category – the Monty Hall problem is usually described in terms of a twentieth century gameshow hosted by the eponymous Monty. In the game contestants were given a choice of three closed doors two of which hid a goat and the other a car. Once the contestant had chosen a door Monty would throw open one of the other two ... to reveal a goat. The question is, on the assumption they prefer the car to the goat, should the contestant now stick with their original choice or twist, and select the other closed door?
The answer is that they should change their mind. This answer usually generates a whole host of angry responses, often from mathematicians and statisticians, but is correct under most reasonable assumptions. Basically the reason is that when you make your original choice the door you choose has a one in three chance of being the car while there's a two in three chance of it being behind the other two. When Monty opens his closed door your door's odds don't change, and neither do the odds on the combination of the other doors.
Disbelievers, Repent
Most of us – me included – initially find this unbelievable and spend hours frantically manipulating card decks in a furious attempt to show that this is incorrect. But it isn't, and the key to understanding this is that Monty already knows where the car is, and his knowledge changes the odds. It's an important lesson for stockpickers when they're dealing with people who know more than them.
Now the thing about this behaviour is that it is strictly irrational because once you sit down and figure out the probabilities it's clear that the optimal strategy is to switch. Yet multiple experiments in many situations have repeatedly shown that virtually everyone fails to figure this out and, even worse, they don't actually improve their performance with experience. In fact, even people trained with transparent doors largely failed to adapt their behaviour when faced with the normal problem.
Explanations, Explanations
It's fairly easy to see why this has attracted so much research attention. If these behaviours – an inability to logically reason about a relatively straightforward problem and an inability to adapt to overcome this inability – transfer into other areas of human activity then they suggest profound implications. In particular, if people can't figure out a basic probability conundrum in a real-life situation because they can't reason about the impact of someone else with more knowledge than them then you can't hold out much hope for the average dealer in stocks.
A whole host of explanations for this result have been put forward, some of them downright contradictory. The first one is that they simply can't perform the calculation to update the conditional probabilities after the first door's opened – which they should be able to do if we're rational maximisers as much of economics has insisted for a century or so. This failure of so-called Bayesian updating, after Bayes' Theorem which describes how to calculate conditional probabilities, would imply that we're not very good at rationally reasoning and would suggest that our rationality problems stem from the difficulty we have in making these updated calculations. Note that this wouldn't mean we aren't fundamentally rational, it would just imply difficulties in performing the necessary calculations.
The other explanations rely more on the concepts of behavioural psychology. So this could be an outcome of the illusion of control, with participants believing that they're exercising skill and that the sight of an empty door merely shows that they've already chosen correctly. Or it could be a side-effect of the status quo effect where people are markedly reluctant to give up something they already own in exchange for something else – probably because they'd feel worse if it turned out what they'd given up was more valuable than what they'd accepted. Sins of commission are always felt more than sins of omission.
Bad Decisions or Bad Design?
As usual, in these types of anomalies, there's no agreement that the underlying effect is caused by behavioural biases over poorly implemented rationality because it's pretty well impossible to tell the difference. Importantly, these are not the same, because poorly implemented rationality can be overcome while hard-wired behavioural bias probably can't; and that makes the world of difference.
In Monty Hall's Three Doors For Dummies Andrea Morone and Annamaria Fiore produced an experimental design that controlled for Bayesian updating by introducing a Monty Hall problem that didn't need it. They reasoned that if they could make clear that the choice was between a one third probability of the chosen door being correct and a two thirds combined probability of the other doors then they ought to be able to make people aware of the real odds. So instead of opening one of the doors after the choice was made they simply offered the participant the option of keeping their current door or choosing both of the other doors. It's the same choice of course, but makes obvious that the odds of changing are the better ones.
Behavioural, Not Bayesian
Why is this important? Well, in this new formulation of the Monty Hall problem, no new information is presented to the participant. No door is opened so no recalculation of Bayesian conditional probability is required. The odds haven't changed. If participants still insist on keeping their original choice it's because they're barking mad, or at least behaviourally challenged. So what happened?
Well, basically the new option led to more people switching and an overall improvement in the learning process, but not to the extent that you'd expect if this was a Bayesian problem. The researchers opined that failures of Bayesian updating don't seem to be a major factor here. More likely you're looking at some kind of facet of the status quo effect. A word of caution on interpreting these results, however – it's a genuinely ingenious study, but it's on a very small sample and it needs further work.
Still, at root, it takes us further from rational economics and more towards behavioural imbalances. If people can't stop behavioural biases preventing them from solving relatively simple problems like this then what chance do they have of managing themselves in the maelstrom of markets? As usual what Monty Hall proved is that it's better to be opening the doors when you know what's behind them than guessing blindly and stupidly when you don't.
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9 comments
Hi Tim,
Yes - I do want to stress that changes to results & forecasts can just as easily be to the downside as to the upside and I did not intend to imply otherwise! Either way, the higher likely degree of variance from forecasts seems to me intrinsically likely to lead to greater volatility, irrespective of whether investors are retail or institutional - just as the smaller liquidity pool doesn't strike me as a retail-specific thing.
Now, I am not at all convinced that this true - and would like to see some numbers to back that often-made (and widely believed) assertion up. I strongly suspect that the proportion of AIM companies (or of companies outside the FTSE350) that caused major losses to their investors as a result (direct or indirect) of the credit crunch is no higher than the proportion of companies within the FTSE350. If one defined "major loss" as a loss of 50% or more to invested value from the start of 2007 level until now I would be very interested to see a comparison. A company does not have to go bust to cause serious damage to your wealth. One thing to bear in mind is that, obviously the absolute number of smaller companies that will have caused their investors big losses is bound to be higher, simply because the universe is larger, so it's proportions (=likelihood) that one must look at to make a comparison.
Just think of all the FTSE350 banks, property companies, construction companies and other heavily indebted companies that have had to undergo major capital reconstructions and as a result win the "50% loser" wooden spoon. Obviously it's important to use the FTSE350 as it stood at the start of the study period and not as it stands now! Unfortunately such a study is a tricky exercise because just looking at share prices is not suffiicient to detect the losers, one must also check for capital restructurings that would have affected the value of a shareholder's investment (Wolseley (LON:WOS) is a good example of this).
Yup, as you say this investment lark is great fun and there are quite a few myths that need debunking. :0)
Best,
Mark
Hi Mark
I didn't mean to imply that "retail investor influence being more prominent on small cap stocks" was equivalent to a "great number of retail investors". There could be more or less, they simply have more impact on smaller stocks as you suggest.
Also although it's true that smaller companies are more likely to exhibit explosive growth they're also far more likely to implode - I forget the numbers but there was some frighteningly high percentage of AIM stocks listed as having been failed a while ago. Of course, although volatility is technically equivalent to risk what really matters to longer term investors is uncertainty. Uncertain events - like an unanticipated credit crunch - are more likely to sink smaller companies than larger ones and changes in levels of certainty are more likely to cause waves of interconnected retail investor behaviour, aka volatility.
Fun, this investment lark :)
Tim
this one is just odd:
http://en.wikipedia.org/wiki/Two_envelopes_problem
Hit and Myth
Humans are human (thank God) -
But sadly we're ALL a bit odd.
We think we can think
With brains on the blink
So deem Monty a stupid old sod.
Hi timarr,
I guess the point here is that they simply have a DIFFERENT set of drivers - and a different set of random influences. "Growing the business" and getting more power and control sometimes have a vastly different value than the outside world might assume. The takeover activities of Chinese companies in the resources sector are a case in point, driven as they are by concerns over security of supply.
ee
Hi ee
Good points – heterogeneity of investor behaviour in theory leads to a more efficient market: as short-term optimists and pessimists push stocks one way or another then valuation gaps open up which are closed by those with a longer term view. That, at least, is the theory.
In practice it’s fairly obvious that the market gets captured by zealots on the upside. Because it’s less risky to go long than short – you can only lose your initial stake on the long side – behavioural factors bias investors against shorting when the market is running heavily against them. Since the only alternative is to sell stock when everyone who wants to exit has left all that remains are enthusiasts who happily trade amongst themselves, bidding stocks higher and higher in a fantasy market until brutal reality eventually impinges.
For hopefully obvious reasons the same sort of thing can happen in bulletin boards when people with negative views get swamped by wide-eyed optimists. That’s why we should treasure our grumpy pessimists even while we disagree with them: there’s no value in a group of people constantly confirming their own views.
There’s also some evidence that smaller stocks are more volatile than bigger ones, which is presumed to be an effect of retail investor influence being more prominent on smaller cap stocks. As for M&A well, watch this space. Suffice it to say that the decision making process for M&A amongst companies and investors is just as biased by random numbers as everything else.
There are a few people who make great traders, but like yourself, I’ve observed that these are few and far between. In fact the limited evidence that there is suggests that most traders make a loss on most trades but when they win they win big. Soros is the ultimate example. Being unable to manage my own biases on a short-term basis I prefer to refrain and try and either try and identify companies that have an outstanding franchise or simply look ridiculously cheap. Which, by default, tends to lead to a long-term holding strategy even in the face of “obvious” falls: mostly nothing is truly obvious in foresight …
timarr
Hi timarr,
Surely, rather than this being due to a greater number of retail investors, it is more likely to be down to a smaller pool of investors interested in a "smaller stock" than a larger one? Where the pool of active investors is smaller, a smaller number shareholders/potential shareholders changing their view and deciding to buy or sell will have a bigger influence on the price - i.e. poorer liquidity.
Another factor must surely be the "elephants can't gallop" adage? Because smaller cap companies are more likely to have "explosive" growth potential, this can lead to a greater disparity in views of their valuation - again leading to greater volatility as results (and new forecasts) replace earlier expectations.
Regards,
Mark
Good article, timarr, and one that raises some interesting issues. I'm especially interested, as I have known fewer than 10 really good traders in the 20 years I worked in and around bank trading rooms.
This point resonates....though I also think of Rumsfeld and his "unknown unknowns" compared to his "known unknowns". I observed, over many years, that the best traders are extremely willing to change their mind and cut their positions....and that this is often on the basis that "the market knows something that they don't". At one level of course this is extremely rational (as with your Monty Hall example), because they KNOW that there are people out there who COULD know more than them. But they aren't certain that is the case - sometimes it is just a random market move - and at other times it proves a temporary blip due to someone buying or selling through another bank. Of course if one doesn't know the end customer first hand, then one is always guessing.....but, in the short term, it is not irrational to assume that "someone knows something" and the odds have changed.
A recent example of where this proved completely wrong, however, was in SOCO shares last week - which suddenly rallied by £1 to nearly £18, following an RNS which every well-informed SOCO-watcher immediately dismissed as irrelevant (concerning a rig for CNV). Ex-post one can fairly clearly see that some institution or dealer had misinterpreted the RNS as indicating that drilling was starting early on a different field (TGD).....but, at the time, the assumption was that "someone knows something" and further, more important, news was...err....imminent. But no doubt people were suckered into the strong move upwards and backed the speculative surge with fresh money.
I'm an LTBH investor who has worked with a lot of traders, both good and bad. I'd observe that I am perhaps prone to the status quo effect, in having failed on several occasions to sell a share that I knew I knew very well and was confident about for the long term..... despite which the price fell as a result of people taking shorter-term views. Plainly in the 2008 slump in stock markets, the correct course of action was to sell everything asap and wait for the slump to bottom out - but it is difficult for an LTBH investor to do such things when nothing fundamentally has changed, especially when he knows he has superior knowledge to the market as a whole.
On the other hand, the weaker traders I have seen over the years have been more prone to the first error you mention above - which is assuming that they have chosen correctly. Traders have no loyalty to (or indeed usually much by way of fundamental understanding of) any asset they trade.....but the poor traders will often cling to losing positions. Nick Leeson is a case in point.
Good question - which is why it is an excellent test for potential traders!
Your closing comment is also clearly correct, but I am left wondering about the influence of the passage of time between the decision point and the revelation of the outcome. In the trading example, of course, this really doesn't matter......timescales are short and the results are more or less immediate - and that is all that matters for traders. However, I'm left wondering about the impact of time in the context of investment......
I have often been content to accept many months (sometimes, rarely, a year or two) of underperformance of an investment because I judge that, in the long run, I will still come out well ahead. Obviously, if I can see such a period coming with a high level of certainty, I would sell and re-enter....but it is rare that markets give such opportunities. Traders (including users of some forms of TA) would effectively assume at some point that "someone knows something" and sell - but that does NOT exclude the possibility of, for example, a takeover bid from someone who is ALSO taking a long-term view.
So I guess this leaves me wondering about two things in your examples:
1) what is the impact of different market participants having different time investment time horizons?
2) what is the impact of heterogenous market participants, in particular the possibility of M&A interest from industry players who may be using different valuation metrics from those that are commonly assumed to be relevant by financial market participants?
rgds
ee