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Wednesday, 9 November 2011

It’s How Big, Not How Often, That Counts

Soros' Batting Record

George Soros, one of the greatest investors of the last fifty years, has a fairly poor batting record when you look at the total number of strikeouts he’s had over his career. By his own account he’s been wrong about investments more than he’s been right. However, when he’s been right he’s been right BIG time:
"It's not whether you're right or wrong that's important, but how much money you make when you're right and how much you lose when you're wrong"; 
Unfortunately human behavioral biases make most of us shy away from taking lots of losses and trick us into giving up the potential big winners. Our problem is that our biased brains punish us much more for failure than they reward us for success: so we prefer frequent small wins and few losses to frequent small losses and few wins. And, as Soros proves, our brains are wrong.  Fortunately there are a few simple techniques that guide us right.

Long-shots and Favourites

The probability of a horse winning a race is encoded in its odds. All things being equal the better the odds then the more likely the horse is to win the race. If we were to only bet on favourites then we’d lose money overall, after the racetracks have taken their cut. What we actually want to bet on are the outsiders whose odds have been calculated incorrectly. The 100-1 outsider with an actual 1 in 5 chance of winning is a better bet than the evens money favourite with a 1 in 2 chance of winning.

Of course, if we always bet on the favourite we’ll get more winners and less losers. And this will make our brains very happy because, as we all know, our brains are loss averse, as we saw in Tiger Woods is Loss Averse, Too. In stock investing , in order to keep our loss averse brains happy, we will sell our winners, in order to make sure they never become losers, and keep our losers, in the hope that they become winners.

This behaviour is perfectly rational from our brain’s perspective because losses cause us pain and winners give us pleasure: a phenomena described in Of Mice and Templeton Moments. Unfortunately from an investment perspective it’s completely stupid, because our best chances of success tend to lie with our winners, not our losers.

Is the Price Right?

This same irrationality drives people to chase glamour stocks, popular firms riding the crest of some wave or another. Of course the earnings forecasts look wonderful, especially if projected forwards to infinity, but when you invest on some company on an earnings multiple of 100 you’re backing an odds-on favourite in conditions that don’t favour it, as the research we looked at in Don't Overpay For Growth showed.

Our mental confusion between frequency of winners and size of winners makes the world of difference to investment returns. Almost without exception the world’s great investors make a calculation of the odds ahead of time. Take Buffett, from this highly relevant paper, Ruminations on Risk:
“Take the probability of loss times the amount of possible loss from the probability of gain times the amount of possible gain. That is what we’re trying to do. It’s imperfect, but that’s what it’s all about.”
So consider a lowly rated stock which is heavily backed by assets – a classic value investment. Usually such stocks are lowly rated because they don’t have much going for them – the chances of a loss may be significant. However, the size of the loss is limited by the underlying assets, so the actual risk to our capital may be minimal. On the other hand although there may be only a small chance of success if the management can turn the business around you might be looking at significant gains. So if the small probability of a large gain has a greater value than the high probability of a small loss then it's worth investing, because even if you'll likely lose money on several such investments it only takes one success to make it worthwhile. 

The Babe Ruth Effect

Thinking about investment this way, worrying about the potential magnitudes of loss and gain, should be fundamental to investors, but all too often the desperate craving of our brains for guaranteed loss avoidance gets in the way. The only way to sensibly counter this is to recognise the urge and to guard against it – preferably by doing the analysis beforehand, rather than after the event.

The technique is far from perfect, but highlighting magnitude over frequency is rarely done, even in professional investing circles. It’s what this article calls the “Babe Ruth Effect”:
"Building a portfolio that can deliver superior performance requires that you evaluate each investment using expected value analysis. What is striking is that the leading thinkers across varied fields—including horse betting, casino gambling, and investing—all emphasize the same point. We call it the Babe Ruth effect: even though Ruth struck out a lot, he was one of baseball’s greatest hitters.

The reason that the lesson about expected value is universal is that all probabilistic exercises have similar features. Internalizing this lesson, on the other hand, is difficult because it runs against human nature in a very fundamental way."
Decision Trees

The classic way to think about this is using decision trees. Decisions trees are really an elementary form of reasoning but they’re very powerful because they force us to think about the odds of all the possibilities, instead of just the ones we prefer – they enforce a form of statistical reasoning, in terms of expected frequencies and magnitudes, that our non-statistical brains tend to shy away from. But the beauty of them is that they do this in a non-statistical way which doesn’t send our wetware into a woeful wipeout.  Indeed, good visualisation of data seems to help us analyse it more effectively, as we saw in Technical Analysis on Display.

This Primer for Decision-making Professionals gives an overview of the decision tree technique.  Of course, putting all of your faith in this type of analysis is another sort of behavioral flaw, another case of man-with-a-hammer syndrome.  As with all systems if you put garbage in you get garbage out, and many of the inputs will be, at best intelligent, and imperfect, guesses.  Even so, if you keep records of these guesses and can then persuade your reluctant brain to go back and visit the scene of past mistakes, most people will generally get better.  And if, after a while, you don't improve then that's your brain telling you something important along the lines of "invest in index funds".

Win Big, Lose Often

The win big, lose often concept goes against the grain, but it emphasises the need to focus on expected value when making investment decisions.  Betting on sure-fire winners is a darn good way of minimising losers, but a darn lousy way of making a decent return: unless you've somehow identified an otherwise unidentified growth star.  On the other hand, buying some gormless company that's odds-on to go bust because it's a value investing opportunity isn't biasing the odds to the upside either.

We don't need to be Soros or Buffett or Babe Ruth to profit from these types of approaches.  Anything that helps us debias our malfeasant investing brains is a good thing, and forcing them to do some elementary probability won't do them any harm when it comes to improving worldly rationality either.  Hey, next thing you know we'll all be hitting home runs as well.


NormanB said...

Your analogy to race track betting is wrong. In a perfect betting world it wouldn't make much difference to the final outcome if you bet favorites or long shots, the 20% vig would hurt everyone.

But in the actual world of betting people take much more risk on than the horse's actual chances. Thus you have favorite bettors 'only' losing about 10% per bet while the long,long shot bettor loses 50% per bet. The alure of making 20x your bet draws more people to that bet than the horse's actual chances. said...

I like your comments on probability of winning versus size of winner. I spent a lot of time trying to learn to trade and that factor alone is what I've tried to use to control risk. I wrote a post about it.