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Thursday 3 December 2009

The Lottery of Stock Picking

Risk Seekers, Risk Fearers

On average stock traders lose money. So do people who play the lottery. Yet both sets of people will often buy insurance as well. On one hand people are risk takers, engaging in risky and usually unprofitable activities, yet on the other they’re risk adverse, looking to protect themselves against possible, although often unlikely, losses.

Mostly we don’t find this particularly odd. Yet it poses a particular problem for economists and psychologists trying to disentangle the various threads that make up the skein of the human condition. They feel we should either be risk seekers or risk fearers: to be simultaneously both suggests something strange is going on. Stock pickers take note: sell insurers, buy lotteries. Or is it the other way around?

Markowitz’s Lottery Puzzle

One of the earliest researchers to note this gambling/insurance peculiarity was Harry Markowitz who we've met before in Markowitz's Portfolio Theory and the Efficient Frontier. In the same year he published the paper that eventually led to modern Portfolio Theory, the efficient markets mayhem and a Nobel Prize he also wrote The Utility of Wealth in which he both described this confused risk model and sought to explain it.

It’s a bit of surprise to find the father of rational investing theories elaborating on a subject which describes how irrational people really are. However his two 1952 papers are linked. While The Utility of Wealth describes how people really behave Portfolio Selection describes how they should behave to maximise their wealth. We can’t blame Markowitz for the investment industry using his ideas with all the subtlety of a Mob family collecting a debt from the man who wasted their mother with a cheesegrater.

Models which really aim to describe the way humans deal with risk are deluded and denuded if they exclude the risk-seeking part of the human experience. Deluded because they ignore the evidence of everyday life and denuded because they strip away the essence of human experience. Humanity would still be trolling around on its knuckles in East Africa if curiosity about what was on the other side of the forest canopy hadn’t got the better of our ancestors.

Utility and Gambling

Yet we can’t ignore the fact that we’re also risk adverse under many conditions. Buying insurance is sometimes an intensely rational thing to do – to pay a small premium to protect against the loss of a large asset such as our home makes a lot of sense. As commonsense people rather than academic economists, we don’t see the problem in a combination of risk seeking and risk aversion. After all, a small flutter on the horses or a bit of bungee jumping adds to the spice of life.

The classical economic explanation of these contradictory behaviours is full of complex equations and inflecting graphs which worry about the nature of something called the utility function. Utility is, roughly speaking, the value that a person gets out of an activity. Utility can be considered, roughly (OK, very roughly), as ‘happiness’ and many people have pointed out that the apparent inconsistency between risk seeking and risk aversion can be explained if you view the positive utility of pleasure people get from gambling as exceeding the utility they lose through the monetary expense.

Utility and Stock Trading

However, there are other sorts of gambling of which, for our purposes, the business of stock trading is the most important. When the same trigger that makes minor gambling on lotteries and horses enjoyable also encourages major risk taking in stock investment this supposedly harmless pastime suddenly becomes a deadly serious problem. As Meir Statman puts it in Lottery Traders:
"People confuse the stock-holding game with the stock-trading game. The stock-holding game is a positive sum game : buyers of stocks can expect to receive, on average, more than they spend. However, the stock trading game is a negative-sum game. In the absence of trading costs, management fees and expenses, stock traders can expect to match the return of an index of all stocks. But they can expect to lag that index once trading costs are considered. "
The problem with utility based models is that they rather ignore the fact that people process information very inefficiently. We can, and often are, fooled into thinking that the utility of a thing is different from what it actually is. So buying a long-term warranty on a fridge is usually a waste of money and so is buying a lottery ticket or actively trading stocks, no matter how much pleasure we get out of these activities. We miscalculate – and sometimes it’s a good job we do, otherwise life would be a drab procession of accountancy courses.

The Utility of Social Class

The problems lie deeper than this. Studies of lottery gamblers show that the people who spend the most money are those who can least afford it. Conversely those who spend the most on insurance are those who can most afford the losses they’re insuring against. Markowitz’s paper points to a possible explanation for this: people aspire to move up from their current social class and to avoid dropping down to a lower one.

Developments of this by Coelho and McClure also offer a hint of an explanation for the old aphorism that there’s nothing more damaging to a man’s happiness than his brother-in-law becoming rich. If our happiness is determined relatively – by assessing our wealth against our peers – then our peers getting richer than us will make us unhappy. Or, in the jargon, our utility reduces. And, the researchers predict, we're likely to gamble more in the short-term to try to make up the defecit until our expectations about our peer group change.

The Illusion of Control

The sheer range of ways to invest gives investors every chance to delude themselves that they’re in charge. Ellen Langer pointed out as long ago as 1975 that illusion of control, the idea that people will behave as though they’re in control in situations where every outcome is actually determined by chance, seems to be part of human nature. As she puts it:
"...the more similar the chance situation is to a skill situation ... the greater will be the illusion of control. This illusion may be induced by introducing competition, choice, stimulus or response familiarity, or passive or active involvement into a chance situation. When these factors are present, people are more confident and are more likely to take risks".
Given that the vast majority of active funds and active traders do worse than simply buying and holding a basic index tracker you’d have thought the message would have got through by now. Illusion of control may cause more than financial risks. People still prefer to drive themselves for the same reason, despite the evidence that cars are the most dangerous way to travel any significant distance.

The only safe way of investing is to be constantly risk averse. There’s no contradiction in stock market investment and risk aversion – it simply means you need to insure yourself against the worst that can happen. Investing as though something is about to go badly wrong is the only safe option. After all, something is always about to go badly wrong, somewhere.

Avoiding Capital Mistakes

What most people can’t do is trade their way safely to riches – that’s to take on the risk seeking side of the equation. To do so at all is one thing, to do it without recognising it as an extension to natural risk seeking behaviour is entirely another.

There’s a part of us which embraces risk in order to better ourselves – to find the next fertile pasture, to seek a better world, to enrich our families and to remove ourselves from the monotony of the everyday grind. Without the drive to explore and take risks we’d still be wrestling chimps for food and using gravel as dental floss.

Risk taking is part of the human condition, to be embraced and cherished. But all things in their time and everything in its place – mistaking the stock market for a real world adventure playground is to make a capital mistake, in every possible sense.

Related Articles: Momentum Trading Madness, Markowitz's Portfolio Theory and The Efficient Frontier, The Psychology of Scams


  1. I don't think that stock investing needs to be risky, Tim.

    We think of it as risky because the dominant model for understanding stock investing (Buy-and-Hold) presumes risk. It doesn't prove that stock investing is risky. It assumes it. What if the model is wrong?

    I think the model is wrong.

    Stocks in the U.S. have been paying an average return of 6.5 real for a long. long time. Is that because stocks are risky and those who invest in them need to be compensated for taking on the risk? Or is it because those who own stocks own a share of U.S. productivity and U.S. productivity has long been sufficient to finance an average return of 6.5 real? I think it is the latter. I don't think risk has anything to do with it.

    Investing risk is optional. It is something that goes with not understanding how stocks work. There's no law of the universe that says that investing needs to be risky. Stocks are risky in the way that walking around in the dark is risky. The risk goes away when you turn on a light. When we learn the realities of stock investing, 80 percent of the risks we worry about today will disappear. At least that's my personal belief re this one.


  2. Very humorous the cheese grater tool. I've splashed around lately in some code that purportedly represents Markowitz' theory. Have not read his papers or books. So going at this from a code hound perspective I must say that I'm amazed at the (lately negative) ink this code/idea/theorem/philosophy receives.
    This code gives you ideal stocks weightings that will allow you to rebalance your portfolio optimally. Yes, based on historical data (there is no other kind).

  3. Hi,
    Interesting article. I don’t think playing the lottery has to be stupid. This view leaves out the value we get from the benefit of anticipation, which can be real pleasure as well. The question is: is the value of anticipation greater than the "cost of disappointment” (from not winning) and the “value of money to play in lottery” combined? I recently had a more detailed look at it:“are-lottery-players-stupid"

    and tell me what you think!
    Thanks, Nick

  4. Hi Nick

    Your point is addressed in the 7th paragraph :) But obviously my interests lie in how this apparently perverse behaviour relates to irrational investing decisions; in this case illusion of control.

    I do like your blog but I’m not sure about the equation! Consider, for instance, the negative ramifications of someone anticipating winning the lottery and not doing so. So you could balance the equation in many different ways, and without knowing the individual psychology of the individual it would be hard to know in advance what would increase happiness. However, if the research I’m quoting is correct then somehow you need to include the concept that happiness is relative to those you think are your social equals and is not purely internal and individual.

    In answer to your article’s question about whether lotteries are cynical enough to exploit their contestants I suggest reading the Meir Statman piece I linked to. The answer, though, is “yes”.

    And, as luck would have it, happiness is the topic of my next article.

  5. Gambling is the worst addiction. In the past one year my husband has been buying lottery tickets incessantly, lying to me, and staying out the entire night. He has got us into so much of debt that we had to sell our car. I usually find him glued to mega millions and play lotto.

  6. Interesting. I do it because I enjoy it. I know that shouldn't the only reason but I enjoy the game.

  7. Using stock index ETF's or futures only, not individual stocks:

    Historically, the way to beat the market is to buy after selling and then sell in sections, after the inevitable ramps back up, never letting your inventory of stock get too high.

    Avoiding buying right when heavy selling is going on is nice too. But you do need a consistent methodology to define your entry and exit points in a constantly changing market - tough.

    Using this buy-low sell-high approach you will:

    - under-perform the market during straight ramps up with hardly a pullback, but still make money

    - outperform the market when it is 'going nowhere'

    - outperform the market when it is selling off