Most people would spend less time to ponder a decision to buy a lottery ticket than they would to buy a share in a lottery company even though, pound-for-pound, the latter is certainly the better investment. For instance, Camelot Group, which runs the UK lottery, manages to wring annually almost £90m of pre-tax profits from the business, even after paying out 78% of the ticket sales to prize winners and to good causes*. After taxes, Camelot shareholders lay claim to almost a penny of every pound spent on lottery tickets. Compare this to the lot of the ticket buyers, who on average can expect a 45p loss.
People find ‘investments’ in lotteries, and securities with lottery-like pay-offs extremely appealing. This is because we humans tend to have an exaggerated dislike of losses, relative to our fondness for profits of the same magnitude, so we are attracted to any investment where the downside promises to be limited. We also have a tendency to misjudge low-probability outcomes, in this case that of scooping the jackpot, and to perceive them as being more likely than they really are. The lottery ticket, and a number of other popular investments, appeal to these common human preferences. There is nothing wrong, of course, with liking this kind of pay off distribution – statistically known as a positively skewed distribution. The only problem is that we tend to pay too much to own it. As a consequence, the long-run returns from holding such securities tends to be disappointing.
If one cannot make any good money from buying positively skewed distributions, you might ask, then perhaps one might do better from selling them. And you would be right, but what does this mean in practice? Well it means:
- owning Camelot rather than being among the hordes of lottery ticket owners;
- selling equity in your owner-managed firm (these tend to be positively skewed) and buying public equity instead;
- offering capital-guarantee products (again positively skewed) if one is a fund manager; - or, as my own parents should have done, ditching your kids’ premium bonds (a widely held, positively skewed retail investment) and buying them a nice toy instead.
A negatively skewed returns distribution is one that combines modest gains most of time with rare, but potentially hefty, losses. For example, returns from most of the world’s stocks and stock indices display precisely this kind of distribution. Most bond returns do too, apart from sovereign bonds and highly rated corporate debt. The pay-offs from many professional investment strategies (such as carry trading – a common practice among currency investors) also have this returns distribution. In fact, most of the securities one can buy, and strategies one can follow in asset markets have pay-off distributions that are negatively skewed. This explains why financial markets are such fearsome places to inhabit: they constantly confront us with the risk of a potentially large loss, to which we have an exaggerated aversion, and which we perceive to be far more probable than it really is. Investing, therefore, involves exposing ourselves to precisely the kind of stimuli that we as human beings find the most unpleasant.
Large swathes of the investing population hold no risky assets at all, such is their distaste for the pay-off distributions of financial securities. Where they do dabble in investment markets, it is often only to buy positively skewed assets like hot IPOs and highly-rated bonds, which consequently become overpriced. At the same time, in eschewing negative skewness, such investors leave those assets trading at a relative discount. Our behavioural preferences thereby give rise to measurable risk premiums in financial markets.
*2015
A version of this article was first published by TCAM Asset Management Ltd