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Appreciating the limitations of the ‘average’: Asset returns have fat tails!
Investing your money can be a risky business. If you play your cards right, you can make substantial returns; on the flip side, if things don’t go to plan, you can lose everything! The reason is that different assets have different risk profiles. For example, equities (shares in companies) tend to be seen as relatively risky – prices can fluctuate wildly from day to day. Buying bonds (lending money to governments or companies) tends to be a bit less risky (but not always!).
Cash tends to be seen as one of the safest assets, but even this isn’t certain: the bank where you hold your cash can go out of business, and if the government doesn’t bail it (and you) out, things can end badly. At the less extreme end of things, the value of cash is eroded by inflation: if inflation turns out to be very high, the real value of your cash can fall substantially.
But even though asset prices can fluctuate wildly, most of the time they don’t. Usually, assets yield a return of a few percentage points
every year. Now and again, their value may fall by a few percentage points and similarly, at certain times, they provide double-digit returns. Extreme returns – very high and very low – are relatively uncommon.
Think of this situation as being a bit like most people having near average birth weight, IQ test scores, blood pressure, height and so on. For example, you don’t see many very tall or very short people, but once in a while you may see someone over 6 and a half feet tall (rarely a good idea to challenge such a person to a game of basketball!).
All sorts of things follow this kind of pattern. In fact, it’s so ubiquitous that it has a name: the normal distribution. In Figure 16-2, the population is normally distributed (according to some variable of interest), which means that most of the population is concentrated near the average. As you move away from the average, observations become less and less frequent.
© John Wiley & Sons
Figure 16-2: The normal distribution.
Observations that are far from average are very rare according to the normal distribution. Sometimes asset returns are approximated using a normal distribution, and so, for example, most of the time if you buy equities you may expect a return of close to 7 per cent per year; however, sometimes you get higher returns and sometimes lower returns.
But financial economists point out that actually a normal distribution isn’t a good fit for asset returns, because as you move away from the mean of a normal distribution, the likelihood of observing an outcome falls dramatically. In technical speak, over two-thirds of observations are within one standard deviation of the mean (the standard deviation tells you how dispersed the data is); over 95 per cent of observations are within two standard deviations, and over 99 per cent are within three standard deviations. You can see this in Figure 16-3.
© John Wiley & Sons
Figure 16-3: Standard deviations from the mean.
If asset returns did follow a normal distribution, you’d expect asset prices to fall sometimes. When they did fall, you’d expect them only to fall by a few percentage points. Maybe once in your lifetime you’d see a substantial fall in asset prices (say, 20 per cent). In reality, however, large asset price falls happen relatively frequently. For example, large stock market falls occurred around the world during the 2008 financial crisis, after the 9/11 attacks, after the dot-com boom of the late 1990s, during the East Asia crisis of 1997 – the list goes on. Clearly, instead of being a once-in-a-lifetime event, large falls in asset prices happen every
few years.
For this reason, economists say that asset returns have fat tails – which basically means that extreme (usually bad) outcomes happen relatively frequently. Fat tails sounds quite funny, at least to us, but the idea is that the normal distribution has ‘thin tails’ because extreme events are so unlikely.
Take a look at Figure 16-3 the tails of the distribution cover those events to the far left and right of the mean. As you can see, those events are so unlikely that the tails are very ‘thin’. To make the distribution of asset returns more representative of reality, we need to fatten up those tails and in particular the left tail. Figure 16-4 shows a distribution that’s closer to the actual distribution of asset returns.
© John Wiley & Sons
Figure 16-4: Asset returns with fat tails.
So here’s the economists’ first line of defence when challenged about their knowledge of financial crises, or rather lack of: ‘Look, we’ve been telling you guys for years, asset returns have fat tails! Some major crisis is always on the horizon!’
Understanding why no one can predict crises
Knowing about economics is unlikely to make you rich – at least it certainly hasn’t for us! But (we hope) it can stop you from being conned.
Be highly sceptical when people tell you that they know what’s going to happen to the price of an asset. As we describe in this section, if what they’re telling you is true and based on public information, it would have already happened today. If you can make money out of this information, a good chance exists that the person has insider information, which is illegal to trade on!
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