It's the most tedious time of the year - when brokers give us their forecasts for where the FTSE 100 will be this time next year. What the brokers don't say, though, is that all forecasts should come with margins of error - and these margins are enormous.
Put it this way. Since 1900, the standard deviation of annual returns has been 20.3 per cent. This is equivalent to over 1000 points. If we apply this to a forecast for the FTSE 100 of just over 5300 for next December (a reasonable view), it implies that there's a two-thirds chance of the FTSE 100 being in the range 4250 to 6400 next December. And it implies that there's a one-third chance of it being outside even this huge range.
This assumes returns are wholly unpredictable. To the extent they are predictable, the range shrinks.
However, over periods as short as a year, predictability is limited. For example, since 1985 (using monthly data), the dividend yield can account for less than 20 per cent of the variation in subsequent annual returns. This leaves 80 per cent unexplained, which still gives us an error margin of 800 points either side of our forecast. More, in fact, because we can never be sure that past statistical relationships will continue to hold.
There's a further uncertainty; how are the risks to a forecast distributed? If returns were normally distributed - that is, as a bell curve - the answer would be simple. There'd be a 15.8 per cent chance of returns being one standard error below our forecast (1000 points, if there's no predictability), and a 2.3 per cent chance of them being two standard errors below expectations. This is what a normal distribution means.
However, returns mightn't be normally distributed, as my chart suggests. Since 1900 the (arithmetic) average annual real return has been 6.9 per cent, with a standard deviation of 20.3 percentage points. If returns were normally distributed, there should have been 17 years of returns better than 27.2 per cent. There have been only 11. And there should have been 17 years of returns worse than minus 13.4 per cent. There have been only 14.
Small deviations, then, have been less frequent than they "should" be.
But larger deviations have been at least as common. The market's worst year was 1974's 58.1 per cent loss. A normal distribution says we should get a loss of this magnitude only once every 1455 years. We've had it once in 109. Of course, one instance proves nothing. But this does corroborate evidence from higher-frequency returns that extreme returns are more likely than a normal distribution predicts.
So, not only is there enormous uncertainty about returns, there's also uncertainty about this uncertainty.
And this is no bad thing. Share prices next December will depend upon the decisions investors make then about valuations and future prospects. Do we we really want to live in a world in which our decisions can be anticipated months in advance? Wouldn't this be a world in which we lack autonomy? Unpredictability is the price we pay for freedom!
