For a long time, this has been in doubt. The good long-run performance of defensive stocks led many to suspect that it is low risk, not high, that's associated with good returns. "There is generally no empirical risk-reward relation," concluded Eric Falkenstein of Pine River Capital Management in one study.
However, new research by Bryan Kelly at the University of Chicago and Hao Jiang of Erasmus University challenges this. They show that aggregate tail risk - measured by the number of shares suffering big losses in a month - leads to good aggregate returns; when tail risk is high, the market subsequently does well. And shares that are especially sensitive to tail risk do better in such times than shares that aren't so sensitive. Both facts are consistent with investors hating tail risk, and so avoiding shares that are exposed to it, with the result that such stocks offer good returns for the braver investor. In this sense, risk does generate returns.
Tail risk, however, is not the same as ordinary volatility or beta. Dr Kelly estimates that tail risk didn't much increase when volatility soared in the 2008-09 crisis - which is corroborated by the fact that the put-call ratio for S&P 500 options wasn't unusually high then; this ratio measures tail risk because if investors fear this a lot, they will want to buy lots of put options. It's quite possible for a share to have high beta and low tail risk - if, say, its covariance with the market is high on ordinary days rather than at times of exceptional losses. And defensive stocks might have high tail risk, if idiosyncratic bad news hits them on quiet days for the market generally.
This poses the question: why does tail risk matter more than ordinary volatility?
One reason might be that we are loss averse. We hate (say) the 5 per cent chance of an 80 per cent loss more than the 20 per cent chance of a 20 per cent loss, even though they have the same expected value. It's this that explains the existence of the insurance industry.
Such loss aversion might just be a preference. But it could be more. A big loss tends to undermine our worldview disproportionately more than does a small one: it dents our self-image as a good stockpicker and our faith in economic stability and competent management. In this, sense, it does psychological harm as well as financial. Big losses on individual assets can also threaten financial stability generally, if they cause their holders to become forced sellers of otherwise healthy assets.
There's another reason why tail risk matters. It can, says Dr Kelly, "have important aggregate real effects". Tail risk creates not just risk but uncertainty. And economists at Stanford University and the IMF have shown that this reduces capital spending and economic growth. It's entirely reasonable for investors to worry about this.
Right now, tail risk - as measured by the put-call ratio - is around its long-term average, so this doesn't tell us much about near-term market moves, But there is a more general message here. It's that the old saying 'you have to speculate to accumulate' might be right after all. It's just that we have to speculate upon a particular type of risk.
