For a long time, I've pointed out that momentum and defensive stocks tend to do better than they should in theory. This poses the question: how risky are they?

My table might help answer this. It shows returns and some standard measures of risk for my no-thought portfolios over the past 10 years: there are of course countless ways of measuring defensives and momentum, but these portfolios are, I hope, representative of the general properties of such stocks.

Risk and return on no-thought portfolios | |||||
---|---|---|---|---|---|

Momentum | Defensives | Value | High beta | FTSE 350 | |

Return | 9.58 | 3.49 | -4.77 | -2.37 | 1.85 |

Std deviation | 20.47 | 13.89 | 31.14 | 33.15 | 18.70 |

Sharpe ratio | 0.47 | 0.25 | -0.15 | -0.07 | 0.10 |

Beta | 0.82 | 0.62 | 1.23 | 1.48 | 1.00 |

Worst month | -17.5 | -20.4 | -37.7 | -43.2 | -25.8 |

Alpha | 8.47 | 2.15 | -4.16 | -2.05 | 0.00 |

(p-value, %) | 5.7 | 37.7 | 51.6 | 71.4 | na |

Annualised data based on weekly returns in the past 10 years |

This shows that momentum has indeed done well. Excluding dividends and dealing costs, momentum has given a return of 9.6 per cent per year against just 1.8 per cent for the FTSE 350. This has come at the price of slightly higher volatility. But despite this the Sharpe ratio for momentum (returns divided by standard deviation) is much better than that for the market.

This extra volatility is not because momentum carries extra market risk. In fact the opposite. Momentum's beta is (on average) less than one.

Nor is the higher volatility associated with greater tail risk. Quite the opposite. The worst monthly loss on momentum has been 17.5 per cent, which is less than the worst loss on the market.

Nor do momentum stocks carry unusual amounts of cyclical risk. I can say this because of the performance of my value portfolio. It suffered catastrophic losses in the 2008-09 recession which haven't (yet) been offset by their subsequent recovery. This tells us that value stocks (or at least those on the very highest yields) are heavily exposed to cyclical risk.

We can therefore assess stocks' cyclical risk by looking at their correlations with my value portfolio. If we look at absolute returns on our portfolios, they are all positively correlated with value and with each other. This is because all have a common exposure to market risk. If, however, we look at returns relative to the market we see a different picture. There is zero correlation between momentum and value. This suggests that momentum doesn't carry very much cyclical risk.

This is not a quirk of my portfolios. Researchers at AQR Capital Management have found that value and momentum are negatively correlated in other data sets.

None of this rules out the possibility that momentum is exposed to some other risks. But the fact that it is relatively lightly exposed to market risk, tail risk and cyclical risk suggests to me that momentum should be attractive to many investors.

Turning to defensive stocks, we see much what we'd expect - a lower but positive beta and less volatility than the market.

Also, defensives are to some extent a mirror image of high beta. Relative returns on the two portfolios are negatively correlated: better than average weeks for defensives usually see worse than average weeks for high beta stocks and vice versa. And while defensives have a good Sharpe ratio, high beta stocks have a bad one. This is consistent with the "betting against beta" theory proposed by Andrea Frazzini and Lasse Heje Pedersen - that high beta assets underperform while low beta ones outperform.

All this is summarised by our portfolios' alphas - their returns controlling for market risk. Momentum has a huge alpha, of 8.5 per cent per year, defensives a respectable one and value and high beta a negative one.

Here, though, lies a surprise. None of these alphas are statistically significant in the standard statistical sense. Even the alpha on momentum has a p-value of 5.7 per cent, which is above the conventional (but controversial) threshold for statistical significance.

Fans of the efficient markets hypothesis might interpret these as evidence that markets are indeed efficient - because the apparently good returns on momentum and defensives might be due to good luck.

They might have a point in the case of the negative alpha on value. This might be an artefact of the fact that the past 10 years contains a catastrophic recession. If you are moderately optimistic about economic volatility, you might believe that our data over-samples disasters and so overstates the defects of value stocks. In a sample in which deep recessions were rarer, value would look better.

Otherwise, though, I'm not sure the objection is right, for two reasons.

One is that there's a difference between statistical and economic significance. Momentum offers us a good chance of beating the market while taking on only moderate risk. This chance might well be worth taking. As Deirdre McCloskey has said, you don't confine your bets on horses to those on odds of 19 to one on or narrower.

Secondly, the evidence that defensives and momentum beat the market is not of course confined to these portfolios. It exists around the world and for long periods and is even found in assets other than equities. My portfolios thus merely corroborate other evidence. It is this wealth of data, rather than any single piece of evidence, that points to momentum and defensives doing well on average. Replicability matters more than p-values.

Nevertheless, these high p-values on our alphas do contain one important message. They tell us that in volatile environments such as stock markets there is a high ratio of noise to signal. This means that in single runs of data such as your own portfolios or particular funds it is difficult to distinguish between genuine outperformance (or underperformance) and mere luck, even over long periods. For me, this is a reason to trust investment strategies more than individual fund managers.