Fischer Black was right. Somewhat

CFM quants show timing and extent of mean reversion using a highly data-intensive study

In a seminal paper published in 1986 called Noise, Fischer Black took the grim view that in the context of financial models, research would rarely lead to any reasonable conclusion because of the noise that creeps into observations.

He argued that because of the effect of noise, one can never really know how far away price is from value. Intuitively, however, he said an efficient market is one in which price and value are within a factor two – meaning the price is more than half of value and less than twice value.

Two was an arbitrary number here of course, but he added that although some might be sceptical of his views, “someday, these conclusions will be widely accepted”.

He wasn’t wrong.

In this month’s first technical, Black was right: price is within a factor 2 of value, Jean-Philippe Bouchaud, chairman and head of research at Capital Fund Management (CFM) in Paris, Stefano Ciliberti, head of alternative beta research, Yves Lempérière, head of alpha research, Adam Majewski and Kevin Sin Ronia, both members of the alpha research team, and Philip Seager, the head of alternative beta, all from CFM, show Black’s assumptions about price and value hold – to a degree.

It has been intuitively understood for a long time that prices tend to mean revert to the true value of the asset in the long term, and that trend following strategies – which buy and sell assets according to the expectation that a price trend will continue – are profitable over short periods of time. But how long each effect hits price movement and by how much have been open questions.

In their new paper, the quants attempt to answer these questions by using a very large dataset, consisting of daily futures prices on indexes, bonds, foreign exchange and commodities since 1960, and monthly spot prices since 1800, to calibrate the mean-reversion time and the factor by which price and value differ.

They start by assuming asset returns are described by a mean-reversion process driven by positively correlated noise – the latter forms the trending part of the model. The model uses four key parameters: the volatility of the price; a mean-reversion timescale; the strength of the trend; and the timescale of the trend.

You can imagine the price as kind of attached to the fundamental value with a string, and if the string is too extended it is going to pull back the price

Jean-Philippe Bouchaud, CFM

The mean-reversion timescale is treated like the spring constant – a variable used to describe the stiffness of a spring in physics. The more the spring is extended, the higher the force in the opposite direction, which brings it back to its original shape. Within the CFM quants’ work, this translates into a higher mean-reverting effect when a considerable amount of time has passed.

“You can imagine the price as kind of attached to the fundamental value with a string, and if the string is too extended it is going to pull back the price,” says Bouchaud.

On calibrating the model to the dataset, the quants find mean reversion tends to kick in roughly after two years of trend following and prices revert to their mean within six years. They also show that prices tend to differ from value by a factor of 1.5 rather than two, as Black postulated.

The long term

The long timescale under which prices revert to value also shows that the efficient markets hypothesis, which assumes arbitrageurs would come in and trade away the difference between price and value, does not hold unless the timescale is very long.

This calls for strategies that act as a hedge to trend following strategies in the long term, says CFM’s Bouchaud, as trend following cannot be expected to go on forever.

“If trend following tends to extend over many, many years, then it is intuitive it is going to stop, so having some element of this universal mean reversion on a very long timescale makes sense,” says Bouchaud.

However, since trend following has a better Sharpe ratio, or risk-adjusted returns, more weight should be applied to trend following.

“Trend following has a long-term Sharpe of around 0.8 to 1 and mean reversion has a Sharpe of 0.2 to 0.3, so there is a factor of 3 between the two. So it makes sense to give three times as much weight to trend following than to long-term mean reversion,” argues Bouchaud, adding a similar strategy has been in place at CFM since March this year.

A number of studies have been carried out in the past attempting to quantify mean reversion. Perhaps the biggest advantages the CFM quants had were the presence of an extensive dataset covering a wide range of asset classes spanning across  200 years, and a simple model to calibrate. While the model is simple, sometimes it pays to let the data do the talking, which is what the quants have done in the paper. A simple look at the data over a longer period of time shows the clear effect of mean reversion on returns. And now that much of the data heavy lifting has been done by the quants, others can use the results to calibrate their strategies.

“This study can help investment professionals to calibrate their cross-asset momentum and value strategies,” says one Paris-based portfolio manager.