Tail risk has become part of the alpha vocabulary. But it’s not always clear what is meant – is it a true black swan event, something entirely unexpected? Arguably a potential Greek default is not a tail event – it’s been telegraphed for months. So maybe tail risk isn’t about building bulwarks against the improbable; maybe it’s more about managing the extreme events whose potential is already being signalled loud and clear. That’s the impetus behind a recent paper, “A constant volatility framework for managing tail risk.”
The authors, Alexandre Hocquard, Sunny Ng, and Nicolas Papageorgiou, all researchers at Brockhouse Cooper Asset Management in Montreal, with the latter also a professor at the HEC business school in Montreal, recently won an award for best research paper, sponsored by the Canadian chapter of the Alternative Investment Management Association and Hillsdale Investment Management in Toronto.
To be sure, traditional risk measures have failed during times of market crisis, most recently in 2008. “The swift and relentless correction in equity, commodity and real estate markets was a clear example of why diversification, both geographically and across assets classes, is neither a sufficient nor reliable risk control mechanism,” write the authors. But it’s not asset correlation that concerns the authors, it’s volatility. Unfortunately, the axiom that underlies modern portfolio theory is that volatility is constant, even though it is demonstrably untrue. Volatility is “time-varying.”
“One of the key assumptions of MPT,” the authors write, “is that asset returns follow a normal distribution with constant volatility. However if we examine Figure 1, which plots the levels of the S&P 500 index (blue line) and its implied volatility (red line) over the last 20 years, it clearly shows that volatility does not remain constant but in fact changes significantly over time. We note that, over the measurement period, the VIX index ranged from under 10% to a peak of over 77%.”
Their idea is not to eliminate volatility, but to manage it – by keeping volatility constant. Actually, it goes further than that. It’s to “normalize” volatility in line with the precepts of MPT.
But that’s easier said than done. “Typically, implementation of tail risk hedging has involved the use of equity put options. Unfortunately, the cost is often prohibitive and as a result the drag on the performance of the portfolio is significant.”
Better then, the authors recommend, to use some version of dynamic hedging. Yes, there will be a drag on performance. But it obviates broker premiums and offers a flexible and liquid approach to managing through changing volatility regimes, by opting for futures to go long and short.
Normalization takes the tail out of what would otherwise be an extreme event. As Papageorgiou et al, write: “The monthly decline in U.S. equity markets during October 2008 would be considered close to a four-standard-deviation event. Under the common assumption that returns are normally distributed … a monthly loss of that magnitude should occur approximately once every 750 years.”
However, October 2008 hardly stands out as the worst loss even in past 100 years, so the historical measure is not especially helpful. “Rather than the historical level, … [i]f we use the prevailing level of volatility as our reference point, the drawdown experienced in October 2008 is closer to a one-standard-deviation event. October 2008 suddenly becomes much less of a Black Swan, just an undesirable white one.”
The authors illustrate the point by comparing two distributions, each with the same mean. One has fatter tails than the other in the figure below. These are not necessarily the returns on two different assets classes, but could be the returns on a single asset, under different volatility conditions.
The authors divide volatility among three regimes: low, medium and high. The last occurs 8% of the time. But that’s where the drawdowns occur, with an average volatility of 33% and an annualized return of -38% Low volatility regimes happen 47% of the time, and produce an average volatility of 6% and a return of 19% – these are bull markets, where monthly returns tend to be serially correlated. In between is the Goldilocks tradeoff, volatility of 12% and returns of 7%.
This has two applications, according to Papageorgiou et al. “Firstly, most significant market corrections have been preceded by an increase in market volatility. By conditioning one’s exposure to the level of volatility in the market, the impact of the market correction will be significantly dampened. Secondly, empirical evidence shows that asset returns tend to be greater during periods of low volatility.”
Does it work? Yes and no. Certainly there is outperformance, as Figure 6 below indicates, using a Canadian pension fund proxy of 50% TSE stocks, 25% S&P 500 and 25% MSCI EAFE.
But it’s not fool-proof. It doesn’t work in all volatility regimes. The results, as illustrated in Table 2, are not terribly compelling for the 2000-2002 tech crash.
Despite that lack of all-weather protection, however, “correlations between the constant volatility funds and their underlying assets are always greater than 90%, demonstrating that the dynamic leverage does not dramatically alter the nature of the return series; it simply smooths the volatility exposure over time.”
There is a deeper message here for alpha managers. Instead of assuming tail events to be unusual, they ought to be treated as quite common – since they are. It’s just that MPT doesn’t capture them. Chasing tails is too important to left to comic strips.