Ignoring Serial Auto-correlation may understate Hedge Fund Volatility by more than 30%!

In a recent paper, Marcos Lopez de Prado of Hess Energy Trading Company and David H. Bailey of Lawrence Berkeley National Laboratory, derive closed form approximations for Expected Maximum Drawdown (MaxDD). They also derive formulae for the expected time to reach the Maximum Drawdown (t*) and the expected Maximum Time Under Water  (MaxTuW) , which under the assumption of IID Normality turns out to be 3 times the time taken to reach the maximum drawdown. Bailey and de Prado show that this ‘Triple Penance Rule’ holds independently of the Sharpe Ratio.

This has important consequences for people who may be using some combination of drawdown and Sharpe Ratio to stop out loss making funds.

Moreover, Bailey and de Prado show that under the more general case when first-order serial-auto-correlation is accounted for the Triple Penance rule may no longer apply as the higher volatility of positively serial auto correlated funds may enable them to recover faster than 3 x the length of time it took the drawdown to occur. 

They state,” We provide a theoretical justification to why investment firms typically set less strict stop-out rules to portfolio managers with higher Sharpe ratios, despite the fact that they should be expected to deliver superior performance. We generalize this framework to the case of first-order auto-correlated investment outcomes, and conclude that ignoring the effect of serial correlation leads to a gross underestimation of the downside potential of hedge fund strategies, by as much as 70%. We also estimate that some hedge funds may be firing more than three times the number of skilful portfolio managers, compared to the number that they were willing to accept, as a result of evaluating their performance through traditional metrics, such as the Sharpe ratio.We believe that our closed-formula compact expression for the estimation of drawdown potential, without having to assume IID cash flows, will open new practical applications in risk management, portfolio optimization and capital allocation”

We replicated the study performed by Bailey and de Prado and substituted the closed form approximation to scaling volatility for first-order serial correlation at lag 1 given by Carol Alexander in Market Models.

Where h= periodicity and q = the AR(1) first-order lag coefficient

We also compared the closed form approximation to the Blundell / Ward filter. See spreadsheet; and found good general agreement.

One of the criticisms of the expected Drawdown calculation is its reported poor out-of sample predictive power. In the case of the Normal IID assumptions there is significant understatement of the expected versus Actual maximum drawdowns experienced. Given that the calculation is entirely in-sample one would hope for e closer agreement. Including the impact of first-order serial autocorrelation does improve the agreement between actual and expected drawdowns quite materially however only at a very high confidence level of 99.6%. 

In line with Bailey and de Prado we found significant levels of first-order auto-correlation for 29 of the 33 HFRI Hedge Fund Indices. The Average level of AR(1) auto-correlation was 0.335 using monthly data which is considerably higher than the insignificant 0.127 and 0.089 for the MSCI World Equities Index and S&P500 Index.

At the average level of around 0.36 this implies that about 13.5% of this months return is influenced by the prior-month versus less than 1% in the case of the S&P500.

Those Hedge Fund Strategies for which there was no statistically significant first-order auto-correlation included; Yield Alternatives Index, Short Bias Index, FOF: Market Defensive Index and Macro: Systematic Diversified Index. The Systematic Diversified Index actually had very slightly negative auto-correlation implying more mean-reversion.

Assuming Normally IID returns, the average expected Maximum Drawdown for all strategies was -15.4% versus the -27.5% Maximum Drawdown actually experienced on average by all strategies. Adding back the impact of first-order autocorrelation generates an expected average Maximum Drawdown of -27.9% which is far closer to the actual.

The improvement is not universal though and the AR(1) calculation still underestimates actual drawdowns for the Equity Hedge (Total), Multi-Strategy, Sector - Technology/Healthcare, Relative Value (Total) , Event-Driven (Total) Index and FOF: Conservative Indices whilst over-estimating the drawdowns for the Emerging Markets (Total), Sector - Energy/Basic Materials, Emerging Markets: Asia ex-Japan, Emerging Markets: Latin America, and Emerging Markets: Russia/Eastern Europe Indices.

Average monthly volatility is some 38% higher when taking auto-correlation into account.

Previously published in "Opalesque Emerging Managers"

You can purchase the corresponding spreadsheet here:

Impact of Autocorrelation on Drawdown

Buy Now