Institutional investors make investment decisions based on a variety of measures of risk and risk-adjusted performance with maximum historical drawdown, defined as the largest peak-to-valley loss, among the most popular measures. In fact, ‘Best practices in alternative investments: due diligence’ (2010)1 require drawdown analysis as part of quantitative due diligence. However, there is a lack of thorough quantitative evaluation of whether drawdown-based approaches to portfolio management positively contribute to performance.
In our research paper ‘Portfolio management with drawdown-based measures,’ forthcoming in the Journal of Alternative Investments, we present results of a comprehensive study of both established and new drawdown-based approaches and the portfolio implications of using drawdowns in allocation decisions. We examine the robustness of approaches to noise in the data and analyse out-of-sample performance using 613 live and 1,384 defunct Commodity Trading Advisors over the 1993-2015 period within the simulation framework of Molyboga and L’Ahelec (2016)2 that incorporates the realistic constraints faced by institutional investors.
First, we investigate the issue of sensitivity of drawdown-based approaches to noise in the data by generating 1,000 random scenarios, calculating weights that minimise each drawdown-based measure and evaluating the weights against the true optimal weights. Each scenario uses five uncorrelated assets with 36 monthly returns that are independent and identically distributed and follow a standard normal distribution. By construction, true optimal weights for each asset are equal to 20% but the introduction of sampling error results in a divergent set of weights. We calculate the average distance between the calculated optimal weights and the true optimal weights to evaluate the sensitivity of each measure to sampling error. We find that a newly introduced drawdown-based measure, Modified Conditional Expected Drawdown (MCED), is more robust than either the conventional maximum historical drawdown (MDD) or the Conditional Expected Drawdown (CED) measures introduced in the research paper by Goldberg and Mahmoud (2014)3.
The range of MCED errors is 64.71%, whereas both CED and MDD have ranges of 100%. The percentage of relatively small errors between -20% and +20% is 94.14% for MCED, which is higher than the 86.90% for CED and the 86.56% for MDD. The standard deviation of its errors is 12.20%, which is lower than the 17.39% for CED and the 17.07% for MDD. Each metric shows that MCED is the most robust of the three drawdown-based measures to sample error.
Second, we evaluate MCED within the large-scale simulation framework of Molyboga and L’Ahelec (2016) imposed on a subset of hedge funds in the managed futures space that contains 613 live and 1,384 defunct funds over the 1993-2015 period. The framework incorporates the standard requirements of institutional investors regarding track record length, the amount of assets under management (AUM), and the number of funds in the portfolio. The methodology closely mimics the portfolio management decisions of institutional investors and incorporates investment constraints and investor preferences to produce results that are relevant for investors. We evaluate out-of-sample performance with several commonly used measures of standalone performance and marginal portfolio contribution.
We find that a modest 10% allocation to CTA portfolios improves the performance of the original 60-40 portfolio of stocks and bonds for all portfolio construction methodologies considered in the study. For the out-of-sample period between January 1999 and June 2015, a 10% allocation to managed futures improves the Sharpe ratio of the original portfolio from 0.365 to 0.390-0.404, on average, depending on the portfolio construction methodology. We repeat the marginal contribution analysis for a range of CTA allocations between 5% and 60%. Fig.3 shows that the average Sharpe ratio of the blended portfolios reaches its highest value of approximately 0.5 at 50% allocation to CTAs.
We also find that on a standalone basis the MCED-based equal-risk approach dominates the other drawdown-based techniques but doesnot outperform the equal volatility-adjusted approach (EVA) highlighted in Molyboga and L’Ahelec (2016).
This finding highlights the importance of carefully accounting for sample error, as reported in DeMiquel et al (2009)4, and cautions against over-relying on drawdown-based measures in portfolio management of traditional and alternative investments such as stocks, bonds, real estate and hedge funds.
1. ‘Best practices in alternative investments: due diligence’ (2010), Greenwich roundtable.
2. Molyboga, Marat, and Christophe L’Ahelec, 2016, A simulation-based methodology for evaluating hedge fund investments, Journal of Asset Management, forthcoming.
3. Goldberg, Lisa, and Ola Mahmoud, 2014, On a convex measure of drawdown risk, working paper.
4. DeMiquel, Victor, Lorenzo Garlappi, and Raman Uppal, 2009, Optimal versus naïve diversification: how efficient is the 1/N portfolio strategy, Review of Financial Studies 22, 1915-1953