Addressing IID Assumptions in Finance: Autocorrelation and Drawdowns in Performance Analysis
Financial data are typically not identically and independently distributed (IID), but standard tools for analyzing performance are based on this assumption with little information about how sensitive they are to violations of IID assumptions. This project will develop the different approaches for addressing autocorrelation observed in financial data that have recently been discussed in the literature.
Functions will be included in PerformanceAnalytics, an R package that provides a collection of econometric functions for performance and risk analysis. That package applies current research on return-based analysis of strategy or fund returns for risk, autocorrelation and illiquidity, persistence, style analysis and drift, clustering, quantile regression, and other topics.
Non-normality and autocorrelation can impact the performance of many standard measures that investors use to make decisions. Various authors, such as Lo (2002) and Burghardt, et. al. (2012), have noted that the effects of autocorrelation can be huge, but are largely ignored in practice. Burghardt observes that the effects are particularly interesting in the case of drawdowns, a widely used performance measure that describes the performance path of an investment.
The concept of drawdown, a cumulative loss of capital from a prior peak level, has long been used by investors to evaluate the performance of investment strategies and managers. The Commodity Futures Trading Commission’s (CFTC) mandatory disclosure even requires managed futures advisors to disclose their “worst peak-to-valley drawdown” as part of their performance description.
The utility of drawdown as a measure remains somewhat unclear. David Harding, Georgia Nakou and Ali Nejjar at Winton Capital Management note their frustration, offering that “... the conventional cursory use of drawdown as a statistic fails most or all of these tests, making it worse than useless.”
Investors are faced with an exit decision under uncertainty for a strategy or manager (sometimes referred to as a “stop-out”) as a fiduciary to protect the well-being of their assets. Consider a multi-strategy firm, where the executive managers must decide where and when to exit an investment agreement with one of their underlying portfolio managers. These decisions can be contentious and emotional, given that there is little theoretical justification for setting expectations and decision points.
Drawdown is a difficult measure to use effectively. On one hand, it is an interesting descriptive statistic and potentially useful when the analyst has an understanding of the return generating process underlying it. On the other hand, drawdown is practically difficult to compare across strategies for decision making.
Fortunately, the academic literature on non-IID effects and their consequences for measures like drawdown has been developing. Notable milestones include Grossman and Zhou (1993) and Meucci (2010), both of which discuss the continuous-rebalancing of the investment in a single asset. Cvitanic and Karatzas (1995) extended the framework to include multiple assets. Yang ans Zhong (2012) recently extended the idea into discrete time, in what they call “Rolling Economic Drawdown.” Checkhlov, Uraysev and Zabarankin (2003, 2005) introduce a risk measure called Conditional Drawdown-at-Risk (CDaR).
Several papers consider a measure of potential drawdown as a quantile as an analog to VaR, including Bailey and Lopez de Prado (2013), Lopez de Prado and Peijan (2004), Mendes and Leal (2005), and Hayes (2006). Magdon-Ismail and Atiya (2004) consider potential drawdown within an extreme value framework. Checkhlov, Uraysev and Zabarankin (2003 and 2005) develop a measure of an average of drawdowns experienced, as an analog to CVaR. Different closed-form and analytic solutions are proposed, such as in Burghardt and Liu (2012), where they employ a moving block bootstrap.
Magdon-Ismail and Atiya (2004) note that Calmar and Sterling ratios can be normalized to these expected drawdown measures.
Drawdown-related measures are only one example of a measure affected by non-normality and time-dependence. Lo (2002) shows that the Sharpe measure may be overestimated when hedge fund returns are autocorrelated. Similarly, common methods of annualization (the “square root of time” heuristic) from lower-frequency data would underestimate volatility.
More general solutions are proposed by Getmansky, Lo and Makarov (2004) and Okunev and White (2003), who offer two different methods to unsmooth hedge fund return series to recompose the “true” performance series. Okunev and White generalize the method developed by Geltner (1993) and Brooks and Kat (2002) to be applied to real estate investments.
The student in this project will develop from a list of specific functions identified from this body of literature to be included in PerformanceAnalytics, a widely used R package that provides a large collection of functions for returns-based performance and risk analysis. New code will be consistent with interfaces of other functions in PerformanceAnalytics.
In addition, the student will write complete documentation for each function using Roxygen2, including key equations and examples. If the reference includes specific data and accompanying code, the student will create an example or demo that shows the results from the paper can be replicated. Students may also consider creating a vignette that goes beyond the functional documentation to show how the functions might be used, perhaps with some extended examples.
In their proposal, students should demonstrate an understanding of the concepts discussed in the literature described above, including a brief discussion about how the ideas might be used by investors.
Applicants should have:
A successful applicant will: