New statistical techniques and the computing power to put them to work is opening a space for effective factor modelling of hedge funds, writes Robert J Frey
Fund returns are generated by two sources. The first are general, the systematic effects of market and economic forces that are shared across a class of funds and are largely beyond the control of the manager. The second are specific, the idiosyncratic elements that can be broadly thought of as manager skill.
If we can separate these systematic and idiosyncratic exposures, then we gain powerful insights into what part of a fund’s returns came from factors beyond the control of the manager – luck, to give it word – and what part came from the skill of the manager.
Looking at funds for the last three or four years it might seem sensible simply to pick funds that had the highest returns. Unfortunately, when we do that, we have no idea if we are selecting managers with superior skill – we often end up selecting inferior managers whose poor performance is camouflaged by systematic exposures; and we tend to select managers with similar systematic exposures, leaving our portfolio far less diversified, and hence riskier, than we think.
Fortunately, there are statistical tools to create what are called factor models that can help us to disentangle these sources of return. Factor models have been used in the management of conventional investments for many years. Unfortunately, hedge funds and similar forms of alternative investments have characteristics that make building an effective factor model particularly difficult. Hedge fund strategies are complex, data are often sparse and incomplete, and strategies evolve and change over time. As a result, the application of factor models in the management of hedge fund investments has either not been done, or done poorly.
However, recent developments in advanced statistical methods, the relentless improvement in computing power and the accumulation of nearly 25 years of data for thousands of funds have, for the first time, provided us with the resources to build factor models of hedge funds.
In the area of statistical theory, Markov chain Monte Carlo (MCMC) techniques allow for the application of Bayesian models that produce robust estimates in the face of fund data that cover a variety of different periods and contain missing or censored data values. One can also build in regime switching that identifies varying economic and market conditions and adapts the model parameters accordingly – for example, to capture the fact that a fund’s behaviour might be qualitatively different during bull markets versus bear markets.
Finally, advances in high performance computing, such as grid computing and the parallel computing architecture, CUDA, allow us to accomplish in minutes what used to take days of processing.
Developing and validating proprietary systems and tools while applying these technologies allows for the building of practical and effective factor models that cover the complex strategies employed in hedge funds.
In the parlance of factor models, a fund manager’s skill is the fund’s alpha and its exposures to various systematic factors are its betas. When sourcing funds, investors should identify those funds whose alphas are both high and statistically significant.
Nonetheless, the traditional approach of producing more standard statistical summaries of each fund’s performance, visiting its offices, interviewing and investigating its managers and performing a detailed due diligence study of its operations and business practices, remains crucial. When funds pass through the filters, they can become part of the investable universe. Portfolios can then be constructed in such a way that their collective factor exposures are balanced so that overall risks are diversified.
To see the benefits of an effective factor model, consider the following two examples using real fund histories. We illustrate the factor analyses of their cumulative log returns. The alpha returns are plotted in dark blue, the systematic returns in solid grey and the total return in light blue.
Figure 1 shows Fund A whose total return significantly outperformed the market over time. A deeper view, however, reveals that most of its returns are generated from its factor exposures and that its alpha is actually negative. Despite the seemingly rosy view of its top-level performance, one could achieve much better results by a slightly leveraged portfolio of various financial instruments, avoiding both the high fees charged and negative alpha of sub-par manager performance. This fund would also be a poor source of diversification because its exposure to various market factors gives it high correlation with similar funds.
We get a very different picture for Fund B in figure 2. It also achieved a total return that out performed the market. However, here the picture is quite different. It has limited factor exposure with most of its performance coming from its alpha – superior manager performance. This fund’s small factor exposures would make it only lightly correlated with other funds, making it an excellent source of diversification.
Advanced proprietary factor models can include the coverage provided by more conventional models. Thus, they can fine-tune a bespoke portfolio of hedge funds that take into account the factor risks of a client’s other investments or one that either takes on or avoids particular systematic exposures according to a client’s specifications.
Robert J Frey is chairman and CIO of FQS Capital, and a research professor and founding director of the programme in quantitative finance in the department of applied mathematics and statistics at Stony Brook University, New York