Keeping track of changing scenarios
This article surveys some recent developments in portfolio risk management spreading through the European fund management industry, and speculates about likely changes in coming years. First it reviews the traditional approach (that is, the state-of-the-art portfolio risk management framework of the 1980s and 1990s). Then it discusses three recent innovations that are already in use by more sophisticated investors and likely to become more widespread: bottoms-up risk models; risk-budgeting; and the incorporation of hedge fund allocations into risk management systems.
The traditional approach to portfolio risk management was born in the 1950s and 1960s through the work of Markowitz, Sharpe and others, who laid the foundations of modern portfolio theory with the mean-variance framework. Subsequent work in the 1970s by Rosenberg, Ross and Sharpe highlighted the usefulness of factor models to capture the common sources of risk among individual assets. Factor models allowed the development of workable individual-security risk models within asset classes such as US equities or Japanese bonds.
The traditional approach uses a two-step methodology. First, the investor examines the allocation of funds across all the asset classes within his investment universe. Asset class returns are proxied by benchmarks designed to mimick the likely component portfolio of securities within the asset class. Trading off risk and return across asset classes, the investor determines an optimal weighting across asset classes. This is called the asset allocation step.
The second tier of the risk management system uses a set of factor models, each one describing the risk relationships of all securities within an asset class. The factor models provide total risk and active risk (risk relative to the benchmark) for the chosen component portfolios considered in isolation. In the traditional two-step methodology, the investor takes the overall asset class weight as given and allocates this fixed amount among the individual securities within the asset class. This is called the security selection step.
Bottoms-up risk modelling: An obvious deficiency of the traditional approach is the use of segmented risk models for separate asset classes. This traditional two-step approach misses the stronger cross-asset-class correlations between some style and industry factors, which are not well proxied by the benchmark correlations. So for example, consider an investor with a component portfolio in UK equities benchmarked to the FTSE-All Share and a component portfolio in US equities benchmarked to the S&P 500. With the traditional approach, the measured risk of his portfolio depends only upon the two asset class weights, the correlations between the two benchmarks, and the tracking error of each component portfolio against its benchmark. Some style and industry factors tend to co-vary across countries more strongly than aggregate market benchmarks. The aggregate portfolio will in fact be riskier if each of the two component portfolios has over-weights in the same industries (eg, both have a high manufacturing industry bias) versus if the two have offsetting industry exposures (eg, the UK component is biased toward manufacturing and the US component biased toward services, relative to benchmarks). The same logic applies to some style tilts associated with value, yield, size, etc.
In addition to cross-national covariances between factors, there are some strong covariances between particular equity and bond factors. For example, value stocks tend to have higher correlation with high-yield bonds than the average stock-bond benchmark correlation. The two-step approach cannot account for these potential sources of additional risk.
One fix-up to the traditional approach (which has been in use for many years) is to overlay a top-down ‘global’ factor model onto the risk management system. However, first-generation ‘global’ factor models cannot capture the level of detail available with single-asset-class factor models. Hence, first generation global factor models underperform individual-asset-class factor models within asset classes, even as they provide some insight into cross-asset-class covariability.
A naïve view is that one should just make the global factor model as rich in detail as the sum of the individual-asset-class models. However, this produces a massive increase in statistical noise in the factor model (due to the exponential increase in the number of covariances with added factors) and the resulting model is too noisy to be useful. So this naïve solution does not work in practice.
A new approach allows a ‘bottoms-up’ integrated factor model by borrowing advanced factor modelling technology from psychometrics. Psychometrics is the statistical measurement of human intelligence and behaviour – the statistical side of the science of psychology. Psychometricians employ a technique called ‘second-order factor modelling’. In second-order factor modelling one begins with a set of factors estimated from a collection of related factor models, and builds a second factor model using them as inputs. Second-order factor analysis is essentially a type of ‘factor analysis of factors’. This allows a large collection of individual-asset-class factor models to be combined into an integrated risk model without swamping the system in estimation noise.
In theory, investors using an integrated bottoms-up risk model do not need to make portfolio decisions in the traditional two-step way. But one advantage of an asset-allocation step and security selection step lies in the added simplicity and insight. With the use of a bottoms-up integrated risk model the asset allocation step usually remains in place but becomes more fluid. The investor can first choose an asset allocation across regions, observe the risk-return decomposition and consider its optimality, then switch to an allocation plan across security types (stocks, bonds, real estate) and observe a reconstituted risk-return decomposition. An integrated bottoms-up risk model gives consistent risk-return perspectives across any chosen classification system.
The bottoms-up integrated approach has opened up some new frontiers in the study of risk and return. For example, it allows one to think about how much of the risk and return associated with, say, UK banking stocks, comes from the UK equity market factor, the global banking industry factor and the residual factor, ‘the purely banking, purely British’ component of this factor return.
Risk budgeting risk: budgeting takes a new approach to portfolio decision-making. One can think of the ‘decision variables’ in the traditional approach as the chosen portfolio weights and the ‘budget constraint’ as the requirement that these weights sum to one. The portfolio manager’s decision problem is to find the collection of weights that optimise the risk/return tradeoff.
With risk budgeting, the investor fixes the amount of total risk for the aggregate portfolio, and then decides on holdings by allocating this risk across assets. The ‘budget constraint’ is the total risk of the portfolio and the ‘decision variables’ are the amounts of portfolio risk coming from each asset. This change in perspective can be insightful, since the investor is working directly in units of risk and return, which are what really determine portfolio optimality.
At first sight, the risk budgeting approach seems to make the choice problem more difficult. Risk does not add across assets so the ‘risk budget’ is not the sum of the risks of the chosen assets. However, marginal portfolio risks do sum across assets. Furthermore, if a portfolio is chosen optimally then the ratio of marginal risk to expected return should be the same for all assets. In the risk budgeting framework it is easy and intuitive to see whether a holding should be increased or decreased to improve the portfolio’s optimality. If an asset class or individual security has higher expected return per unit of marginal risk than others, then the investor should allocate more funds to it. This simple and intuitive decision rule gives the risk-budgeting approach great intuitive appeal. The new risk budgeting approach has applications both at the asset allocation level and also for individual security selection decisions.
Incorporating hedge funds into portfolio risk management systems: The phenomenal growth of hedge funds and their perceived outperformance has prompted new techniques for their inclusion in portfolio risk management systems.
There are three challenges: hedge funds’ lack of transparency, the observed autocorrelation of their measured returns, and their return nonlinearity.
Since hedge funds are typically unwilling to reveal asset positions or even their aggregate factor exposures, it is necessary to proxy their risk exposures from the limited information provided. Current best practice is to infer factor risk exposures from the average factor exposures of hedge fund indices with the same investment style classification (eg, equity long-short, fixed income arbitrage). The risk exposures of the style indices must be estimated from historical return analysis.
Many hedge funds (particularly within certain style classications such as convertible bond arbitrage) show strong positive autocorrelation in their returns. This reflects their marked-to-market valuations based on illiquid prices. This needs to be corrected for to determine true risk, which will be higher than the autocorrelated, marked-to-market returns seem to indicate. Nonlinearity in returns (particularly for hedge funds with substantial derivative positions) are difficult to treat adequately given the lack of transparency of hedge fund positions. Risk managers employ Monte Carlo and scenario stress testing to get a rough guide to their influence on portfolio risk.
Gregory Connor is a scientific adviser in the London office of Barra Inc