More than painting by numbers

Understanding correlation is essential to consistent investment achievement, but it takes more than just a good head for numbers

Correlation, defined as the extent to which different assets or asset classes are affected by the same market conditions, is a key part of any risk-management strategy in a multi-asset trading environment. Correlation estimates are a crucial element of any hedge fund's investment strategy, both in terms of identifying opportunities and mitigating risk. After all, a key raison d'être for hedge funds is the ability to deliver returns that are uncorrelated to major market movements. However, over the past 10 years, the increased globalisation of trade flows has contributed to a marked increase in correlation both within and between major asset classes. As competition among the world's 9,000 hedge funds intensifies, few if any can afford the accusation of ignoring this trend.

As investors expect multi-strategy funds to provide protection against overly correlated returns, due diligence should establish the measures fund managers take to achieve sustained portfolio. But how can investors effectively differentiate between funds that have constructed their portfolios properly and those that have taken insufficient measures? How do hedge funds manage the balance between the ancient art of stock-picking and the science of quantitative analysis to deliver alpha?

Hedge funds dealing with multiple asset classes look at correlation from a number of different angles. Not only does the fund need to consider the levels of correlation within and between trading teams, they must also weigh up risks across asset classes and geographic markets. For multi-strategy global arbitrage funds such as Lionhart, measuring correlations between different assets (and asset classes) helps identify opportunities and calculate the risk inherent in new strategies.

As an arbitrage fund, Lionhart's strategies typically involve an assessment of the relationships between similar assets, perhaps part of the same capital structure, such as preferred and common shares in the same company, or part of the same sector, for example selling one oil stock and buying another.

vital statistics

From this perspective, monitoring correlation is as fundamental to delivering returns as stock analysis or assessing default probability. At the individual trader and team level, it is comparatively simple to ensure that trading strategies, say in Asian stocks and European stocks, are uncorrelated through monitoring the volatilities and return distributions and/or other standard risk measurements. As a case in point, although a high Sharpe ratio, for example, may suggest a positive impact of a new strategy on a portfolio's returns, the trader must also run scenario testing to demonstrate the extent to which these returns are correlated to his team's portfolio.

Of course, multi-strategy, cross-asset funds must also calculate the correlation between portfolios focusing on different markets and assets to reduce risks. This task is complicated by the constantly changing nature of correlations between asset classes.

Over the past 10 years - a period that has witnessed increasingly higher levels of correlation between the US, European and Asian markets - some traditional market assumptions hold true (for example, the inverse relationship between equity and bond markets), but others may no longer hold (such as a long commodity position as a hedge for a long equity position).

In principle, historical analysis has demonstrated that correlations between markets are lower when market volatility is lower and higher when market volatility is higher.

Therefore, changes in correlation as a result of dramatic market shocks can come quickly, and funds need to ensure they can manage both gradual and sudden changes in correlations across asset classes.

balancing the risk book

It is the responsibility of a chief risk officer (CRO) - or chief investment officer (CIO), at some smaller funds - to balance the overall risk book and to ensure portfolios can handle sudden shocks.

In some respects, the role of CRO is similar to the head of investment at a fund of funds in that they usually look for the highest returns combined with the lowest correlation across all investment options in order to generate maximum alpha, with negatively correlated hedge funds or portfolios often the most highly valued.

Unlike a fund of funds, however, a hedge fund should be able to reallocate capital very quickly towards more advantageous trades and, as a result, can mitigate risk in a matter of minutes or hours or trade out of a complex portfolio position completely in a few days. Additionally, hedge funds are free to divert capital (and indeed human resources) towards particular market opportunities, rather than automatically allocating capital in advance.

So, on what basis does the CRO mitigate cross-asset correlation risk? A first step toward understanding the overall risk to returns may be to identify both the key risks and maximum potential losses across each individual trading book. For a fund with multiple independent trading teams, such as Lionhart, this approach helps build up an accurate picture of which common risks are impacting different asset classes in order to develop an appropriate counter-strategy or strategies with a global or macro view.

In normal market circumstances, science (that is, quantitative analysis and standards risk measurement techniques, such as multi-factor models, Value at Risk (VaR) and Monte Carlo simulations) is employed to identify and quantify risks, including increased correlation. Lionhart uses many tools, applications and models to ensure that risks are calculated and managed in a variety of ways: by calculating risk exposure to help ensure that all investments are suitably hedged; by comparing normal and high-volatility correlations; and by examining the potential effect of various scenarios or market changes on the fund's portfolio.

Once standard correlation, volatility estimates, and maximum loss calculations (on both a per product and systematic basis), have identified and quantified risks, multi-factor analysis models calculate a portfolio or fund's exposure to any single variable.

The CRO might compare the impact of an oil price rise (both in isolation and in combination with other factors, such as a rise in volatility or widening credit spreads) across a number of markets, such as US stocks, emerging market debt, or oil futures.

However, no matter the sophistication of the risk-measurement tools, the science of risk mitigation also relies heavily on the art or the experience of the chief risk officer, both in terms of deciding which risks to explore and what strategy to undertake to minimise risk.

For example, when oil prices are falling, a short-term mathematical analysis of an appropriate hedge might suggest a particular strategy, say, investment in a high-tech stock, but the CRO will still need to make the judgement on whether any particular stock (such as Apple Computer or Microsoft) is really related to the initial event to reduce the risk that the correlations suggest.

mathematical meltdown

Nevertheless, one can fall prey to a number of fallacies by relying only on mathematical modelling to avoid heightened correlation.

First, correlation between two events or price movements is not an indication of cause and effect, as it is so often mistakenly assumed. Just because the price of one stock has dragged another up with it, one cannot assume that the first movement has triggered the second.

Second, the mathematics that underpin risk models are subject to many caveats that can be conveniently swept under the carpet. When a stock reaches a new high (a common enough occurrence in a bull market), it moves out of its historical sampling range and as such its future behaviour cannot be predicted using the same assumptions. When a stock breaks through the $200 barrier, for example, one cannot rely on trading patterns established when it ranged between $150-175 to plot its future course.

Finally, apparent correlations must stand up to the reality test. For example, in these environmentally conscious times, the adult population of the US are increasingly buying hybrid cars while at the same time, the equity markets increase. Correlated? Yes. Useful as a predictive model towards risk management? Unlikely. The same applies for the predictions of Super Bowl winners and hundreds of other correlations monitored each year. It is always crucial to understand any potential correlations within the broader market context.

know the limit

To manage risk effectively, one must be constantly aware of the limitations of risk models. For example, some VaR calculations assume a normal distribution of returns for an asset or an asset class, which stands firmly at odds with experience. For a portfolio that includes hundreds of securities, testing the entire portfolio across a single scenario may also not be appropriate. Therefore, it is hugely important to understand what cannot be reliably quantified by the models yet to ensure that these risks too are fully understood, measured, and managed.

While cross-asset risk-management modelling has received a considerable amount of academic and theoretical investigation, producing a wide range of practical tools, choosing which tools to use means each fund manager may have a subtle or even vastly different approach to handling risk.

In more extreme market circumstances, reliance on mathematical calculations and correlation estimates is tempered even further. As volatility increases or a market shock hits, funds need to rely on more than statistics to make the right decisions. The fund manager's market experience and know-how must come to the fore in order to avoid or offset the consequences of market correlation.

Moreover, he must decide at what stage the assumptions underpinning the science of risk management become untenable and at which stage they still provide valuable guidance. In times of crisis, art may hold sway over science, but preparation, prediction and scenario testing are still crucial to effective decision-making.

Take, for example, the US dollar's comparatively steady and predictable level of correlation against other major currencies and asset classes. The dollar's performance has defied even the Sage of Omaha, but Warren Buffet's bet against the greenback may yet deliver in the event of a marked switch out of dollar-denominated assets in Asia. This would clearly have far reaching and unpredictable effects in many markets, but should leave no hedge fund exposed.

As the warning flags increase in frequency, (for example, changes in US interest rate policy), so should the hedge fund's willingness to consider a departure from normal assumptions and tactics. Using confidence intervals to judge when risk models become less reliable and when to seek insurance against the portfolio's exposure is one strategy that could be employed in the event of a sharp drop in the value of the dollar.

For the most likely sources of market crises, some hedge funds - including Lionhart - have catastrophe plans in place and have already tested their portfolios against crisis scenarios, with blueprints for likely trading tactics.

In times of relative market calm, it is tempting to play down the potential speed, impact and frequency of shocks to the financial system. However, it only takes a short leap of imagination to map the path to a major crisis from recent worrying headlines such as Thailand's flirtation with exchange controls to Russia's dominance of gas supplies to Europe.

Even if one estimates conservatively the frequency of major market shocks (perhaps every two years), funds of funds and other investors need to understand how hedge funds protect their returns when extreme circumstances threaten a wide range of trading strategies.

discovering correlation risk

For potential investors seeking to assess a multi-strategy, cross-asset fund's risk-management strategy and ability to avoid correlation risk, there are many questions to ask. For the purposes of this article, I have attempted to boil them down to the following areas:

Tools - As well as interrogating the way funds use VaR and other standard risk-management models within the investment process it is important to ask which non-statistical methods they use to calculate and offset correlation.

Style drift - As past performance is no guarantee of future returns, investors should explore how sustainable a fund's activities are and whether the opportunities that are currently bringing in returns will still exist in the future.

Unexpected returns - Funds should be able to explain both unexpectedly good and bad returns as this displays the necessary command of the factors that influence price change across markets. Risk may show itself in the form of excess profits before it produces large losses.

Uncorrelated by design - Finally, and most crucially, every hedge fund should be able to justify its investment approach by demonstrating to investors that it generates returns in a way that is demonstrably unique.

No hedge fund can guarantee perfect uncorrelated returns across all asset classes at all times, and certainly should not attempt to convince investors that purely statistical models can achieve this in isolation.

Unquestionably, the science of investment is being enhanced through the application of technology to the process, but for the time being at least it still requires the artist to complete the picture.