1. A remedy for pension deficits
Lyxor’s Nathaniel Benzakien opened the event with a sobering reminder of the vast size of many pension fund deficits. Subsequently, a panel of pension fund allocators discussed their approach to alternative assets and their allocation.
Kathryn Graham, director of the BT Pension Scheme, the largest UK pension fund, said it has 2.5% allocated to hedge funds through both funds of funds and single manager funds. The UK’s second biggest pension fund, USS, now has 4% of its £32 billion of assets directly invested in hedge funds according to Roger Gray, the chief investment officer. The second largest US scheme, CALSTRS, has so far only allocated 1.5% of its $150 billion assets, but this proportion will grow over time. CALSTRS only started doing so two years ago, with macro and currency managers, who will soon be joined by commodity specialists, its Investment Officer Carrie Lo said. Both of these schemes are emphasising uncorrelated strategies due to their historically and persistently high equity weightings.
Currencies are one asset class that appealed to the panel. Simon Cox of consultants Mercer said that non-profit making participants created opportunities in the market, especially for emerging market currencies, an exposure USS leaves unhedged. CALSTRS also likes currencies and has four foreign exchange managers, while the BT scheme accesses currencies via multi-asset class macro traders.
Commodities are also popular. Mercer contended that the Goldman Sachs Commodity Index is not an efficient way to own commodities, and recommended using active managers in the space. USS, for its part, agreed that the GSCI is not ideal. It was noted that the BT scheme uses a mix of index and active managers. Mercer observed that there is an extra risk premium in infrastructure. This is an asset class sought out by the BT pension fund for inflation protection. CALSTRS said it applies the same rationale to its commodity allocation.
Contentious fees debate
Mark Fawcett of the new, nationwide enrolment UK pension scheme NEST was the only panellist that faced an over-riding constraint in the form of hedge fund fees, which he said should slide down as assets grow so that management fees only cover costs. Yet some the other participants advocated radical changes to fee structures. Albourne’s Simon Ruddick expressed a personal desire for what he termed ‘de-beta-ized’ performance fees – to apply only to the alpha component of returns – but said this need not necessarily entail lower fees for many hedge funds. Ruddick said traditional asset managers are actually more expensive than hedge funds if the actively managed element is accurately identified, because most of their returns come from beta that could be accessed at ultra low cost. USS and CALSTRS were both keen to see performance fee payment terms aligned with their investment holding periods of three to six years. USS said it does not generally expect fee discounts unless it seeds a manager.
2. Explaining hedge fund returns
Ruddick’s point about separating alpha from beta was explored by acclaimed author Professor Francois Serge L’Habitant of EDHEC and of Kedge Capital in his lecture about using factor models to explain hedge fund returns. Included here are highlights of just a few broad themes from the detailed discussion that referred to a number of seminal academic papers.
L’Habitant argued that factor models can often statistically explain the performance of hedge fund indices, but are far less successful for individual hedge funds, echoing EDHEC’s stated view that a satisfactory factor model for hedge fund returns continues to be elusive. The reasons for this range from explanatory variables being overlooked to delayed correlations being ignored. Other reasons include omitting to look at non-linear links and forgetting regime changes.
To start with the first area where analysis may be remiss, L’Habitant said that the apparent discovery of a pure alpha manager is often an illusion, because more often than not, an analyst has not been imaginative enough in the search for explanatory factors. Investors therefore need to experiment with using wider libraries of factors and indices to figure out what is really driving hedge fund returns.
Even when investors have identified the relevant factors, they may still miss the trick as lagged relationships may not show up in contemporaneous correlations. So, investors also need to incorporate variable time lags into their models, sometimes to allow for ‘stale pricing’ issues.
What often matters more is that hedge funds have non-linear return patterns that do not register as correlations, which measure only linear relationships. Two examples of non-linear links are squared functions and option type payoff profiles, and investors also need to add these to their analytical toolbox to understand many hedge funds. L’Habitant even argued that hedge funds with linearly explainable return profiles are best ignored by investors because the added value of hedge funds comes from their non-linearity, for instance in terms of asymmetric return profiles.
L’Habitant also cautioned against interpreting market timing as security selection alpha. If variable beta in bull and bear markets is driving returns, then the top down market direction call rather than bottom up security selection is the source of returns. Whether tactical beta is a type of alpha was not discussed, but investors should be clear about what species of alpha they are getting.
3. Portfolios and risk forecasting
The quadratic and option-like return profiles discussed by L’Habitant are just two of many hedge fund return patterns that do not conform to a normal distribution. In fact, normally distributed bell curve hedge fund return profiles are the exception rather than the rule, and the New Edge Prime Brokerage Advanced Modelling for Alternative Investments research chair at EDHEC has been investigating the issue further.
Every single hedge fund strategy fails the Jarque – Bera test of normality, according to Professor Lionel Martellini. That throws into question the use of standard mean variance optimisation techniques, since the mean and variance only fully describe a normal distribution. To gauge a non-normal or non-Gaussian distribution, higher order moments – and co-moments for portfolio construction purposes – need to be calculated: namely skewness, kurtosis, co-skewness and co-kurtosis.
This can be a computationally intensive: a 100 asset portfolio, for example, has over 4 million co-kurtosis coefficients. To address this ‘dimensionality’ problem and the heightened risk of incorrect estimation when more parameters are estimated through space than through time, EDHEC uses special statistical techniques to shrink the number of parameters that need to be estimated.
The result is more reliable estimates of the co-skew and co-kurtoisis: so we now have actionable and practical metrics that can feed into the quantitative fund selection process. If investors typically assess new investments in terms of their marginal contribution to portfolio volatility, they should also consider appropriately calculated ‘coskewness beta’ and ‘cokurtosis beta’: the extent to which adding an investment to a portfolio increases (or reduces) its skewness, or its kurtosis. EDHEC research suggests these extra estimates would have led to better returns per unit of risk. Focusing on top down allocations, convertible bond arbitrage and equity market neutral have historically had a neutral impact on skew and kurtosis, which have typically been increased by long/short equity and event driven strategies. The two strategies that have tended to reduce the asymmetry of returns and the fatness of tails are CTAs and global macro.
Tail risk forecasting
To drill deeper into one aspect of non-normal hedge fund return distributions, Stoyan Stoyanov of EDHEC’s Singapore office has done research into whether the ‘tails’ or extremes of return distributions, rather than the central or base case scenarios, are best used to forecast risk.
To start with, Stoyanov argued that fat-tailed distributions are here to stay, because volatility has a habit of clustering, whereby high volatility begets further volatility. These volatility patterns would soon throw markets off the Gaussian course, even if return distributions started out with a nice bell curved shape. And in practice the starting point is not even normal: even if the factors that drive hedge fund returns are normally distributed, Stoyanov asserted, harking back to L’Habitant’s talk, that hedge fund returns are not linearly related to the factors.
Because volatility correlates better across markets than returns, the trick is to forecast it rather than returns in trying to better gauge the chances of extreme outcomes. EDHEC have concerns about many volatility forecasting methods, including Modified VaR, Extreme Value Theory and Exponentially Weighted Moving Averages. However useful these models may be most of the time, they often reveal flaws during the extreme tail circumstances where a good forecast is most badly needed. Specifically, many models run into problems when the most extreme 5% of outcomes are encountered.
In contrast to the advanced techniques recommended by other EDHEC research, Stoyanov’s substantial survey of the volatility forecasting industry arrived at a relatively simple conclusion: that good old fashioned implied volatility (inferred from option prices) is often still the best forecaster, even if options do not exist for all markets. For instance, the much quoted VIX index is only based on the S&P 500 US equity index, and has no inputs from bond, currency, credit or commodity markets. A compromise solution EDHEC suggested is building a broader, multi-asset class VIX index as a proxy for hedge fund volatility – and incorporating this into forward looking portfolio construction.
4. Augmenting OTC valuation methods
It is undeniable that both investors and portfolio managers are now very occupied with the methods of valuing OTC derivatives. Not long ago such instruments had a low profile behind the scenes in the back office. What changed?
For starters, when liquidity evaporates as it did in 2008 by definition there are no bids in the market so far more assets have to be marked to models. Moreover, structured product regulations in France and Luxembourg force participants to justify their basis for pricing. Sometimes the very solvency of a fund can hinge upon valuation disputes: to have any hope of effectively challenging a margin call from a broker, hedge funds must be able to demonstrate defensible valuation methods.
Societe Generale said that the repercussions of the credit crisis have increased not only the extent but also the complexity of pricing many over the counter derivatives. More inputs need to be collected from a wider array of sources and there is also more latitude for varying other pricing assumptions.
• Credit risk, once overlooked in the structured products world, is now, pace Lehman, a valuation input and sometimes a critical one.
• A euro swap on the Euribor curve, involving different maturities, can no longer be discounted with one curve. Variables that decoupled during the credit crisis have still not re-converged, so there may be a need to build each yield curve afresh and also to maintain updated curves.
• The speed of events in 2008 also required other inputs to be recalibrated more often, but Soc Gen sayvolatility changed so fast that the calibration process still became less reliable. That made it harder to price currency options, for instance.
Soc Gen structure their pricing unit into three divisions: the middle office sets up and carries out the routines; the financial engineers design and maintain all manner of models, and keep checking for discrepancies against other models, prices and participants; while the data management department is responsible for gathering and cleaning data (such as seasonally adjusting inflation) from multiple sources – not always a simple task. For example, yield curves could come from Bloomberg and dividend estimates from IBES, while over the counter brokers would need to provide equity volatility inputs for swaptions, and exotic variables, like estimates of implied correlation, would come from investment banks.
When so many stages are involved, there is no shortage of things that can go wrong every day. ‘Garbage in, garbage out’ is only the most obvious problem arising from inaccurate data. Higher class conundrums include badly specified models, such as overfitted ones and sometimes no benchmark exists to validate outputs. When exotic and structured products are involved there is not even a consensus over what model to use, let alone how to benchmark its results: Monte Carlo simulations and trees are just two widely used models for path dependent products.
The analysis of discrepancies is also a multi-dimensional task. The static price of the derivative is only the most visible variable – sensitivity to changes in underlyings also needs to be considered. For some products expected cashflows are the real yardstick, while others are measured against implied parameters such as the probability of hitting an option strike price or barrier. Mismatches can be caused by data quirks, differences between how data is mapped into models and the choice of method to hedge more exotic parameters such as correlation.
Soc Gen are pragmatic enough to accept that neither their rigorous, independent third party valuations nor actual counterparty quotes provide any guarantee of being able to unwind at that level: they are just indications. Soc Gen also seems to be realistic in not expecting to perfectly synchronise their prices with other quotes or valuations. The objective is to keep discrepancies within an acceptable margin rather than eliminate them altogether.
Research papers, with appropriate academic citations, formulas and so forth can be downloaded free of charge from the “research” tab at www.edhec.com