John Maynard Keynes wrote in 1924 that, “in the long run, we are all dead”. Existential concerns of a rather more pressing nature afflict pension funds in the Europe and the US as they wrestle with a combined shortfall of more than $600bn (€504bn). The ‘perfect storm’ of falling equity values and tumbling interest rates that caused the gaping hole between assets and liabilities has prompted regulators to scrutinise schemes as never before.
Solvency rules that were once applied to insurance and banking are spreading to the domain of pension funds. Denmark started down this path in 2002 when a new accounting rule required that pension liabilities be measured using a standard long bond rate (similar to that now applied by IAS 19). That was followed by solvency test that measured what would happen to a fund if there were a 12% decline in equity values and a 0.7% decline in bond yields. Such a scenario seems far from theoretical today.
Sweden now applies solvency rules and a strict regime will be introduced by De Nederlandsche Bank, the Dutch regulator, in 2007. As well as applying the now usual strict mark-to-market accounting methodology for assets and liabilities, Dutch funds will be expected to maintain a funded ratio of at least 105%, or make good the difference within 12 months.
Though there are no specific solvency rules in the UK, the Pensions Act (2004) places a clear duty on the sponsor to properly fund its pension scheme. When the lingerie group Sherwood tried to buy back its shares last year, the regulator told the company it must first put £8m (€11.7m) into its under-funded pension fund.
Faced with these strictures pension fund officers might be tempted to wish that their long-run fate was rather closer to hand. It is clear that old approaches such as consensus-driven asset allocation strategies applied across thousands of heterogeneous pension funds (the 60% equity/40% bonds magic bullet) no longer fit the bill.
The good news is that there are tools and insights available from quantitative finance that can help address these practical issues. One particular innovation in risk management is ‘Within horizon risk measurement’, which evaluates risk of loss throughout the investment horizon rather than just at the end of it.

Pension funds have enjoyed the luxury of end of the investment horizon thinking. The duration of pension fund liabilities are typically between 15 and 30 years and pension officers, with the help of their actuaries and consultants, have typically conducted asset liability studies once every three or five years. But new solvency regulations have made within horizon risk measurement a necessity. You never know when the regulator will call.
For a typical European pension plan, the probability of a 10% loss (net of change in the present value of the liabilities) at the end of a five-year horizon is 17.6%. Using within horizon risk measurement, the probability of that a typical pension plan will experience a 10% loss at any point in time within the next five years is 54.6%.
Another way to think about risk as it is actually experienced by pension plans is ‘Regime dependent risk estimation’. Since Harry Markowitz introduced the idea of mean variance optimisation to create efficient portfolios, a common complaint has been that quants have been guilty of over-estimating the mean and under-estimating the variance; the result has been extreme portfolios that bearlittle resemblance to the real world choices of pension funds. Various methodologies have attempted to rein in this tendency, such as the equilibrium approach of the Black-Litterman model .
Regime dependent risk estimation takes a different tack, arguing that risk parameters (variance) such as standard deviation and correlation are not stable through time. Historical returns can in fact be separated into two regimes: one regime where risk is at normal levels and another defined by market turbulence. This division allows investors to estimate risk more realistically, in two distinct regimes
For European investors the volatility of domestic equities increases by more than 7% during periods of market turbulence. Similarly, the volatility of unhedged US equities, from a European perspective, increases by more than 8%. Not only do the assets become more volatile, the average correlation between them also increases by 4% during periods of market stress. That is double-trouble. Not only has risk increased overall
but the benefit of diversification
disappears just when we need it most.
Most often risk parameters are estimated from full samples of historical data, ignoring the Keynesian observation about the limitations of the long run. Risk parameters derived from events may better represent portfolio risk during turbulent regimes.
Within horizon risk management and regime dependent risk estimation can be combined. For example, within horizon risk measurement tells us that a European pension fund faces the probability of a 10% loss of 54.6% at some point in the next five years. In a turbulent regime that likelihood increases to 70.9%.
One of the great innovations of risk management in recent years has been to think about risk and return at the overall plan portfolio level. Risk budgeting has revolutionised how pension funds weigh up asset
allocation and manager selection decisions. The days when a fund manager could sell a hot product with an impressive five-year track-record to institutions without reference to its impact to overall plan level risk are now gone.
These new measures of risk are additional tools that can help asset owners to stress test their overall portfolios and point to ways to make them more robust. These portfolios will typically have higher allocations to alternative asset classes, particularly commodities. Commodity futures sound risky, summoning as they do images of boorish speculators in loud jackets. But at the overall portfolio level they make sense. Commodities are generally negatively correlated to financial assets, which makes them particularly valuable during turbulent markets.

The broad array of market neutral strategies are also attractive because as correlations rise, volatility falls. This is not necessarily intuitive, but a long/ short market neutral portfolio can be thought of like an immunised bond portfolio that precisely matches the assets (long) of a pension fund with its liabilities (short). The volatility of the surplus is zero. Likewise rising correlations in a long/short portfolio can actually lower the volatility of the net return. The ability to short also increases the efficiency of a portfolio if the fund manager can demonstrate skill.
The long-run is not quite what it used to be. It is worth remembering that in 1999 US pension funds were over-funded to the tune of $250bn and the average funding ratio of Dutch plans was 130%. The one thing we have all learnt since the bubble burst in 2000 is that markets are savage and history seems to be accelerating.
In another age pension fund officers might have relied on accumulated experience and gut instinct to guide them through these difficult waters. But the past is another country. Today the tools of quantitative finance can be applied to offer practical solutions to real investment problems. The cerebral is supplanting the abdominal and that is changing the asset management and pensions industries for the better.
Andrew Capon is editor-in-chief at State Street Global Markets Research in London. Sébastien Page is CFA vice-president at State Street Associates in Boston