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Considering Hedge Funds in a LDI Perspective

Dr Gabriele Susinno, Unigestion

September 2008


The sequence of adverse financial events characterising the market behaviour of the new millennium has forced institutional investors, such as life insurances and pension funds, to revisit the paradigms applied to manage the asset over liabilities equilibrium. Indeed, potential difficulties embedded in periods of bear equity markets and falling interest rates combined with the increasing longevity (in Western countries life expectation increases by one year every four years) and new accounting rules have fostered the pace at which institutional investors are revisiting the potential synergies between the two fundamental poles of competence: actuary and asset management.

As we outline in the sequel, the liabilities profile of life insurance and pension funds is characterised by the sale of a pre-agreed financial payoff at a given maturity and over a time interval. Therefore, in financial terms, the risk distribution of the present value of their liabilities is characterised by a left skew, typical of short volatility positions.

In summary, life insurance and defined benefit pension schemes are short options (figure 1) as they give guarantees in exchange of a stream of payments1 2.

Figure 1: Payoff Profiles of Defined Contribution (DC) and
Defined Benefits (DB) Pension Schemes.

In the old Eldorado of rising equity markets and high interest rates, most of the options embedded in defined benefits(DB) pension schemes or life insurance were out of the money, thus allowing for a strict dichotomy between actuarial estimates and asset allocation principles. However, pushed by the development and applications of finance theory, the changes in capital markets and amendments in the regulatory and accounting structures, institutional investors are progressively moving towards a more integrated view3. This is largely done by identifying the volatility of the funding ratio as the main risk factor to monitor and manage via a suitably adapted approach (figure 2).


Figure 2: Main Sources of Volatility Attached to the Liabilities and Outline of the LDI Risk Budgeting Approach.

Click on the image for an enlarged preview

Between the key ALM strategies used to control the relative equilibrium between assets and liabilities4, the best market practices are moving towards the liability driven investing (LDI), which constitutes the latest and more sophisticated form of ALM 1 5 6.

In this context the “ liability matching” and the “ return booster” objectives are clearly separated and the relative weight between the two is defined by the degree of risk tolerance (risk budget) of the sponsor. If the risk budget is large enough, the LDI approach will allow the sponsor to take advantage of additional investment opportunities. As the aim of LDI is to secure the expected liability cash flows at the lowest cost to the sponsor15, risk must always be measured against a liability benchmark to ensure that the risk budget is spent in the most effective way. LDI will then be judged against a liability benchmark such as “bonds plus x%”.

As shown in figure 2, LDI begins with a forecast of the liability cash flows and with the analysis of all the sources of volatility. This strategy, where investment decisions are made in reference to the liability profile, has already become popular in the UK who was an early mover into fair value accounting for pension funds with its accounting rule (FRS 17) fully implemented in January 2005, and is catching on in continental Europe, US and Asia.

It is only when the global framework is well established and the targets defined, that investors can outline the desirable properties of investments falling in the returns booster category.

Bringing Hedge Funds in the Context

As modern liability benchmarks are characterised by seeking an over performance with respect to classical fixed income instruments, a desirable property of any investment falling in the LDI return booster category is that it should, in the long term, grant a Libor+ like return. However, as the present value of the embedded options in the liability side is driven also by the asset’s volatility, the over performance cannot come at a cost of an increased volatility. In this context, volatility may be controlled either by seeking those investments which exhibit a systematic low correlation with the traditional markets or, more importantly, by seeking those investment opportunities which are able to adapt their dependency structure to the market state should it be bull or bear. In this case, the investment will be able to generate an appealing performance by exhibiting a dynamic beta whose variations depend upon market conditions. Last but not least, liabilities being characterised by a left skewed profile as they represent the sale of a guarantee, return booster investments cannot come at a risk of magnifying negative fat tails.

This is where the properties of alternative investments such as hedge funds must be considered. Indeed, hedge edge funds, being investment funds able to operate under fewer constraints than long-only traditional vehicles, are globally able to achieve interesting returns under a controlled volatility regime. However, “ hedge fund” is just a name to call a complex and heterogeneous universe7. A more specific analysis is therefore mandatory, in our view, to identify the subset of strategies which share most of the desired properties outlined above.

Hedge Funds Strategies Characterisation

In an effort of characterising the universe of hedge funds, it is possible, by analysing common characteristics, to recognise three main styles into which any specific hedge fund strategy may fall. The three styles, whose characteristics are described in table 1, are: tactical trading, arbitrage, and equity hedge.

Table 1: Simplified Hedge Funds Classification

Click on the image for an enlarged preview

  • Equity hedge strategies are those strategies highly active in equity management using long and short positions. They are characterised by a systematic high correlation and asymmetric excess returns with respect to an equity benchmark.
  • Arbitrage strategies are characterised by the constant quest of temporary/local market inefficiencies to be exploited. As it may be implicit in the name arbitrage, these strategies are characterised by a low volatility but, as they use local inefficiencies, they may be exposed to large downside deviations (fat tail risk). Managers belonging to this style may look for inefficiencies in non traditional risk factors which may add some liquidity and valuation risks.
  • Finally, tactical trading is the set of strategies that seek to improve a portfolio's return per unit of risk taken by actively managing deviations in asset allocation8. Returns are generated through views on relative value in global equity, bond, currency and commodity markets. They may be applied on a discretionary basis like global macros, or on a systematic basis like CTAs.

Figure 3: Beta of the Equity Hedge Style with World Equities, US Bonds and Commodities (Monthly Data from 31 Dec 1997 to 31 Mar 2008)


Click on the image for an enlarged preview

Figure 4: Beta of the Arbitrage Style with World Equities, US Bonds and Commodities (Monthly Data from 31 Dec 1997 to 31 Mar 2008)

Click on the image for an enlarged preview

Figure 5: Beta of the Tactical Trading Style with World Equities, US bonds and Commodities (Monthly Data from 31 Dec 1997 to 31 Mar 2008)

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Correlation and Adaptability to Market Conditions

As shown in figures 3, 4 and 5 representing the sensitivity of the three styles (respectively equity hedge, arbitrage and tactical trading) versus world equities, US bonds and commodities, we may observe the different historical behaviour of the three universes for different market conditions.

Indeed as expected, equity hedge strategies such as long/short, event-driven, and emerging markets are characterised by a quite stable high correlation with equity markets making these strategies of little use in a diversification process within a portfolio already exposed to equity markets. Arbitrage strategies are characterised by a systematically low correlation with equity markets. However, tactical trading strategies such as global macro, CTA, and short sellinga tend to exhibit a dynamical behaviour with respect to market conditions, being able to be low or even highly negatively correlated with equities in bear markets while being positively correlated with equities in bull markets.

Figure 6: Correlogram of Equity Hedge Strategies with Respect to Different Market Factors.

Click on the image for an enlarged preview

Note: Red corresponds to correlation at 1, while black corresponds to correlation at -1.
The first line being the correlation of the strategy index with itself is used as a test.


Figure 7: Correlogram of Arbitrage Strategies with Respect to Different Market Factors.

Click on the image for an enlarged preview

Note: Red corresponds to correlation at 1, while black corresponds to correlation at -1.
The first line being the correlation of the strategy index with itself is used as a test.

Figure 8: Correlogram of Tactical Trading Strategies with Respect to Different Market Factors.

Click on the image for an enlarged preview

Note: Red corresponds to correlation at 1, while black corresponds to correlation at -1.
The first line being the correlation of the strategy index with itself is used as a test.

The analysis of the evolution of correlation with respect to different market factors confirms that equity hedge strategies (figure 6) have a stable high correlation with equities and average negative correlation with bonds. Arbitrage (figure 7) and tactical trading (figure 8) strategies exhibit an interesting adaptability to market conditions over the full range of market factors. However darker colours in tactical trading strategies (figure 8) are the signature of a higher adaptability to market conditions and a desirable property of an investment candidate for a return booster block in a LDI framework.

Figure 9: Dynamic Estimate of β to Equities for Tactical Trading Strategies

Click on the image for an enlarged preview

The ability of tactical trading strategies to dynamically react to market changes can be investigated using advanced filtering techniques9. As opposed to traditional linear regressions who force the analyst to consider a constant beta over a rolling window, thus introducing a systematic lag in the observations of sensitivities, filters are techniques that allow considering time dependent betas. This enables the analyst to investigate synchronous behavioural changes via the observation of historical dynamic betas. Figure 9 clearly shows that sign changes of tactical trading beta versus equities (red line) appear in coincidence with the bull bear transition in equity market.

Distributional Analysis: Fat Tails

Another interesting characteristic to be investigated is the general distributional behaviour. As exposed in the introduction, life insurance and pension funds being exposed to a negative skew due to the short embedded options sold with the policies and pension plans, it is of utmost importance to control the left tail behaviour of investments to be included in the returns booster block. Again the three styles exhibit a specific profile when tails are analysed.

Figure 10: Quantile-Quantile (q-q) Plotsb for Different Hedge Fund Strategies

Click on the image for an enlarged preview

Figure 10 (cont1): q-q Plots for Different Hedge Fund Strategies

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Figure 10 (cont2): q-q Plots for Different Hedge Fund Strategies

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In figure 10, we show the quantile-quantile (q-q) plots for the three hedge fund styles. We may observe that, while equity hedge and arbitrage strategies are exposed to large negative fat tails, tactical trading strategies have negative fat tails close to normal (low deviation from the dashed red line representing the tail of a normal distribution).


The close-to-normal behaviour of tactical trading, coupled with the ability to produce a dynamic sensitivity to market factors, makes this strategy suitable to be included in a return booster block in the plight of an LDI exercise. Moreover the analysis of the rolling performance of tactical trading shows that these strategies show a reasonably good capacity to outperform Libor, which is in line with the need of beating a “bond + x%” liability benchmark.



This article is first published by Unigestion in June 2008.



1 D Blake, Pension Economics, John Wiley & Sons, 2006

2 G Susinno et al, Optional Insurance, Risk Books: The Cutting Hedge Collection, 2003

3 P Embrechts, 1998

4 T Ziemba, M Mulvey, Worldwide Assets and Liability Modeling, Cambridge University Press, 1999

5 D Blake, Pension Finance, John Wiley & Sons, 2006

6 B Scherer, Liability Hedging and Portfolio Choice, Risk Books, London, 2005

7G Susinno, M Miceli Using Trees to Grow Money, Risk Magazine, November 2003

8 D Potjer, C Gould Global Tactical Asset AllocationRisk Books, 2007

9 M. Grewal, A Andrews, Kalman Filtering: Theory and Practice, John Wiley & Sons, 2001


a We do include short selling within the tactical trading style as it constitutes a sort of insurance to be tactically integrated in a portfolio management process.

b The q-q plot is a graphical technique for determining if two data sets come from populations with a common distribution. In figure 10, we compare the probability distribution of hedge fund returns (points) with the one we would have obtained if returns were drawn from a normal distribution (red dashed line).

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