Given the capacity constraints on local inflation-linked bond markets, what are other options for hedging long-term inflation-linked liabilities? This is a question Ontario Teachers’ Pension Plan has been deliberating on as it supports an academic chair at EDHEC-Risk Institute with a focus on analysing the design of novel forms of liability-hedging portfolios that do not solely rely on inflation-linked securities. *Lionel Martellini and Vincent Milhau from EDHEC discuss the research.*

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**Hedging inflation-linked liabilities without inflation-linked bonds **

A long-term concern over possible enhanced inflation uncertainty has increased the need for investors to hedge against changes in price levels, a problem of particularly critical importance for pension funds that have pension payments explicitly indexed with respect to changes in consumer price levels.

The implementation of liability-hedging portfolios (or LHP), also known as liability-driven investment portfolios (or LDI portfolios) for inflation-linked liabilities has become relatively straight forward in situations where either cash instruments (inflation-linked bonds, or IL bonds, also known as Treasury Inflation Protected Securities (or TIPS), when the issuer is a sovereign state) or dedicated over-the-counter (OTC) derivatives (such as inflation swaps) can be used to achieve perfect hedging.

More generally, however, the lack of capacity for inflation-linked cash instruments and the increasing concern over counterparty risk for derivatives-based solutions leaves most investors with the presence of non-hedgeable inflation risk.

Another outstanding problem, even when perfect inflation hedging is possible, is that such solutions generate very modest performance given that real returns on inflation-protected securities, negatively impacted by the presence of a significant inflation risk premium, are typically very low.

In this context, the Ontario Teachers’ Pension Plan (OTPP or Teachers’) has been supporting an academic research chair at EDHEC-Risk Institute with a focus on analysing the design of novel forms of liability-hedging portfolios that do not solely rely on inflation-linked securities.

The main research question addressed in the initial stages of the research project was the following: *In the presence of capacity constraints on the local inflation-linked bonds market, can one expect a suitably-designed portfolio, potentially involving nominal bonds, foreign inflation-linked bonds and real assets, to be a reliable, and robust across economic regimes, substitute for real bonds in the context of hedging long-term inflation-linked liabilities? *

**Liability risk hedging versus inflation risk hedging **

The focus for a pension fund with inflation-indexed liabilities should not be on inflation risk hedging, but on liability risk hedging.

While the two concepts coincide at liability maturity, they do not coincide otherwise because the *present value *of liabilities is exposed to interest rate risk (unexpected changes in real rates) in addition to inflation risk (unexpected changes in realised inflation).

As clear evidence of this distinction, while long-term IL bonds with corresponding duration are the best liability-matching instruments for IL liabilities, the short-term correlation between changes in inflation and the return on long-term IL bonds is close to zero.

From a quantitative standpoint, our analysis unambiguously shows that for long-term constant maturity inflation-linked liabilities, real rate risk strongly dominates realised inflation risk within liability risk. This is because real rate uncertainty is compounded by time-horizon, while inflation risk uncertainty is not. In other words, unexpected changes in real rates explain an overwhelming fraction of short-term changes in the funding ratio for a pension fund with inflation-linked liabilities. It is only at liability maturity that interest rate risk vanishes and inflation risk remains the only source of uncertainty.

In the end, only IL bonds allow for a perfect match for IL liabilities over both short horizons and long horizons.

**Expected inflation risk versus realised inflation risk **

In a situation where inflation-linked bonds or inflation swaps are not available, at least not at all times and not for the whole inflation exposure, natural substitute candidates would be nominal bonds, since they have well-defined interest rate exposure.

One key concern, however, is that nominal bonds are exposed to changes in *nominal *rates, as opposed to changes in *real *rates.

In other words, the value of a nominal bond portfolio is impacted by changes in real rates but also changes in *expected *inflation, while IL bonds and IL liabilities are only exposed to changes in real rates (and also changes in realised inflation, but this again is not a substantial problem when assessing the short-term risk of long-dated liabilities).

In other words, while *realised *inflation risk is not a serious problem for long-term constant maturity IL liabilities, *expected *inflation risk can be because it has no impact on IL liabilities but has a deep impact on nominal bond portfolios that are typically used as substitutes for IL bonds. This is because the expected inflation duration is equal to the real rate duration (and also equal to the standard duration) for nominal bonds, while the expected inflation duration is zero for inflation-linked bonds.

The concern here would be a strong increase in expected inflation, which would lead to a drop in nominal bond prices assuming real rates stay constant, while it would leave liability values unaffected. In fact, the strong positive correlation between realised inflation and expected inflation would imply, everything else being equal, a positive performance of IL liabilities in the case of a positive shock to inflation expectations.

Our historical analysis going back to the ‘60s confirms that a large positive shock to expected inflation has almost always led to a drop in nominal bond prices and an increase in liability values (estimated based on a qualified proxy for expected inflation). In such situations, we have also found that commodities (proxied by the Goldman Sachs Commodity Index or GSCI) have generated strong positive performance most of the time. In this context, one can expect the introduction of real assets in the liability-hedging portfolio to compensate for the poor performance of nominal bonds in the case of a jump in break-even inflation.

One key problem, however, is that while real assets such as commodities may indeed have attractive inflation hedging properties, they have poor interest rate hedging properties, since there is no well defined duration measure for commodities or even for real estate. As a consequence, introducing substantial allocations to real assets in liability-hedging portfolios would generate high volatility in the funding ratio in most market conditions, even though it might help in extreme situations with a high increase in expected inflation. We can summarise the investment policy implications as follows.

**Diversifying versus hedging expected inflation risk in nominal bond portfolios **

In a nutshell, we can look at the problem in this way:

- Most of the time, nominal bonds would be very good substitutes for inflation-linked bonds, with which they share well-defined real interest rate risk exposure, and they should therefore dominate in liability-hedging portfolios.
- That nominal bonds cannot be used to hedge the realised inflation risk exposure in IL liabilities is not a quantitatively meaningful problem in terms of short-term volatility of the funding ratio for long-term liabilities.
- On the other hand, since nominal bonds are exposed to expected inflation risk in addition to real rate risk, while IL liabilities are not, the liability-hedging qualities of nominal bonds would deteriorate in the case of large increases in expected inflation uncertainty, especially when shocks to expected inflation are driven by factors that are not related to interest rate risk.

From a conceptual perspective, two main approaches can be used to manage this risk of mismatch between the non-zero exposure of nominal bonds to changes in expected inflation and the zero exposure of inflation-linked bonds to the same risk factor.

*Focus on diversifying away expected inflation risk*

The strategy here would consist in holding at all times a dynamic mix of the liability-hedging portfolio that is optimal under different particular regimes (i.e., with more real assets or less), where the weights assigned to each liability-hedging portfolio at any point in time are taken to be a function of the estimated probability of being in each regime.

This dynamic diversification strategy contrasts with a static diversification strategy, where a static mix of the hedging portfolios that are optimal under each particular regime, which would involve holding too much of the real assets in the high expected inflation regime, and too little otherwise.

*Focus on hedging away expected inflation risk*

While a long-only position in nominal bonds will always have a negative exposure to unexpected inflation, long-short nominal-bond portfolio strategies can in principle be designed to achieve zero exposure to changes in unexpected inflation, while having a target exposure to changes in real rates equal to that of the liabilities. What remains to be thoroughly analysed is whether this strategy can be effectively implemented in practice. In particular, one needs to carefully assess the out-of-sample robustness of quantitative strategies based on imperfect parameter estimates that may suffer from sample risk.

*Diversifying expected inflation risk in nominal bond portfolios *

For the diversification of expected inflation risk we find the following:

- While realised and expected inflation risks have been relatively limited in the recent past in developed economies, a long-term analysis suggests that the presence of possible regime switches needs to be taken into account. A formal statistical analysis confirms that regimes with high expected inflation and low speed of mean-reversion in expected inflation would lead to a profound mismatch between long-only nominal bond performance and liability returns.
- Given that our analysis has confirmed that real assets in general, and commodities in particular, have been formally verified to perform well in the case of large positive shocks to expected inflation, in particular when these shocks are driven by increases in commodity prices, substantial benefits can be generated from a strategy dynamically weighting a nominal bond-dominated liability-hedging portfolio and a real asset-dominated nominal bond portfolio as a function of the probability to stay in the normal regime versus entering a high expected inflation regime.
- The benefits of such a strategy are robust with respect to the introduction of a realistic lag in terms of recognising the emergence of the high expected inflation regime. This finding is particularly important because the real-time identification of regime switches is a serious statistical challenge. In particular, formal Markov regime switching models would typically identify periods of increasing inflation risk, without distinguishing clearly between increases and decreases in expected inflation, and simpler, more robust approaches would therefore be recommended.
- In addition to substantial levels of turnover generated by the switch from a bond-dominated to a commodity-dominated liability-hedging portfolio, the strategy involves holding a liability-hedging portfolio with little or no fixed-income instruments in high expected inflation regimes, which is not only at odds with standard practice but also can prove a serious problem in the case of a substantial drop in real rates.

*Hedging expected inflation risk in nominal bond portfolios *

On hedging expected inflation risk, our findings can be summarised as follows:

- Liability risk management is about matching risk exposures of assets and liabilities. Real rate exposure (also known as real rate duration) can be explicitly measured for bonds as a function of observable variables, while it has to be empirically estimated for real assets, and can therefore be made to match the real rate exposure in the liabilities.
- On the other hand, the exposure of inflation-linked liabilities to expected inflation is zero, and therefore it should also be neutralised on the asset side to avoid introducing an ALM mismatch. While a long-only position in nominal bonds will always have a negative exposure to unexpected inflation, long-short nominal-bond portfolio strategies can in principle be designed to achieve zero exposure to changes in unexpected inflation, while having a target exposure to changes in real rates equal to that of the liabilities.
- In principle, a suitably-designed long/short nominal bond portfolio would have a substantially lower (if not zero) exposure to shocks to expected inflation compared to a standard long-only bond position, while allowing for an exposure to real rate risk targeted to be similar to that of the liabilities.
- The long duration bond has a higher sensitivity to changes in expected inflation but changes in expected inflation are less volatile for the long term; conversely, the short duration bond has a lower sensitivity to changes in expected inflation but changes in expected inflation are more volatile for the short-term. The suitable dynamic hedging strategy emerges from the quantitative analysis of this trade-off.
- In the presence of uncertainty about speed of mean reversion parameter estimates, our analysis suggest that a robust implementation of this strategy can generate substantial benefits, if not allowing for a perfect hedge, a conclusion which is supported by a detailed statistical analysis of the dynamics of the term structure of expected inflation.

**Policy implications **

Three main policy implications can be drawn from our research:

**Policy implication #1:**A static exposure to commodity (more generally real assets) in the liability-hedging portfolio would not be a good solution; whatever the exposure, it would be too high most of the time, in normal regimes where the poor interest rate hedging properties of real assets would generate substantial short-term funding ratio volatility, and too low in those rare market conditions with extreme increases in expected inflation.**Policy implication #2:**A dynamic exposure to commodity (more generally real assets) in the liability-hedging portfolio would be a reasonable approach to diversifying away the risk of a large positive shock to expected inflation. Using a parsimonious model based on an observable, persistent, state variable such as expected inflation, one would be able to switch, even with some reasonable delay, from a bonds-dominated liability-hedging portfolio to a commodities-dominated liability-hedging portfolio in the case of a strong increase in the likelihood of a regime with high expected inflation.**Policy implication #3:**A duration matching strategy involving long-short allocation to nominal bonds of different maturities would be a reasonable approach to hedging away the risk of a large positive shock to expected inflation. Aiming at setting to zero the exposure of the bond portfolio to expected inflation requires parameter estimates that tend to be noisy, a robust implementation of the strategy can be performed, based on the finding that changes in expected inflation are consistently larger in absolute values for short maturities versus long maturities.

*Lionel Martellini, professor of finance, EDHEC Business School, scientific director, EDHEC-Risk Institute*

*Vincent Milhau, deputy scientific director, EDHEC-Risk Institute*

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