Inflation Hedging with Alternative Investments

EAID 2008 Alternative Investment Conference Wednesday December 10, 3:15 pm - 4:45 pm Inflation Hedging with Alternative Investments Volker Ziemann Senior Research Engineer EDHEC Risk and Asset Management Research Center volker.ziemann@edhec.edu www.edhec-risk.com

Outline 1. Introduction 2. Difficulties with ad-hoc inflation hedging solutions 3. Horizon-dependent inflation hedging Modelling the inflation term structure Hedging potential of various asset classes 4. Conclusions and future research

Introduction Recent developments demonstrate the high uncertainty with regards to the level of inflation (very volatile in 2008) The current risk of deflation together with recession (=depression) will most certainly call for inflationary monetary policies (risk of overshooting) Institutional investors are exposed to unexpected shocks to future realized inflation (current low expected inflation may turn out into a nightmare!!!) Ad-hoc inflation hedging solutions are either costly (TIPS) or not available, depending on the considered measure of inflation Alternative investments have shown to offer attractive inflation hedging characteristics especially in times of inflation spikes Stability of inflation process calls for distinction between short-run and long-term analyses

Introduction Econometric theory offers such a distinction Based on a suitable econometric model we assess inflation hedging potentials of alternative investments classes and subclasses depending on: the investment horizon the type of inflation The idea is to propose customized inflation hedging portfolios depending on the investor s investment horizon and regulatory or client s constraints regarding the type of inflation More precisely we distinguish between consumer price index (CPI) inflation and Wage and Salary index (WAS) inflation Various sectors of commodity and real estate indices are utilized to hedge against inflation

Outline 1. Introduction 2. Difficulties with ad-hoc inflation hedging solutions 3. Horizon-dependent inflation hedging Modeling the inflation term structure Inflation hedging potential of alternative investments 4. Conclusions and future research

Difficulties with ad-hoc inflation hedging solutions Implementation of inflation-hedging portfolios has become relatively straightforward through TIPS TIPS allow to eliminate inflation risk and thus to define initial contribution so as to meet real benefit commitments Source: «Inflation-linked bonds from a central bank point of view, Garcia & van Rixtel, (Banco d Espana)

Difficulties with ad-hoc inflation hedging solutions Problem 1: Investment Horizon vs. available maturities Currently available TIPS maturities in the US: 5, 7, 10, 20 and 30 years But: future pension payments occur continuously Especially in the long run TIPS do not allow to alleviate the concern of price level uncertainty Problem 2: Costliness TIPS and inflation swaps usually exhibit low real returns (e.g. lack of inflation risk premia) as a consequence, inflation-protected LHP solutions generate very modest performance and limit the upside potential of the portfolio requiring high allocations to the more risky PSP so as to cut down the contributions illiquid market; inflation swaps additionally are exposed to bankruptcy risk of the issuer

Difficulties with ad-hoc inflation hedging solutions Problem 3: What if pension payments are indexed by something else then CPI-inflation such as Wages and Salaries? correlation coefficient: 36% CPI is the Consumer Price Index For All Urban Consumers and WAS the index entitled Compensation of Employees: Wages & Salary Accruals. Both series are seasonal adjusted. Details on http://research.stlouisfed.org/fred2/

Difficulties with ad-hoc inflation hedging solutions Problem 3: What if pension payments are indexed by something else then CPI-inflation such as Wages and Salaries?

Modelling the inflation term structure Vast literature on evidence for stock return predictability Dividend/Price ratio predicts stock returns similar relationships can be observed for earning-price ratios the economic reasoning is that the ratio of earnings (dividends) and prices should move one-on-one (Gordon growth model used by the FED)

We work with log-returns and log-prices: VAR model for stock returns (Campbell & Viceira (QJE, 1999): Price levels and there first differences enter into the above model This is the basic idea of VECM models The Cambpell-Viceira model can be seen as a restricted VECM model Inflation Hedging with Alternative Investments Modelling the inflation term structure + + = t t t t t t t t p d rf r c c p d rf r 2, 1, 1 1 1 2 2 1 1 2 1 ε ε β α β α t t t t t t t r R P P P P p = + = = = Δ ) log(1 log ) log( ) log( 1 1

Modelling the inflation term structure Price-Earning ratio highly auto-correlated (ACF1=0.994; ACF12=0.884) and highly stable (around a long-term average of roughly 16) High persistence in earning allows us to compare prices at different points in time if P/E substantially deviates from the long-term average we expect reversion to longterm equilibrium (e.g. high P/E -> P/E likely to decrease -> negative returns)

Modelling the inflation term structure This framework can be extended by: adding further predictive variables such as term spread, credit spread, nominal yields and T-Bills introducing further asset classes such as bonds, real estate and commodities adding CPI and WAS price indices to the set of variables accounting for long-term relationships between price indices and asset classes that will be determined by a statistical model rather than imposed by ex-ante economic theory (e.g. dividend-price ratio) VAR and VEC models deliver model-implied forward-looking returns and variances via the process of innovations ε: Δy = c + αβ ' y + ΓΔy + ε t+ 1 t t t+1

Modelling the inflation term structure Traditional Assets: Stocks: CRSP Value-weighted index of NYSE and AMEX listed stocks Bonds: Lehman US Treasury Aggregate T-Bill: 1 month treasury bills from CRSP Alternative Assets: Commodities: Goldman Sachs Commodity Indices (Energy, Industrial Metals, Precious Metals, Agriculture, Livestock) Real Estate: - REIF indices (Industrial, Office, Apartment, Retail) Economic predictive variables: Credit Spread: Difference of Moody s Baa and Aaa Corporate Bond yields Term Spread: Difference between 10Y and 3M treasury constant maturity yield Dividend yield from CRSP Data from Q1 1978 through Q4 2007

Modelling the inflation term structure We estimate the following econometric model: Δy = c + αβ ' y + ΓΔy + ε t+ 1 t t t+1 where Δy contains log-returns of stocks, bonds and alternative asset classes as well as economic predictive variables β hosts the co-integrating relations that define a long term equilibrium the number of co-integrating relationships is determined by the Johansen procedure and thus non-discretionary Writing the above model as and endless sum of past innovations (inverting the AR model to an MA model which requires stability) allows us to establish model-implied variances and correlations that depend on the investment horizon In order to address the concern of estimation risk we set up a base set of variables (stocks, bonds, economic predictors) + one of the price indices (CPI or CPI) and add subsequently one of the alternative asset classes a time

Hedging Potential of various asset classes Broad indices VAR overstates the long-term risks of stocks Correlation figures suggest that stocks better hedge wage inflation than CPIinflation Correlation increases with the investment horizon *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Broad indices VAR overstates the long-term risks of bonds Mean-reversion induced by longterm equilibria But, VAR also overstates correlation with price indices. Bonds are good hedgers in the long run, but VECM strongly cuts expected benefits *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Broad indices VAR overstates the long-term risks of Commodity index when modeled with CPI More importantly, VAR also underestimates correlation with price indices. very weak potential for wage-hedging *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Broad indices very stable volatility and correlation across different investment horizon Correlation with CPI implied by VECM sharply deviates from VAR-implied correlation REIFs seem to have desirable features for longterm CPI hedging constant correlation across time with WAS (above 40%) *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Sector indices VAR substantially overstates long term risks Correlation of energy sector more stable than in the case of the composite index *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Sector indices Important Differences between VAR and VECM implications (example of the equilibrium relation follows!!!) highly correlated with CPI especially in the medium and long term *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Sector indices VECM predicts very high correlations with CPI in the long-run (example of the equilibrium relation follows!!!) Decent correlation in the short-run with wage index (alternative to stocks since far less risky) *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Sector indices Best correlated asset with Wage index especially in the short run *dashed lines correspond to VAR-implied numbers and solid lines to VECM-implied numbers

Hedging Potential of various asset classes Example: Long-term equilibrium with Prec. Metals and CPI Estimated co-integration relationship: -21xCPI + 1.1xPrecMetals - 1.1xStocks + 11.6xBondPF We define the deleveraged LHP: 5.5%PrecMetals 5.5%Stocks + 62%BondPF Then, LHP and CPI move together (investor could put the remaining 38% in cash to assess upside potential)

Hedging Potential of various asset classes Example: Long-term equilibrium with Retail and CPI Estimated co-integration relationship: 20xCPI 2xRetail + 1.8xStocks 12.4xBondPF We define the deleveraged LHP as: 10% Retail 9% Stocks + 62% BondPF Then, LHP and CPI move together (investor could put the remaining 37% in cash to assess upside potential)

Hedging Potential of various asset classes Recap List of potential candidates for liability hedging portfolios Horizon Type of infl. Short Term (1-3 years) Medium Term (3-10 years) Long Term (10-40 years) CPI Energy Office Retail Prec. Metals Retail Prec. Metals WAS Retail Office Office Stocks Gov. Bonds Stocks Office

Conclusions and future research Some alternative asset classes exhibit attractive inflation hedging properties as measured by correlation with the price index (CPI or WAGE) Inflation hedging properties depend on investment horizon and type of inflation VAR and VECM implied correlations and variances are substantially different (e.g. for CPI-inflation, VAR overstates potential of Bonds and understates the potential of alternative classes such as precious metals and retail in our sample) Trade-off between complexity of the model and robustness (notably, we should assess the stability of long-term equilibria) These models may then be used in an ALM context where liabilities are driven by inflation (CPI or WAGE) Based on the econometric model we may assess the trade-off between expected surplus and shortfall probability of customized LHPs compared to TIPS or swaps (no expected surplus, no shortfall)