R E ALM F EAL STATE IN AN RAMEWORK THE CASE OF FAIR VALUE ACCOUNTING Dirk Brounen, Melissa Porras Prado and Marno Verbeek October 12, 2007 Keywords: Real Estate, Asset Liability Management, Liability Hedge Credit We thank Carolina Fugazza and Frank de Jong for many helpful comments and constructive suggestions. We would also like to thank the participants at the 2007 Netspar Workshop and the 2007 European Real Estate Society Annual Conference for comments on earlier drafts of this paper. Brounen is Associate Professor of Finance and Real Estate, Porras Prado is PhD Candidate, and Verbeek is Professor of Finance, all at the Finance Group of RSM Erasmus University. Correspondence: RSM Erasmus University, Attn. Melissa Porras Prado, Burg. Oudlaan 50 (T9-29), 3062 PA, Rotterdam, The Netherlands, Tel.: +31 104081276, Fax: +31 104089017, Email: [email protected] 0 R E ALM F EAL STATE IN AN RAMEWORK THE CASE OF FAIR VALUE ACCOUNTING Abstract This study examines the liability hedging characteristic of both direct and indirect real estate, in the advent of fair value accounting obligations for pension funds. We explicitly model pension obligations as being subject to interest and inflation risk to analyze the ability of real estate investments in hedging the market value of pension liabilities and to quantify its role in an ALM portfolio. Based on a sample period of 1984-2006, direct and indirect real estate merit inclusion in an ALM portfolio because of their attractive risk-reward properties and its diversification potential, rather than its liability hedging abilities. Keywords: Real Estate, Asset Liability Management, Liability Hedge Credit 1 R E ALM F EAL STATE IN AN RAMEWORK THE CASE OF FAIR VALUE ACCOUNTING Introduction Real estate assets have traditionally been regarded as safe investments with inflation hedging capabilities that offer diversification potential and high absolute returns. Nevertheless there is no consensus as to its role within an investment context. In the selection of portfolios based on means and variances of returns the role for real estate, as a diversifier in a portfolio, appears to be substantial. For real estate allocations the mean-variance literature predicts allocations of at least 20% to be optimal1. Conversely, institutional investors like pension funds are not solely aspiring for maximum returns at a selected level of risk in their portfolio choice. Their focus in making asset allocation decisions is on considering risk on a relative basis versus liabilities to optimize their risk adjusted surplus. When taking pension liabilities as the starting point and coordinating the management of assets and liabilities in order to maintain a surplus of assets beyond liabilities the role for real estate seems much more limited. Chun, Ciochetti and Shilling (2000) offered the first empirical analysis of real estate allocations within an ALM framework. In their research they recognize real estate assets’ correlation and diversification potential with other assets, while simultaneously adjusting for the covariance with the liability stream. The diversification potential on the liability side as a hedge against inflation turns out to be more limited and accounts for the reduced exposure to this asset class as witnessed in institutional portfolios. Even so, this earliest achievement in the asset-liability literature circumvents the imperfections associated with real estate by focusing on real estate securities (REITs) and as such limits the opportunity set of assets to solely indirect real estate. Furthermore, Chun, Ciochetti and Shiling (2000) focus on the reported value of projected benefit obligations and in the advent of fair value accounting 1 For empirical evidence on real estate allocation within mean variance optimizations we like to refer to: Friedman (1971), Fogler (1984), Brinson, Diermeier, Schlarbaum (1986), Firstenberg, Ross and Zisler (1987), Irwin and Landa (1987), Ennis and Burik (1991), Hoesli, Lekander and Witkiewicz (2003) and Lee and Stevenson (2005). 1 obligations for pension funds it becomes of interest how real estate performs in hedging the market value of liabilities. This paper adds to the existing literature by examining the liability hedge qualities of real estate in light of liabilities being denominated at market value. With the introduction of fair value accounting standards the dynamics of liabilities are likely to change. We study US data for the period 1984-2006 to quantify the assets’ impact on the pensions fund’s future funding surplus and quantify the utility that investors with liabilities can derive from real estate in view of other asset classes. This will enable us to determine whether to classify real estate and other assets as reserve asset, asset which moves in tandem with liabilities, or return-generating asset, an asset that merits an inclusion in the portfolio because of its attractive risk-reward characteristics (see Black and Jones, 1988). We widen the investment opportunity set by distinguishing between direct and indirect real estate investments and find that the hedging utility of real estate with respect to the market value of liabilities is limited and that both direct and indirect real estate provide return enhancement properties as rather than interest and inflation properties. Nonetheless, direct and indirect real estate do provide more utility than stocks and as such merit an inclusion in an ALM portfolio, in contrast to the findings of Chun, Ciochetti and Shilling (2000). The remainder of the paper is organized as follows: we present a synthesis of the most relevant theoretical and empirical analyses on real estate allocations and liability relative investing. In the third and fourth section the data set and the methodology of the empirical tests are presented. We initially proceed by quantifying real estate allocations assuming an asset-only mean variance optimization. Special consideration will be given to the impact of smoothed data on the calibration of optimal portfolios. Next, in section six, we analyze the liability hedging potential of various assets classes, results that will be used in section seven to compute optimal ALM portfolios and asses the interplay between the different weights attached to liabilities, levels of risk tolerance and funding levels of pension schemes. Finally, the last section summarizes our most important findings. Literature Review In the context of real estate allocations Friedman (1971) was one of the first to use the mean-variance methodology to select optimal direct real estate and mixed-asset portfolios. 2 The inclusion of real estate assets within modern theory based portfolios resulted in a widespread belief that actual real estate allocations in investment portfolios fall short. Bajtelsmit and Worzala (1995) put forward that on average American pension funds allocate less than 4% of their assets to equity real estate. In their survey among 96 pension funds the dominant asset classes were domestic stock (42.6%) and bonds (32%) followed by international stocks (7.2%). More recently, Dhar and Goetzmann (2005) surveyed leading investment managers from the U.S. and found the reported allocation among funds who invest in real estate to be relatively small 3%-5%, although a large number of funds announced plans to increase their respective allocations. Hoesli, Lekander and Witkiewicz (2005) explicitly compare the actual and suggested weights of real estate in the institutional portfolio and find that against the classic mean-variance framework, the predicted allocations are still inconsistent with reported allocations. The discrepancy between actual allocations and theoretical predications in this asset-only view lead Chun, Ciochetti and Shilling (2000) to re-examine pension plan investments in an asset-liability framework using U.S. REITs. The relationship between assets and liabilities seems to be at the heart of explaining the limited exposure to real estate. Within the mean- variance framework real estate plays an important role as a diversifying asset class, but when accounting for liability obligations real estate seems to offer reduced diversification benefits as a hedge against inflation on the liability side of the balance sheet. The latter diversification potential accounts for the reduced exposure to this asset class as apparent among institutional portfolios. Chun, Ciochetti and Shilling (2000) also found cross-sectional differences in REIT allocations. For overfunded plans the optimal allocation is higher than for underfunded funds. Following this first empirical ALM study on real estate allocations Craft (2001) further examined real estate investments by distinguishing between private and public real estate allocations, while correcting for appraisal smoothing. The asset-liability framework predicts an allocation of 12.5% to private real estate and 4.7% to public real estate. And as the returns increase the private real estate allocation decreases sharply while the allocation to public real estate decreases at a lower progressive pace. Moreover, overfunded pension plans are in accordance with Chun, Ciochetti, and Shilling (2000) much more likely to hold both private and public real estate than underfunded counterparts (Craft, 2005A, 2005B). The 3 particular and conditions of a pension fund apparently influence the allocation decision. In accordance Booth (2002) finds considerably different optimal portfolios depending on the liability structure of the pension funds. For mature U.K. schemes (whose members have already retired) direct real estate allocations prevail around 10%. For immature pension plans (active members) index-linked U.K. government bonds and U.S. equities replace real estate allocations. Finally, another strand of literature by Fugazza, Guidolin and Nicadono (2007) and Hoevenaars, Molenaar, Schotman and Steenkamp (2005) incorporates predictability of asset returns in the optimal portfolio choice. Fugazza, Guidolin and Nicadono (2007) explicitly distinguish the time-varying properties of indirect real estate in light of bonds and stocks. When allowing for linear predictability patterns in indirect real estate returns the optimal allocation should obtain a weight between 12% and 44%, depending on the risk tolerance, parameter uncertainty and investment horizon. On the other hand when optimizing returns in excess of liabilities, Hoevenaars, Molenaar, Schotman and Steenkamp (2005) find that the role for indirect real estate in a liability driven investment portfolio is negligible. This paper extends the work of Chun Ciochetti and Shilling (2000), Craft (2001) and Booth (2004) by examining the market value liability hedge qualities of real estate in light of other asset classes. We explicitly model liabilities as being subject to interest and inflation rate risk and summarize the assets’ impact on the pensions fund’s future funding surplus. To do so, this study applies a liability framework as developed by Sharpe and Tint (1990), which arises from a traditional mean-variance optimization problem. More specifically, it involves a mean variance surplus optimization model which optimizes the expected surplus return minus a risk penalty (variance surplus return) divided by risk tolerance, while taking into account the change in pension liabilities and their covariances with assets. The latter, also referred to as the liability hedge credit, quantifies the utility due to assets correlation with a pension fund liabilities. This methodology further allows for a differential in emphasis attached to liabilities, the level of risk tolerance and the funding level of pension schemes. This enables us to determine how sensitive the results are to these factors, but more importantly it permits pension funds to tailor their portfolios to their particular nature and objectives. And most notably, it allows institutional investors to quantify the liability hedging utility of each asset class. 4 Methodology To determine real estates’ role as a reserve asset (asset which moves in tandem with liabilities) or a return-generating asset we apply a single-period surplus optimization investment framework of Sharpe and Tint (1990) that explicitly links investment opportunities and pension-plan obligations. The objective of the pension fund is to maximize surplus, defined as: S = A −kL , (1) t+1 t+1 t+1 where A represents the value of the fund’s assets at t+1, L the value of the relevant t+1 t+1 liability concept and k the attached importance to it. Choosing k=1 means that full importance is attached to the liabilities, k=0 corresponds to an asset-only optimization. Denoting the return on the asset portfolio by R and the growth rate of the liabilities by A, t+1 R the surplus can be written as: L, t+1, ( ) L ( ) S = A 1+R −k t 1+R , (2) t+1 t A,t+1 A L,t+1  t where L/A denotes the fund’s current inverse funding ratio. t t Maximizing the expected utility of S is equivalent to maximizing that of t+1  L  Z = R −k t R (3) t+1 A,t+1  A  L,t+1 t Accordingly, Sharpe and Tint (1990) formulate the optimization problem of the pension fund as  1  ( ) ( ) maxE Z − var Z , (4)  t t+1 λ t t+1  where λ denotes a fund’s risk tolerance. If the portfolio weights to be chosen are denoted by ∑ w, we have R = w R , where R denotes the return on asset i. A,t+1 i i i,t+1 i,t+1 Following Sharpe and Tint (1990) let us focus on the second term in (4), which can be written as 5  L  var R −k t R    t A,t+1 A L,t+1 t ( ) L2 ( ) L ( ) = var R +k2 t var R −2k t cov R ,R (5) t A,t+1 A2 t L,t+1 A t A,t+1 L,t+1 t t The second term is irrelevant to the outcome of the maximization problem. The difference with the standard asset-only optimization problem is concentrated in the last term. It stresses that the assets’ covariances with the growth rate of the liabilities are key for the optimal allocation. Sharpe and Tint (1990) define the liability hedge credit for any asset i as 2 L ( ) LHC = k t cov R ,R , (6) i λ A t i,t+1 L,t+1 t while the LHC of the entire portfolio is simply ∑ LHC = w LHC . (7) a i i i The total objective function follows a standard asset-only optimization problem, the expected surplus return minus a risk penalty, while considering the change in pension liabilities and their covariance with assets (LHC ). a [ ] max Expectedreturn−Riskpenalty+ LiabilityHedgeCredit  var (R )  (8) maxR − t A,t+1 + LHC   A,t+1 λ a Other things being equal, an asset whose returns are highly correlated with liabilities provide better liability hedging and receive a greater liability hedging credit. This ultimately results in a higher weight in the ALM portfolio than under the traditional mean variance optimization. Data description Our study employs data from the United States, as for this country broad data coverage on both appraisal based property indices and property share indices are available. The analysis of the asset returns is estimated over the 1983 to 2006 period, taking quarterly observations. Data on stock returns were taken from Datastream Advance. Stock returns are approximated by the returns on the MSCI US index, and direct real estate returns are from 6 the NCREIF series. NCREIF provides income, capital and total returns disaggregated by sector and region based on a sample of institutional-owned properties. Indirect real estate returns are based on Global Property Research (GPR) General National index. The data is available since the last quarter of 1983. The fixed income assets consist of a 20-year Treasury bond and Moody's Seasoned Aaa Corporate bond. Furthermore we use a 10-year constant maturity yields as a proxy for pension liabilities. Both the 10-year constant maturity and Moody's Seasoned Aaa Corporate bond yields, are from the US Federal Reserve Bank website2. Moody's Seasoned Aaa Corporate Bond Yield are averages of daily data. The 20- year Treasury bond is based on an index from Lehman Brothers. Table 1 presents a summary of the performance of the asset categories that are considered in our study. Table 1: Sample Statistics The mean returns and standard deviations are computed for the 1984-2006 sample period. We document the highest return for indirect real estate, while direct real estate seems to have been outperformed by all asset classes. However, the Sharpe ratio of direct real estate, calculate as annualized excess return divided by the annualized standard deviation of returns, is particularly favorable, 0.56 versus 0.27 for stocks, 0.26 for indirect real estate, 0.25 long- term Treasury bond and 0.46 for Corporate Aaa bonds. The returns on appraisal based direct real estate document the lowest standard deviations, and appear to be biased by strong autocorrelation. In line with the Geltner (1993) approach we adjust the private real estate return series for first-order autocorrelation. The advantage of this procedure is that it avoids the assumption that returns in the private property market are uncorrelated. Geltner’s model applies a reverse filter on the capital growth component of private real estate returns in order to recover the underlying unsmoothed property returns3. Following Geltner (1993) we assume that the volatility of commercial property is in the vicinity of half of that of the stock 2 http://research.stlouisfed.org/ (R* −(1−a)R* ) 3 Ru = t t−1 , where RUis the unsmoothed return at time t, R*is the observable appraised- t a t t based index return at time t and a is a parameter between 0 and 1 whose value depends on the confidence factor α (α=0.5) and seasonality factor f (f= 0.15). 7 market, which results in an aof 0.404. By unsmoothing the direct real estate returns the level of autocorrelation is strongly reduced, while the standard deviation doubles in magnitude. For the analysis of the liability returns we assume that the return on liabilities follows the return of the long-term constant maturity bond, estimated over the 1983 to 2006 period. Our specification abstracts from inflows and outflows, the fund is assumed to be in a stationary state, the distribution of the age cohorts and pension rights are assumed constant over time. The liability return is derived as a function of the log yield of the constant maturity bond, assuming duration of 17 years, the average duration of pension liabilities. 1 1 (1+r ) = D (1+Y )−(D − )(1+Y ) = Y −(D (Y −Y )) n,t+1 n,t n,t n,t 4 n−1,t+1 4 n−1,t+1 n,t n−1,t+1 n,t Y is the log annualized yield of a n-year maturity bond at time t. We further approximate n,t Y by Y , a common assumption also made by Hoevenaars, Molenaar, Schotman and n-1,t+1 n,t+1 Steenkamp (2005). We further distinguish two series of nominal and real liability returns. In quantifying the utility a pension fund can derive form various asset classes we use nominal liabilities as the starting point, in the advent of indexation we consider the hedging capabilities surrounding real liabilities. We calculate both the nominal (r ) and the real liability return(rr ). We decompose the t+1 t+1 nominal yield into a real return (rr )and inflation compensation, where the inflation t+1 compensation reflects expected inflation (π ) and an inflation risk premium, which for t+1 reasons of simplicity we assume constant. Ynom =Yreal + E[π ] t t t+1 We further assume that inflation expectation follows a fourth order autoregressive function. The coefficients are estimated using rolling regressions and 10 years of history (40 quarterly observations). Thus we assume that for each quarter investors form expectations on the 4 In appendix A we also test alternative specifications by unsmoothing real estate returns at a-factors of 0.3 and 0.5 in order to isolate the impact of this assumption on our overall results. 8