The Role of Private and Public Real Estate in Pension Plan Portfolio Allocation Choices

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1 The Role of Private and Public Real Estate in Pension Plan Portfolio Allocation Choices Executive Summary. This article examines the portfolio allocation decision within an asset/ liability framework. Here portfolio weights are chosen not just by an asset s return and variance but also by its correlation with pension liabilities. This results in assets that are highly correlated with pension liabilities being weighted higher in the portfolio. Typical mean-variance models estimate allocations to both public and private real estate as high as 40%. In the asset/liability model, allocations to both private and public real estate are lower and closer to what is actually observed in pension plan portfolios. *Wichita State University, Wichita, KS or craft@twsu.edu. by Timothy M. Craft* Introduction Over the past twenty years, a large volume of study has been devoted to understanding the contribution of real estate to a mixed-asset portfolio. Foremost was the idea that real estate offered diversification benefits because of its low correlation with other asset classes. Many studies in the 1980s, such as Folger (1984), Hartzell, Heckman and Miles (1986), Webb and Rubens (1987) and Firstenberg, Ross and Zisler (1988), concluded that real estate should comprise 20% 30%, or more of a diversified portfolio. In the 1990s, work by Kallberg, Lui and Greig (1996), Ziering and McIntosh (1997) and Ziobrowski and Ziobrowski (1997) also found that real estate should still be a significant part of an overall asset portfolio. However, actual pension plan allocations to real estate fall far below these findings, averaging between 3% and 4%. This becomes an even more interesting problem when you consider the institutional changes that occurred in the last few years with regard to pension plans and public real estate. Prior to 1993, pension plans were effectively constrained from investing in real estate investment trusts (REITs) by the five or fewer rule. Since the top five shareholders in a REIT could not own more than 50% of the shares outstanding, pensions, who normally take large positions in the stocks they own, would have found it difficult to invest in REITs and not break this rule. However, in 1993, the rule was changed so that pension plans are not considered one investor but instead defined as a conduit for all the beneficiaries of the plan. Pension managers were now free to investigate REITs as a potential new investment class. Journal of Real Estate Portfolio Management 17

2 Timothy M. Craft A few studies have looked specifically at the addition of public investments in real estate like REITs within an asset allocation decision. Geltner, Rodriguez and O Connor (1995) and Sanders (1999) both look at investments in both private and public real estate within a mean-variance framework. The results are similar to previous work where allocations to private and public real estate are weighted at levels much heavier than what is seen in practice. A new body of literature concerning pension plan allocation emerged in the 1990s. These asset/ liability or surplus return models of portfolio diversification take into account not only asset returns and variances but also changes in pension liabilities and their covariance with asset returns. Research beginning with Leibowitz (1987), Sharpe (1990) and Leibowitz, Kogelman and Bader (1994) suggests that pension managers are concerned with maximizing the risk-adjusted surplus value (assets minus liabilities) of the pension. In such an optimization model, asset allocations can differ greatly from the standard mean-variance framework. Peskin (1997) concludes that corporations can reduce the costs and risks of their pension plans by following such a model. Work by Chun, Ciochetti and Shilling (2000) applies the model to pension plan asset allocation decisions involving real estate. They predict allocations to real estate of between 6% and 13%. However, their research considered only private equity real estate. This study adds to the literature by examining for the first time both private and public real estate within the context of an asset/ liability model. The rest of the article is structured as follows. First, a brief summary of the standard Markowitz mean-variance model is provided along with the data used and the model s estimated portfolio allocations. Next, the asset/ liability model is developed and applied to the same data. The new portfolio allocations are then discussed and the results summarized. Typical Mean-Variance Model In the typical mean-variance model of portfolio allocation without short selling and no riskless borrowing or lending, the pension manager s objective is to minimize the risk of the portfolio subject to a given level of return and the constraints that the asset weights are all non-negative and sum to one. By varying the return between the minimum variance portfolio return and the maximum variance portfolio return, the manager can trace out the efficient frontier. In this analysis, the pension manager can choose from five broad categories of asset returns: common stocks, long and intermediate-term government bonds, private real estate and public real estate. International investments were not examined given the real estate focus of this article and the inherent problems with estimating international returns and volatility. The stock returns are computed from the S&P 500 Index. Both bond series returns are reported from Ibbotson Associates SBBI 1999 Yearbook. Public real estate returns are the total return from equity REITs reported by the National Association of Real Estate Investment Trusts (NAREIT). Estimated returns on private real estate are more problematic. The principal source used is the quarterly return index produced by the National Council of Real Estate Investment Fiduciaries (NCREIF). This index consists of returns from commercial real estate properties, primarily in metropolitan areas. This fact compares well with the types of properties pension plans select for investment. However, the index has a large drawback most values are based on appraisals and not actual transactions. The result is to smooth returns over time and to greatly underestimate the volatility. Since the volatility is underestimated, a mean-variance model would allocate more to real estate. Several papers have been written attempting to correct this bias, most notably Geltner (1993) and Fisher, Geltner and Webb (1994). Using the 1994 methodology, NCREIF returns can be unsmoothed by using autoregressive and ordinary least squares regression models, which result in a truer underlying estimated return and volatility. These quarterly returns are then annualized over the time period. The result is a time series for private real estate returns that has higher volatility. 18 Vol. 7, No. 1, 2001

3 Pension Plan Portfolio Allocation Choices Exhibit 1 Annual Asset Returns Asset Mean Return (%) Std. Dev. Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate For example, from 1979 to 1998, the standard deviation of the reported NCREIF returns was 6.8% while it was 10.0% for the unsmoothed NCREIF returns. Data used is annual from 1979 to This time period is chosen mainly as a function of the availability of the NCREIF real estate data, which begins in However, another reason for this time period is due to the vast changes in the REIT market, REIT return data from before 1980 are probably of little current empirical value. Exhibit 1 reports the mean and standard deviations of the five asset classes. The asset correlation matrix is shown in Exhibit 2. Here, notice the relatively low correlation of both public and private real estate with stocks and bonds. As expected, these low correlations lead to high allocations to real estate. The results of a standard mean-variance portfolio allocation model are reported in Exhibit 3. The minimum variance portfolio consists of 37.6% private real estate and 3.9% public real estate. As you move up the efficient frontier, the allocation to private real estate continually declines to zero. The allocation to public real estate increases to a maximum of about 17% and then decreases back to zero. Although these results are consistent with the high predicted allocations for private and public real estate from previous research, they are hardly consistent with actual pension plan asset allocations. Pension managers do not only allocate funds based on mean-variance considerations. For example, the minimum variance portfolio also includes very high allocations to bonds. However, few managers would choose such a portfolio. Most pension plans operate at higher levels of risk. In addition, managers, using their own judgment and past experience, place limits on the portfolio concentrations of certain asset classes. Asset/Liability Model Asset/ liability models of portfolio diversification take into account not only asset returns and variances but also changes in pension liabilities and their covariance with asset returns. Here, the pension manager is worried about the surplus value or difference between plan assets and liabilities, and thus seeks to maximize the risk-adjusted surplus return. In this framework, assets with returns that are highly correlated with the changes in pension liabilities are added to the portfolio to help reduce the risk of the surplus value. In the typical mean-variance model, the optimizer tries to combine assets that are negatively (or less positively) correlated with each other. Such a combination greatly reduces the risk of the portfolio. Exhibit 2 Correlation of Asset Returns Asset Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate Journal of Real Estate Portfolio Management 19

4 Timothy M. Craft Exhibit 3 Optimal Asset Allocations in a Mean-Variance Framework Portfolio I Portfolio II Portfolio III Portfolio IV Portfolio V Portfolio Return Std. Dev Allocation (%) Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate Total Exhibit 4 Correlation of Asset Returns and Pension Liabilities Asset Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate Pension Liabilities Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate Pension Liabilities However, in an asset/liability model, you can think of the pension liabilities as an asset that the corporation has shorted. In this case, pension liabilities represent the firm-indebtedness held by employees. The optimizer now searches for assets that are highly correlated with the pension liabilities. Shorting one of two positively correlated assets is equivalent to combining two assets that are negatively correlated. In order to implement such a model, the first step is to measure changes in pension liabilities. These data are available from the Business Information file of Compustat, which include pension assets, number of employees, and most importantly, the pension plan s projected benefit obligation (PBO). PBO represents the actuarial present value of all benefits earned by employees to that date plus the projected benefits attributable to future salary increases as determined by the plan s benefit formula. By 1988, firms were required by the Financial Accounting Standards Board (FASB) Statement #87 to report PBO annually. Following the methodology of Chun, Ciochetti and Shilling (2000), a panel of pension plans was constructed using only firms reporting PBO over the entire time period. The annual percent change in PBO was calculated for each pension plan and standardized by the number of employees. The mean annual rate of change in pension liabilities was 9.45% and the standard deviation of Exhibit 4 shows the correlations between liabilities and the five asset classes. The two bond assets have the highest correlation with changing liabilities followed by stocks. However, the correlation with both private and public real estate is very low; a fact that will greatly affect the final results of the model. The next step is to estimate the level to which pension plans were overfunded or underfunded over the time period. The funding ratio is usually 20 Vol. 7, No. 1, 2001

5 Pension Plan Portfolio Allocation Choices Exhibit 5 Optimal Asset Allocations in an Asset/Liability Framework Portfolio I Portfolio II Portfolio III Portfolio IV Portfolio V Portfolio Surplus Return (%) Std. Dev Allocation (%) Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate Total defined as pension plan assets divided by the present value of pension plan liabilities. From 1989 to 1998, the mean funding ratio, weighted by plan size, was 1.03, meaning the average pension plan was slightly overfunded. With data on changes in pension liabilities and funding ratios along with estimates of the correlations between liabilities and different asset classes, an asset/ liability model of portfolio allocation can be estimated. Analogous to the model used in Chun, Ciochetti and Shilling (2000), the pension plan manager seeks to minimize the variance of the surplus subject to a given level of change (i.e., return) in the pension surplus. Therefore, the optimization problem becomes: N N N A,i A,i L L A,i A, j ij i 1 i 1 j 1 j 1 N w A,i w L il. i 1 Minimize w w w w Subject to: N wa,i s i 1 N A,i i 1 w 1, (1) wl Ri RL R SP, (2) s w 0, (3) A,i R 0, (4) SP where w A,i is the portfolio weight of each asset i, A,i is the standard deviation of each asset and R i is the return on each asset. To be consistent with the asset portfolio weights, w L is defined as the ratio of liabilities to assets (the reciprocal of the funding ratio), R L is the return or change in liabilities, and L is the standard deviation of pension liabilities. For the surplus return, the asset and liability returns are weighted by s, the ratio of the surplus to assets. The surplus return on the portfolio, R SP, is constrained to be at least zero, and no short selling or riskless borrowing or lending is allowed. Solving this problem for the typical pension plan with a funding ratio of 1.03 (i.e., an w L of 0.97) and return data from results in the efficient frontier outlined in Exhibit 5. In the minimum variance portfolio, the allocation to private real estate is 12.5% while public real estate is 4.7%. As the surplus return increases, private real estate quickly leaves the portfolio while public real estate decreases slowly to zero. This result is quite different from the mean-variance model in Exhibit 3 where private real estate starts out at almost 38% and public real estate increases to 17% before falling back to zero. The main reason for the difference is the low correlation between changes in liabilities and real estate returns. Given the greater correlation between liabilities and bond and stock returns, those assets are weighted more in the portfolio because they reduce the risk of the surplus return. From Exhibit 5, moderate risk portfolios would still consist of 2% or 4% public real estate. However, given that the entire market capitalization of Journal of Real Estate Portfolio Management 21

6 Timothy M. Craft Exhibit 6 Optimal Asset Allocations in an Asset/Liability Framework Portfolio I Portfolio II Portfolio III Portfolio IV Portfolio V Portfolio Surplus Return (%) Std. Dev Allocation (%) Stocks Long-Term Government Bonds Intermediate Government Bonds Private Real Estate Public Real Estate Total equity REITs was at most $140 billion during this time period, it would probably be impractical for pensions, especially large ones, to hold that percentage of their assets in REITs for fear of moving the market. Most pension plans in setting up their overall asset allocation to real estate would probably use some guideline such as a real estate portfolio consisting of 90% private real estate and 10% public real estate. One limitation in using the liability data is that the PBO return series is only available from 1989 while the asset return series starts in Thus, the results from Exhibit 5 are based on only ten years worth of data. In order to see how sensitive the results were to the short time period, the asset/ liability model was estimated again using the pension liability returns and correlations from but using the asset returns and correlations with other assets from The results in Exhibit 6 show that the estimated allocations to real estate are slightly higher. In the minimum variance portfolio, the allocation to private real estate is 16.2% while public real estate starts at 0%. As the surplus return increases, private real estate decreases while public real estate increases to almost 10% before falling back to zero. How sensitive are the portfolio allocations to the pension s funding ratio? As the pension plan becomes more underfunded (i.e., w L increases), the portfolio includes less private and public real estate at all levels of risk. As the pension plan becomes more overfunded (i.e., w L decreases), more private and public real estate is included at lower levels of risk and the allocation percentage declines more slowly as you go up the efficient frontier. These results are as expected since an overfunded pension plan has the luxury of taking on more risk, which in this case means holding more private and public real estate. On the other hand, an underfunded pension plan cannot take as many risks and invests more in bonds. Conclusion Typical asset portfolio models conclude that real estate should have a much higher portfolio allocation than what is actually observed. However, this does not mean that pension managers are irrational. What they may really be doing is minimizing the variance of the surplus return of the portfolio. In this asset/ liability framework, portfolio allocations are not only determined by asset returns and variances but also by the correlations with the changes in the liabilities of the pension plan. Assets with higher correlations to pension liabilities would receive higher weights. Over the 1979 to 1998 time period, a meanvariance model would predict private real estate allocations of as much as 37% and public real estate allocations of 17%. However, in an asset/ liability framework, these allocations are only at most between 12% and 16% for private real estate and between 4% and 10% for public real estate. These lower estimated allocations result from the low correlations between both private and public real estate with pension liabilities. Overfunded 22 Vol. 7, No. 1, 2001

7 Pension Plan Portfolio Allocation Choices pension plans are much more likely to hold both private and public real estate than underfunded plans. Of course this is not the only reason real estate might have a low allocation in the portfolio. Other issues include the high transaction costs and management fees for private real estate relative to other assets. Illiquidity of both private and public real estate investments would also be an issue. The main conclusion of this article is that an asset/ liability model predicts much lower allocations to both private and public real estate than the standard mean-variance model. References Chun, G. H., B. A. Ciochetti and J. D. Shilling, Pension Plan Real Estate Investment in an Asset/ Liability Framework, Real Estate Economics, 2000, 28:3, Firstenberg, P. M., S. A. Ross and R. C. Zisler, Real Estate: The Whole Story, Journal of Portfolio Management, 1988, 14, Fisher, J. D., D. M. Geltner and R. B. Webb, Value Indices of Commercial Real Estate: A Comparison of Index Construction Methods, Journal of Real Estate Finance and Economics, 1994, 9, Folger, H. R., 20% in Real Estate: Can Theory Justify It?, Journal of Portfolio Management, 1984, 10:2, Geltner, D. M., Estimating Market Values from Appraised Values without Assuming an Efficient Market, Journal of Real Estate Research, 1993, 8:3, Geltner, D. M., J. Rodriguez and D. O Connor, The Similar Genetics of Public and Private Real Estate and the Optimal Long- Horizon Portfolio Mix, Real Estate Finance, 1995, 12:3, Hartzell, D. J. Hekman and M. Miles, Diversification Categories in Investment Real Estate, Real Estate Economics, 1986, 14, Kallberg, J. G., C. H. Lui and D.W. Greig, The Role of Real Estate in the Portfolio Allocation Process, Real Estate Economics, 1996, 24:3, Leibowitz, M. L., Liability Returns: A New Look at Asset Allocation, Journal of Portfolio Management, 1987, 13:2, Leibowitz, M. L., W. Kogelman and L. N. Bader, Funding Ratio Return, Journal of Portfolio Management, 1994, 21:1, Peskin, M. W., Asset Allocation and Funding Policy for Corporate-Sponsored Defined-Benefit Pension Plans, Journal of Portfolio Management, 1997, 23:2, Sanders, G., An Updated Look at Asset Allocation: Private and Public Real Estate in a Multi-Asset Class Portfolio, The Real Estate Finance Journal, 1999, 14:3, Sharpe, W. F., Asset Allocation, In John L. Maginn and Donald L. Tuttle (Eds.), Managing Investment Portfolios, Second Edition, Boston, MA: Warren, Gorham, and Lamont, Webb, J. R. and J. H. Rubens, How Much in Real Estate? A Surprising Answer, Journal of Portfolio Management, 1987, 14: 2, Ziering, B. A. and W. McIntosh, Revisiting the Case for Including Real Estate in a Mixed-Asset Portfolio, The Journal of Real Estate Finance, 1997, 13:4, Ziobrowski, B. J. and A.J. Ziobrowski, Higher Real Estate Risk and Mixed-Asset Portfolio Performance, Journal of Real Estate Portfolio Management, 1997, 3, The author thanks the editor and two anonymous referees as well as participants of the University of Wisconsin-Madison Real Estate Seminar for their helpful comments. Journal of Real Estate Portfolio Management 23

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