Some Tests of the Risk-Return Relationship Using Alternative Asset Pricing Models and Observed Expected Returns

This study examines the performance of three asset pricing models: the CAPM, the APT and the UAPT using observed expected returns from a three-phase dividend discount model with Value Line analyst estimates of future company-level earnings, dividends and growth rates. Our study is the first we know of to test the three major asset pricing models using observed expected returns. Our results are similar to prior research using ex post (realized) returns in that we find that the UAPT using macroeconomic factors is the best performing model, followed by the APT and the CAPM. However, our results also suggest that the importance of macroeconomic factors is much greater to expected returns than to realized returns, and the corresponding R2 values for models using expected returns are much higher than for models using realized returns. Combining our results for the UAPT with those of Marston and Harris (1993) for the CAPM suggests that these models are more successful in tests using observed expected returns than in tests using realized returns as proxies for expected returns. Unit root tests suggest that monthly observed expected returns follow the classic random walk without drift model while monthly realized returns do not.     

Market Signals Associated with REIT IPOs

Previous studies have found significant but time-varying valuation effects associated with real estate investment trusts initial public offerings (REIT IPOs). Because REIT IPOs may disclose relevant information about real estate market conditions, they may serve to revalue existing real estate securities. To determine whether REIT IPOs signal information that is impounded into the share prices of other real estate securities, we assess the returns on rival portfolios of existing real estate securities upon the issuance of the IPO. On average, the rival portfolios experience insignificant effects on the REIT IPO filing date, but negative and significant abnormal returns around the issue date. A cross-sectional analysis of combined effects at the time of the filing date and issue date shows that the negative effects on the rival portfolios are more pronounced when (1) the size of the REIT IPO is larger, (2) market conditions are relatively weak, (3) more REIT IPOs come to market, and (4) the IPO is not associated with an umbrella partnership REIT.     

Index Option Pricing Models with Stochastic Volatility and Stochastic Interest Rates

This paper specifies a multivariate stochasticvolatility (SV) model for the S & P500 index and spot interest rateprocesses. We first estimate the multivariate SV model via theefficient method of moments (EMM) technique based on observations ofunderlying state variables, and then investigate the respective effects of stochastic interest rates, stochastic volatility, and asymmetric S & P500 index returns on option prices. We compute option prices using both reprojected underlying historical volatilities and the implied risk premiumof stochastic volatility to gauge each model's performance through direct comparison with observed market option prices on the index. Our major empirical findings are summarized as follows. First, while allowing for stochastic volatility can reduce the pricing errors and allowing for asymmetric volatility or leverage effect does help to explain the skewness of the volatility smile, allowing for stochastic interest rates has minimal impact on option prices in our case. Second, similar to Melino and Turnbull (1990), our empirical findings strongly suggest the existence of a non-zero risk premium for stochastic volatility of asset returns. Based on the implied volatility risk premium, the SV models can largely reduce the option pricing errors, suggesting the importance of incorporating the information from the options market in pricing options. Finally, both the model diagnostics and option pricing errors in our study suggest that the Gaussian SV model is not sufficientin modeling short-term kurtosis of asset returns, an SV model withfatter-tailed noise or jump component may have better explanatory power.     

Corporate Real Estate and Stock Market Performance

An interesting question in corporate real estate literature is whether real estate can improve the stock market performance of property-intensive non-real estate firms. Using a data set comprising 75 non-real estate corporations that own at least 20 percent properties, this paper empirically assesses and compares the pair-wise return, total risk, systematic risk and Jensen abnormal return performance of composite (with real estate) and hypothetical business (without real estate) firms. We employed Morgan Stanley Capital International world equity index instead of a local market index to provide some insights into the performance of the local market relative to the global market during the 1997–2001 volatile periods experienced by many Asian countries. Our results suggest the inclusion of real estate in a corporate portfolio appears to be associated with lower return, higher total risk, higher systematic risk and poorer abnormal return performance. It is therefore likely that non-real estate firms own properties for other reasons in addition to seeking improvement in their stock market performance. Further research is needed to explore the main factors contributing to corporate real estate ownership by non-real estate firms.     

Commercial Real Estate Return Performance: A Cross-Country Analysis

This paper investigates the return performance of publicly traded real estate companies. The analysis spans the 1984–1999 time period and includes return data on over 600 companies in 28 countries. The return data reveal a substantial amount of variation in mean real estate returns and standard deviations across countries. Moreover, standard Treynor ratios, which scale country excess returns by the estimated beta on the world wealth portfolio, also reveal substantial variation across countries in excess real estate returns per unit of systematic risk. However, when we estimate Jensens alphas using both single and multifactor specifications, we detect little evidence of abnormal, risk-adjusted returns at the country level. We do, however, find evidence of a strong world-wide factor in international real estate returns. Furthermore, even after controlling for the effects of world-wide systematic risk, an orthogonalized country-specific factor is highly significant. This suggests that real estate securities may provide international diversification opportunities.     

The “Rent-To-Own” mortgage and prepayment risk

The most important risk factor in the mortgage and mortgage-backed security market has been prepayment risk. Various innovations have arisen to deal with it but none hedge it fully. The Rent-To-Own (RTO) mortgage discussed here is a mortgage instrument that reduces or even reverses prepayment risk. It does so by creating an incentive structure within the framework of the mortgage contract that penalizes prepayment when interest rates are low and rewards it when interest rates are high. This is the opposite of standard mortgages. The RTO incentive structure is based on a unique buyout feature. Borrowers who want to buy out the financial interest of the lender may do so whenever they want, but the buyout price is a negative function of the market interest rates prevailing currently, that is, at the time of the buyout. Hence the lower these rates, the higher the buyout price. Other advantages of the RTO mortgage are also described.     

Optimal Consumption Taxes and Social Security Under Tax Measurement Problems and Uncertainty

A representative individual lives for two periods; works when young and depends on savings and a government operated social security system when old—the returns on both sources of income, when old, are random. Due to administrative problems the returns to savings are observed with some measurement error. Two alternative consumption tax systems are considered; the Registered Asset Treatment (RAT) and the Non-Registered Asset Treatment (NRAT). The advantage of the RAT is that it can perform a social insurance role while the disadvantage is that it imposes measurement error risk. Correlation between the random return on saving and its measurement error can provide a risk-hedging role that can be further strengthened by the RAT version. The NRAT version neither provides social insurance nor imposes measurement error risk. Both tax systems hedge against the uncertainties in the social security system. The taxpayer engages in precautionary saving in response to future uncertainty.     

To the Water’s Edge,and Beyond: Effects of Shore Protection Projects on Beach Development

The effects on real estate development of shore-protection efforts that lower erosion rates and storm hazards are both controversial and difficult to detect. A simple theoretical model indicates that shore protection is likely to tilt development from areas a few hundred feet inland toward beachfront property. A modified repeat-sale house price index is used to measure price appreciation rates to the waters edge. We are able to formulate an extremely sensitive empirical test for a tilt in rates of house-price appreciation implied by a tilt in development. Surprisingly, we find no significant evidence that shore-protection efforts have produced additional beachfront development in the Florida counties studied. The method used in this article is quite general and could be used in a number of applications where an environmental effect impacts real estate differentially over space.     

The Value of the Rent Control Option

In this paper, we combine direct arbitrage arguments and an option-pricing approach to develop a method of pricing the option for rent control. For a lump-sum payment of key money, a tenant acquires the right to rent a real estate unit for an exogenously determined controlled rent, as opposed to paying the free-market rent. The tenant may continue exercising this right as long as he or she lives. Alternatively, the tenant may sell the right to occupy the controlled rent unit and receive a fraction of the key money paid by the subsequent tenant. We value the equilibrium key money, in a representative agents partial equilibrium, while endogenously determining the expected tenure duration in a controlled rent unit. We propose a procedure for valuing rent control options different from the representative agents. Our analysis shows that under real-world levels of conditional life expectancy, the level of the fraction of the key money retained by a departing tenant has an insignificant effect on the expected tenure duration in a controlled rent unit and on the level of key money.     

Computing a Multivariate Normal Integral for Valuing Compound Real Options

We extend the Geske (1979) model to a multivariate normal integral for the valuation of a compound real option. We compared the computing speeds and errors of three numerical integration methods, namely, Drezner's improved Gauss quadrature method, Monte Carlo method and Lattice method, together with appropriate critical value finding methods. It is found that secant method for finding critical values combined with Lattice method and run by Fortran took merely one second, Monte Carlo method 120 seconds. It is also found that the real option decreases with interest rate, not necessarily positively correlated with volatility , a result different from that anticipated under financial option theory. This is mainly because the underlying of real option is a non-traded asset, which brings dividend-like yield into the formula of compound real options. Dividend-like yield rises with the multiplication of correlation coefficient and . High indicates the poor diversification advantage of the new investment project in relation to the existing market portfolio, and the value of real call option decreases with . Conversely, when is low, the proposed project provides better diversification advantage and the real call option rises with . Irrespective of the value of , when interest rate increases, the value of real call option drops, especially when is high, the value of the project is dominated by interest rate.     

Determinants of stock market volatility and risk premia

Summary. We show the dynamics of diverse beliefs is the primary propagation mechanism of volatility in asset markets. Hence, we treat the characteristics of the market beliefs as a primary, primitive, explanation of market volatility. We study an economy with stock and riskless bond markets and formulate a financial equilibrium model with diverse and time varying beliefs. Agents states of belief play a key role in the market, requiring an endogenous expansion of the state space. To forecast prices agents must forecast market states of belief which are beliefs of others hence our equilibrium embodies the Keynes Beauty Contest. A market state of belief is a vector which uniquely identifies the distribution of conditional probabilities of agents. Restricting beliefs to satisfy the rationality principle of Rational Belief (see Kurz, 1994, 1997) our economy replicates well the empirical record of the (i) moments of the price/dividend ratio, risky stock return, riskless interest rate and the equity premium; (ii) Sharpe ratio and the correlation between risky returns and consumption growth; (iii) predictability of stock returns and price/dividend ratio as expressed by: (I) Variance Ratio statistic for long lags, (II) autocorrelation of these variables, and (III) mean reversion of the risky returns and the predictive power of the price/dividend ratio. Also, our model explains the presence of stochastic volatility in asset prices and returns. Two properties of beliefs drive market volatility: (i) rationalizable over confidence implying belief densities with fat tails, and (ii) rationalizable asymmetry in frequencies of bull or bear states.This research was supported by a grant of the Smith Richardson Foundation to the Stanford Institute for Economic Policy Research (SIEPR). We thank Kenneth Judd for constant advice which was crucial at several points in the development of this work. We also thank Kenneth Arrow, Min Fan, Michael Magill, Carsten Nielsen, Manuel Santos, Nicholas Yannelis, Ho-Mou Wu and Woody Brock for comments on earlier drafts. The RBE model developed in this paper and the associated programs used to compute it are available to the public on Mordecai Kurzs web page at http://www.stanford.edu/ mordecai.This revised version was published online in January 2005 with corrections to the Cover date.     

Asymmetric Information and the Predictability of Real Estate Returns

This article examines the relation between systematic price changes and the heterogeneity of investors information sets in real estate asset markets. The empirical implications rely on a theoretical economy in which information asymmetry alters the dynamic relation between returns and trading volume. We employ a filter-rule methodology to determine predictability in returns and augment the return-based conditioning set with trading volume. The additional conditioning information is necessary since the model is underspecified when predictability is based on returns alone. Our results provide new insight into the coexistence of informational and noninformational exchange in the speculative markets for real estate assets. Specifically, we find that the predictability of real estate returns is generally more indicative of portfolio rebalancing effects than an adverse-selection problem. These results are unique in addressing the time-variation in information asymmetry.     

The Pricing of Event Risks with Parameter Uncertainty

Financial instruments whose payoffs are linked to exogenous events, such as the occurrence of a natural catastrophe or an unusual weather pattern depend crucially on actuarial models for determining event (e.g., default) probabilities. In many instances, investors appear to receive premiums far in excess of these modeled actuarial probabilities, even for event risks that are uncorrelated with returns on other financial assets. Some have attributed these larger spreads to uncertainty in the probabilities generated by the models. We provide a simple model of such parameter uncertainty and demonstrate how it affects rational investors' demand for event risk exposures. We show that while parameter uncertainty does indeed affect bond spreads, it does not tend to increase spreads by much. Indeed, the spread increases due to parameter uncertainty in our numerical examples are on the order of only 1–2 basis points. Moreover, in many instances, including those that have the most sensible correlation settings, parameter uncertainty tends to decrease the size of bond spreads. We therefore argue that parameter uncertainty does not appear to be a satisfactory explanation for high event-risk returns.     

Interest-only and principal-only mortgage strips as interest-rate contingent claims

Interest-only (IO) and principal-only (PO) mortgage strips are valued in a stochastic interest-rate environment. The prepayment rate of the underlying mortgages is affected by two considerations not present in the pure financially rational model: (1) The property owner's holding period is assumed to follow a Gamma distribution, resulting in the possibility of prepayment due to the sale of the property (i.e., prepayment that is too early based on market interest rates); and (2) borrowers are assumed to face heterogeneous transaction costs related to refinancing the existing mortgage, and delay refinancing when market conditions make it optimal to do so (refinancing too late). Properties of IO/PO strips are identified by the finite difference method.     

Strategic default,workout, and commercial mortgage valuation

This paper extends existing equilibrium commercial mortgage pricing models by endogenizing negotiated workout into the usual noncooperative lending game. Workout is a feasible subgame strategy for the lender to play whenever foreclosure transaction costs exist for either party to a loan transaction. In particular, negotiated workout solutions Pareto dominate the foreclosure alternative when default occurs. To obtain our results, we embed a cooperative bargaining game within a noncooperative mortgage loan/default game. We also address the valuation wedge problem that occurs when foreclosure transaction costs are introduced. Through the notion of replacement game equilibrium, we find symmetric mortgage pricing solutions that eliminate the valuation wedge and thus suggest that lending will occur in commercial real estate mortgage markets even when foreclosure transaction costs exist.     

Performance Evaluation and Corporate Income Taxes in a Sequential Delegation Setting

We consider a setting where a firm delegates an investment decision and, subsequently, a sales decision to a privately informed manager. For both decisions corporate income taxes have real effects. We show that compensating the manager based on pre-tax residual income can ensure after-tax NPV-maximization (goal congruence) for each decision problem in isolation. However, this metric fails if both decisions are nontrivial, since it requires asset-specific hurdle rates and hence precludes asset aggregation. After-tax residual income metrics (e.g., EVA) allow the firm to consistently apply its after-tax cost of capital as the hurdle rate to its aggregate asset base. We show that existing tax depreciation schedules may explain why firms in practice use more accelerated depreciation schedules than those suggested by previous studies. Our findings also rationalize the widespread use of dirty surplus accounting for windfall gains and losses for managerial retention purposes.     

Coping with Technological Change: The Case of Retail

Functional obsolescence in real estate occurs because of technological change. A theoretical model suggests that the early years of building life are characterized by functional obsolescence that is undiminished by reinvestment (cures in appraisal terminology). Later, observable functional obsolescence is eliminated by cures. A national, proprietary data set consisting of department store sales is utilized to test these propositions. The test is structured within a hedonic model in which the effect of age represents functional obsolescence and technological change, while other variables control for physical condition and location quality. The empirical results do not permit the rejection of the hypotheses developed from the theory. The measured rate of techological change in retail real estate is 1.7 percent per annum.     

The impact of settlement period on sales price

This study is an empirical investigation of the impact of settlement period on sales price while controlling for marketing period and standard explanatory variables. The hypothesized positive relationship between settlement period and sales price is confirmed by the results of this study. The estimated coefficient on settlement period is 0.0008 meaning that our market, on average, exacts a premium of 0.08 percent per day of settlement period beyond a norm of 60 days. The estimated coefficient on marketing period (a control variable) is –0.0003 meaning that our market, on average, requires a discount of 0.03 percent per day of marketing period. Our findings show the relative importance of settlement period in making real estate pricing decisions.     

A Spatial Model of Housing Returns and Neighborhood Substitutability

This article provides a method for estimating housing indices at the local level. It develops a distance-weighted repeat-sales procedure to exploit the factor structure of the error-covariance matrix in the repeat-sales model. A distance function defined in characteristic and geographical space provides weights for the generalized least-squares model, and allows the use of all of the repeated sales in a metropolitan area to measure returns for the specific neighborhood of interest. We use distance-weighted repeat sales to estimate return indices for all zip codes in the San Francisco Bay area over the period 1980--1994.When distance is defined in terms of socioeconomic characteristics, we find that median household income is the salient variable explaining covariance of neighborhood housing returns. Racial composition and educational attainment, while significant, are much less influential. Zip-code level indices often deviate dramatically from the citywide index, depending upon income levels. This has implications for investors and lenders. Our results indicate that rates of return may vary considerably within a metropolitan area. Thus, simply using broad metropolitan area indices as a proxy for capital appreciation within a specific neighborhood may not be justified.     

Rational Delays: The Case of Real Estate

Real estate markets, for both commercial real estate and single family homes, typically respond to a large negative demand shock with a period during which the volume of transactions and liquidity of real estate declines. Explanations for these periods have focused on overly optimistic owners, imperfections in real estate markets and/or minimum down payment requirements. These are important characteristics of real estate markets, but they do not provide a satisfying explanation for the long-term declines in the number of transactions and liquidity of real estate that frequently follow negative demand shocks. This paper presents estimates, for a specific real estate market (Los Angeles single family dwellings), of the option-like value of an owners interest in a property. Our estimates imply that when an owner has little or negative equity, the value of waiting to sell is likely to exceed the net carrying cost. Consequently, the option value of a potential sellers interest may eliminate the possibility of an otherwise mutually advantageous transaction.