Universal bounds for asset prices in heterogeneous economies

We establish universal bounds for asset prices in heterogeneous complete market economies with scale invariant preferences. Namely, for each agent in the economy we consider an artificial homogeneous economy populated solely by this agent, and calculate the “homogeneous” price of an asset in each of these economies. Dumas (Rev. Financ. Stud. 2, 157–188, [1989]) conjectured that the risk free rate in a heterogeneous economy must lie in the interval determined by the minimal and maximal of the “homogeneous” risk free rates. We show that the answer depends on the risk aversions of the agents in the economy: the upper bound holds when all risk aversions are smaller than one, and the lower bound holds when all risk aversions are larger than one. The bounds almost never hold simultaneously. Furthermore, we prove these bounds for arbitrary assets.      

Consistent price systems and arbitrage opportunities of?the?second kind in models with transaction costs

In contrast with the classical models of frictionless financial markets, market models with proportional transaction costs, even satisfying usual no-arbitrage properties, may admit arbitrage opportunities of the second kind. This means that there are self-financing portfolios with initial endowments lying outside the solvency region but ending inside. Such a phenomenon was discovered by M. Rásonyi in the discrete-time framework. In this note, we consider a rather abstract continuous-time setting and prove necessary and sufficient conditions for a property which we call no free lunch of the second kind, NFL2. We provide a number of equivalent conditions elucidating, in particular, the financial meaning of the property B which appeared as an indispensable “technical” hypothesis in previous papers on hedging (superreplication) of contingent claims under transaction costs. We show that it is equivalent to another condition on the “richness” of the set of consistent price systems, close to the condition PCE introduced by Rásonyi. In the last section, we deduce the Rásonyi theorem from our general result by using specific features of discrete-time models.     

The Optimal Choice for Lenders Facing Defaults: Short Sale,Foreclose, or REO

When mortgage borrowers default and have no desire or ability to keep their property, then loss mitigation involves a sale of the property via one of the following options: (1) the lender allows pre-foreclosure “short sale” by the borrower, (2) the lender institutes the foreclosure process under a notice of default and the property is sold during the process by the borrower, and (3) the lender forecloses on the property, takes title, and sells the property in the market as real estate owned (REO). Sale of the property in the above three options is conducted by a motivated seller, either the owner or the lender, who desires to sell the property as quickly as possible. Thus, relative to a no-default sale, the house is most likely to be sold at a discounted price. It is generally expected that the discount would be lower in the case of a “short sale.” This option, however, may result in a longer marketing time, thus a higher total loss, than the other two options. We developed a model that allows simultaneous estimation of price and time-on-market effects of “short sales,” foreclosures, and REO options. We find that the short-sale option has the lowest-price discount, but significantly higher costs associated with marketing time. The pattern of price discount and marketing time reverses as we move to a sale while in the process of foreclosure and to a sale with an REO status.     

Risk-neutral compatibility with option prices

A common problem is to choose a “risk-neutral” measure in an incomplete market in asset pricing models. We show in this paper that in some circumstances it is possible to choose a unique “equivalent local martingale measure” by completing the market with option prices. We do this by modeling the behavior of the stock price X, together with the behavior of the option prices for a relevant family of options which are (or can theoretically be) effectively traded. In doing so, we need to ensure a kind of “compatibility” between X and the prices of our options, and this poses some significant mathematical difficulties.     

The numéraire portfolio in semimartingale financial models

We study the existence of the numéraire portfolio under predictable convex constraints in a general semimartingale model of a financial market. The numéraire portfolio generates a wealth process, with respect to which the relative wealth processes of all other portfolios are supermartingales. Necessary and sufficient conditions for the existence of the numéraire portfolio are obtained in terms of the triplet of predictable characteristics of the asset price process. This characterization is then used to obtain further necessary and sufficient conditions, in terms of a no-free-lunch-type notion. In particular, the full strength of the “No Free Lunch with Vanishing Risk” (NFLVR) condition is not needed, only the weaker “No Unbounded Profit with Bounded Risk” (NUPBR) condition that involves the boundedness in probability of the terminal values of wealth processes. We show that this notion is the minimal a-priori assumption required in order to proceed with utility optimization. The fact that it is expressed entirely in terms of predictable characteristics makes it easy to check, something that the stronger NFLVR condition lacks.      

The marginal cost of public funds and the flypaper effect

A lump-sum intergovernmental transfer has a “price effect”, as well as an “income effect”, because it allows the recipient government to reduce its tax rate, which lowers its marginal cost of public funds, while still providing the same level of public service. This reduction in the effective price of providing the public service helps to explain the “flypaper effect”—the empirical observation that a lump-sum grant has a much larger effect on spending than an increase in personal income. Contrary to the assertions of Mieszkowski (Modern Public Finance, 1994) and Hines and Thaler (J. Econ. Perspect. 9:217–226, 1995), a model of a benevolent local government financing its expenditures with a distortionary tax predicts flypaper effects from lump-sum grants that are similar to those observed in many econometric studies.     

What is the Natural Scale for a Lévy Process in Modelling Term Structure of Interest Rates?

This paper gives examples of explicit arbitrage-free term structure models with Lévy jumps via the state price density approach. By generalizing quadratic Gaussian models, it is found that the probability density function of a Lévy process is a “natural” scale for the process to be the state variable of a market.      

Common (stock) sense about risk-shifting and bank bailouts

If a bank is facing insolvency, it will be tempted to reject good loans and accept bad loans so as to shift risk onto its creditors. We analyze the effectiveness of buying up toxic mortgages in troubled banks, buying preferred stock, and buying common stock. If bailing out banks deemed “too big to fail” involves buying assets at above fair market values, then these banks are encouraged ex ante to gamble on bad assets. Buying up common (preferred) stock is always the most (least) ex ante- and ex post-efficient type of capital infusion, regardless of whether the bank volunteers for the recapitalization.     

Asset price bubbles from heterogeneous beliefs about mean reversion rates

Harrison and Kreps showed in 1978 how the heterogeneity of investor beliefs can drive speculation, leading the price of an asset to exceed its intrinsic value. By focusing on an extremely simple market model—a finite-state Markov chain—the analysis of Harrison and Kreps achieved great clarity but limited realism. Here we achieve similar clarity with greater realism, by considering an asset whose dividend rate is a mean-reverting stochastic process. Our investors agree on the volatility, but have different beliefs about the mean reversion rate. We determine the minimum equilibrium price explicitly; in addition, we characterize it as the unique classical solution of a certain linear differential equation. Our example shows, in a simple and transparent manner, how heterogeneous beliefs about the mean reversion rate can lead to everlasting speculation and a permanent “price bubble.”     

The makings of an information leader: the intraday price discovery process for individual stocks in the DJIA

The main purpose of this paper is to construct an intraday arbitrage price series for each stock in the DJIA using information in the Diamond Trust Fund ETF. We then compute the information shares (Hasbrouck in J Finan 50(4):1175–1199, 1995) for the actual versus the arbitrage prices for each stock. While previous literature documents that ETFs lead stock indices in information origination, we find that some firms are “information leaders” in that the information share that comes from the stock price is larger than that which comes from the ETF-related arbitrage price. Further analysis is conducted to uncover the firm-specific factors that are related to a stock’s role in information generation.     

Home Price,Time-on-Market,and Seller Heterogeneity Under Changing Market Conditions

This paper develops a formal model to examine the effect of changing market conditions and individuals’ selling constraints on selling price and time-on-market. Using the concept of Relative Liquidity Constraint (RLC)—a stochastic variable that captures the randomness of future individual constraints and market conditions—the study presents the first ex ante analysis that extends the investigation of the issue of seller heterogeneity to the point of the buying decision, that is, from the perspective of the buyer’s (future seller’s) point of view. We show that seller constraint, as well as the uncertainty of such a constraint, significantly depresses the expected selling price and increases risk. Our closed-form formulas provide a set of simple quantitative tools that enable buyers and sellers to adjust the “market average” to their ex ante “individual expectations”.     

Analysis of efficient markets

A simple trading model is presented in which Bayes’ rule is used to aggregate traders’ forecasts about risky assets’ future returns. In this financial market, Bayes’ rule operates like an omnipotent market-maker performing functions that in 1776 Adam Smith attributed to an “invisible hand.” We have analyzed two distinct cases: in the first scenario, the traders’ forecast errors are uncorrelated, and in the second scenario, the traders’ forecast errors are correlated. The contribution of our paper is fourfold: first, we prove that the “efficient market” mean-return can be expressed as a complex linear combination of the traders’ forecasts. The weights depend on the forecast variances, as well as on the correlations among the traders’ forecasts. Second we show that the “efficient” variance is equal to the inverse of the sum of the traders’ precision errors, and is also related to the correlations among the traders’ forecast errors. Third, we prove that the efficient market return is the best linear minimum variance estimator (BLMVE) of the security’s mean return (in the sense that it minimizes the sum of the traders’ mean squared forecast errors). Thus, an efficient market aggregates traders’ heterogeneous information in an optimal way. Fourth, we prove that an efficient market produces a mean return (price) as a Blackwell sufficient (most informative) experiment among all possible aggregated expected return (price) forecasts.     

A Quarterly Transactions-based Index of Institutional Real Estate Investment Performance and Movements in Supply and Demand

This article presents a methodology for producing a quarterly transactions-based index (TBI) of property-level investment performance for U.S. institutional real estate. Indices are presented for investment periodic total returns and capital appreciation (or price-changes) for the major property types included in the NCREIF Property Index. These indices are based on transaction prices to avoid appraisal-based sources of index “smoothing” and lagging bias. In addition to producing variable-liquidity indices, this approach employs the Fisher-Gatzlaff-Geltner-Haurin (Real Estate Econ., 31: 269–303, 2003) methodology to produce separate indices tracking movements on the demand and supply sides of the investment market, including a “constant-liquidity” (demand side) index. Extensions of Bayesian noise filtering techniques developed by Gatzlaff and Geltner (Real Estate Finance, 15: 7–22, 1998) and Geltner and Goetzmann (J. Real Estate Finance Econ., 21: 5–21, 2000) are employed to allow development of quarterly frequency, market segment specific indices. The hedonic price model used in the indices is based on an extension of the Clapp and Giacotto (J. Am. Stat. Assoc., 87: 300–306, 1992) “assessed value method,” using a NCREIF-reported recent appraised value of each transacting property as the composite “hedonic” variable, thus allowing time-dummy coefficients to represent the difference each period between the (lagged) appraisals and the transaction prices. The index could also be used to produce a mass appraisal of the NCREIF property database each quarter, a byproduct of which would be the ability to provide transactions price based “automated valuation model” estimates of property value for each NCREIF property each quarter. Detailed results are available at .     

A new paradigm for forecasting security returns in a market regulated by price limits

Numerous futures markets in the US and many stock markets around the world set a “limit” price before each trading session, based on the settlement price at the end of the previous trading day. Price limits are boundaries set by market regulators to restrict large daily fluctuations in the price of securities. Once the return limit is triggered, traders cannot observe the equilibrium return that would have prevailed in the absence of such regulation. We develop an innovative approach for forecasting security returns (and prices) in a market regulated by price limits. Our forecasting model allows for multiple limit-hits. The model is robust, straightforward and easy for practitioners to use. A few numerical predictions are provided for hypothetical securities, and for seven traded futures contracts.     

Volatility Decomposition and Correlation in International Securitized Real Estate Markets

This study contributes to the literature in international securitized real estate market volatility in three ways. Each market’s conditional volatility is decomposed into a “permanent” or long-run component and a “transitory” or short-run component via a component-GARCH model. Even though with the same number of common factors derived from the “permanent” and “transitory” volatility series, their loadings are not similar and consequently the long-run and short-run volatility linkages for some markets are different. Finally there are significant volatility co-movements between real estate and stock markets’ “permanent” and “transitory” components suggesting that real estate markets are at least not segmented from stock markets in international investing.     

Arbitrage Opportunities in Diverse Markets via a Non-equivalent Measure Change

We study arbitrage opportunities in diverse markets as introduced by Fernholz (J Math Econ 31:393–417, 1999). By a change of measure technique we are able to generate a variety of diverse markets. The construction is based on an absolutely continuous but non-equivalent measure change which implies the existence of instantaneous arbitrage opportunities in diverse markets. For this technique to work, we single out a crucial non-degeneracy condition. Moreover, we discuss the dynamics of the price process under the new measure as well as further applications.Both authors gratefully acknowledge financial support by the National Centre of Competence in Research “Financial Valuation and Risk Management” (NCCR FINRISK). The NCCR FINRISK is a research program supported by the Swiss National Science Foundation. The first author also thanks Credit Suisse Group for financial support.     

Skewness of Returns, Capital Adequacy, and Mortgage Lending

We calibrate a simulation model of credit value-at-risk for mortgage lending to UK experience. Simulations to capture the skewness of returns that might arise in the context of a financial crisis suggest that the IRB calculations of the new Basel Accord can substantially understate prudential capital adequacy. The same model shows that raising capital requirements has only a small impact on bank funding costs. We conclude that Pillar 2 supervisory review should increase capital requirements above IRB levels for secured bank assets—those whose returns can potentially fall furthest, relative to other, normally “riskier” assets, in extreme outcomes. JEL classification: G21, G28, R31. Presented at the December 2003 conference at the University of Tor Vegata, Rome. We are grateful for comments from William Lang, Mario Onarato, Larry Wall, and from an anonymous referee. All errors and omissions are our own responsibility. “The lady doth protest too much, methinks. The Queen's response to the players in Hamlet, Act 3, scene 2.     

Long-Range Dependence in U.S. Home Price Volatility

The existence of GARCH effects in a financial price series means that the probability of large losses is much higher than standard mean-variance analysis suggests. Accordingly, several recent papers have investigated whether GARCH effects exist in the U.S. housing market, as changes in house prices can have far-ranging impacts on defaults, foreclosures, tax revenues and the values of mortgage-backed securities. Some research in finance indicates that the conditional variance of some assets exhibits far greater persistence, or even “long memory”, than is accounted for in standard GARCH models. If house prices do indeed have this very persistent volatility, properly estimating the conditional variance to allow for such persistence is crucial for optimal portfolio management. We examine a number of U.S. metropolitan areas, and find that, for those with significant GARCH effects, more than half indeed exhibit the very high persistence found in other assets such as equities. We also find that, for those markets exhibiting such persistent volatility, C-GARCH models typically do a better job in forecasting than standard GARCH models. Moreover, there is some tentative evidence that metro areas with the fastest appreciation may be most likely to have such long memory conditional variance. These findings should help in improving risk management, through, for instance the construction of better-specified value-at-risk models.