Optimum consumption and portfolio rules with money as an asset

This article generalizes Merton's optimum consumption and portfolio rules in continuous time by introducing money as a capital asset and allowing for uncertain inflation. Assuming that prices are log-normally distributed, a three-funds theorem is derived and the introduction of money is shown not to change the form of the standard inflation-adjusted CAPM but to change the market price of risk. The individual's consumption-portfolio problem is completely solved under uncertain inflation if his utility function is iso-elastic in its arguments. Comparative statics are used to assess the influence of changes in exogenous parameters on the individual's optimal rules.     

Stock and Bond Liquidity and its Effect on Prices and Financial Policies

An asset is liquid if it can be traded at the prevailing market price quickly and at low cost. We show that in addition to risk, liquidity affects asset prices and returns. Theories of asset pricing suggest that the expected return of an asset is increasing in its risk, because risk-averse investors require compensation for bearing more risk. Because investors are also averse to the costs of illiquidity and want to be compensated for bearing them, asset returns are increasing in illiquidity. Thus, asset prices should depend on two asset characteristics: risk and liquidity. This paper surveys research on the effects of liquidity on asset prices and returns, showing that liquidity is an important factor in capital asset pricing.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced byan expected-utility maximizing investor who, over a given timehorizon, is constrained to hold an asset which cannot be replicatedby dynamic trading and which therefore does not have a uniqueno-arbitrage price. We first derive the private valuation whichthe investor assigns to the nontraded asset in order to determinehis optimal investment in the traded assets. We thereby showthat, as part of this portfolio, the investor hedges the privatevaluation process of the nontraded asset, rather than its marketprice process. We also study the price at which the investorwould be willing to sell the nontraded asset if he were subsequentlyprohibited from trading in it, as well as the amount the investorwould be willing to pay to remove the trading restriction. Allthree values are shown to depend in an intuitive manner on theinvestor’s risk aversion, the residual risk of the nontradedasset unhedged by the traded assets, the difference betweenthe constrained holding and optimal unconstrained holding ofthe asset and the length of the time horizon over which theasset cannot be traded. JEL Classification: G11     

Cash demand,liquidation costs and capital market equilibrium under uncertainty

In this paper, the portfolio and the liquidity planning problems are unified and analyzed in one model. Stochastic cash demands have a significant impact on both the composition of an individual's optimal portfolio and the pricing of capital assets in market equilibrium. The derived capital asset pricing model with cash demands and liquidation costs shows that both the market price of risk and the systematic risk of an asset are affected by the aggregate cash demands and liquidity risk. The modified model does not require that all investors hold an identical risky portfolio as implied by the Sharpe-Lintner-Mossin model. Furthermore, it provides a possible explanation for the noted discrepancies between the empirical evidence and the prediction of the traditional capital asset pricing model.     

Optimal Hedging and Valuation of Nontraded Assets

This paper examines a number of valuation problems faced by an expected-utility-maximizing investor who, over a given time horizon, is constrained to hold an asset which cannot be replicated by dynamic trading and which therefore does not have a unique no-arbitrage price. We first derive the private valuation which the investor assigns to the nontradedasset in order to determine his optimal investment in the traded assets. We thereby show that, as part of this portfolio, the investor hedges the private valuation process of the nontraded asset, rather than its market price process. We also study the price at which the investor would be willing to sell the nontraded asset if he were subsequently prohibited from trading in it, as well as the amount the investor would be willing to pay to removethe trading restriction. All three values are shown to depend in an intuitive manner on the investor's risk aversion, the residual risk of the nontraded asset unhedged by the traded assets, the difference between the constrained holding and optimal unconstrained holding of the asset and the length of the time horizon over which the asset cannot be traded.     

An alternative measure of the “world market portfolio”: Determinants, efficiency, and information content

The world market portfolio plays an important role in international asset pricing, but is unobservable in practice. We first propose a framework for constructing a market proxy that corresponds to the “market portfolio” of financial theory. We then construct this proxy, analyze its determinants and test its efficiency and explanatory power over the period 1975-2007 with respect to the return generating processes of a broad asset universe. We show that its major determinants are traded assets and that it is not efficient. However, it is significant for explaining individual asset returns over an asset universe that includes stocks, bonds, money markets and commodities. The explanatory information is incremental to what is available in traded asset prices and the significance of this information is robust with respect to diversified portfolios generated by factor analysis and to characteristic-sorted portfolios as well as to various model specifications, including the single-index model, the Fama-French (1992) three factor model for stocks, and various specifications of multi-index models hedged and unhedged for foreign currency risk.     

International asset pricing under segmentation and PPP deviations

We analyze the impact of both purchasing power parity (PPP) deviations and market segmentation on asset pricing and investor's portfolio holdings. The freely traded securities command a world market risk premium and an inflation risk premium. The securities that can be held by only a subset of investors command two additional premiums: a conditional market risk premium and a segflation risk premium. Our model is empirically supported with important implications for tests of international asset pricing.     

Capital asset prices with heterogeneous beliefs

Assuming continuous trading in continuous time with Brownian motion processes, the basic capital asset pricing model of Sharpe, Lintner, and Mossin is developed under arbitrary distributions of investors' beliefs consistent with available information. Results on the processing of information are reported, and properties of investors' portfolios are derived.     

A continuous-time model for reinvestment risk in bond markets

When comparing standard bond market models with practice we observe that, whereas the literature places no restrictions on the time to maturity of traded bonds, this is actually the case in practice. Hence, standard models ignore the reinvestment risk present in practice when considering contacts with longer time to maturity than the longest bond traded in the market. In this paper we propose a model including this reinvestment risk. We place a restriction on the bonds traded in the market by limiting the time to maturity of traded bonds. At fixed times, new bonds are issued in the market, thus extending the time of maturity of traded bonds. The initial prices of the new bonds issued in the market depend on the information generated by the market and a stochastic variable independent thereof describing the reinvestment risk. In order to quantify and control the reinvestment risk we apply the criterion of risk-minimization.     

Estimating the Divisional Cost of Capital: An Analysis of the Pure-Play Technique

This paper suggests that the pure-play technique can be used in conjunction with the capital asset pricing model to determine the cost of equity capital for the divisions of a multidivision firm. Since the beta for a division is unobservable in the marketplace, a proxy beta derived from a publicly traded firm whose operations are as similar as possible to the division in question is used as the measure of the division's systematic risk. To provide empirical support for using the pure-play technique, a sample of multidivision firms and pure-play associated with each division is examined. It is shown that an appropriately weighted average of the betas of the pure-play firms closely approximates the beta of the multidivision firm.     

Mechanics of good trade execution in the framework of linear temporary market impact

We define the concept of good trade execution and we construct explicit adapted good trade execution strategies in the framework of linear temporary market impact. Good trade execution strategies are dynamic, in the sense that they react to the actual realisation of the traded asset price path over the trading period; this is paramount in volatile regimes, where price trajectories can considerably deviate from their expected value. Remarkably, however, the implementation of our strategies does not require the full specification of an SDE evolution for the traded asset price, making them robust across different models. Moreover, rather than minimising the expected trading cost, good trade execution strategies minimise trading costs in a pathwise sense, a point of view not yet considered in the literature. The mathematical apparatus for such a pathwise minimisation hinges on certain random Young differential equations that correspond to the Euler–Lagrange equations of the classical Calculus of Variations. These Young differential equations characterise our good trade execution strategies in terms of an initial value problem that allows for easy implementations.     

Exchange‐Traded Fund Introductions and Closed‐End Fund Discounts and Volume

Exchange‐traded funds (ETFs), like closed‐end funds (CEFs), are managed portfolios traded like individual stocks. We hypothesize that the introduction of an ETF in an asset class similar to an existing CEF results in a substitution effect that reduces the value of the CEF's shares relative to that of its underlying assets. Our event studies show that upon the introduction of a similar ETF, CEF discounts widen significantly and relative volume declines significantly. Single‐equation and systems estimation models show that the widening in discounts and reduction in volume are related to returns‐based measures of the substitutability of ETFs for CEFs.     

Price discovery and common factor models

If a financial asset is traded in more than one market, common factor models may be used to measure the contribution of these markets to the price discovery process. We examine the relationship between the Hasbrouck (J. Finance (50) (1995) 1175) and Gonzalo and Granger (J. Bus. Econ. Stat. 13 (1995) 27) common factor models. These two models complement each other and provide different views of the price discovery process between markets. The Gonzalo and Granger model focuses on the components of the common factor and the error correction process, while the Hasbrouck model considers each market's contribution to the variance of the innovations to the common factor. We show that the two models are directly related and provide similar results if the residuals are uncorrelated between markets. However, if substantive correlation exists, they typically provide different results. We illustrate these differences using analytic examples plus a real world example consisting of electronic communications networks (ECNs) and other Nasdaq market makers.     

Do ADRs enhance portfolio performance for a domestic portfolio? Evidence from the 1990s

American depository receipts (ADRs) represent an increasingly popular and convenient mechanism for international investing. We analyze ADRs traded throughout the 1990s and find that these securities offer a diversification and portfolio performance benefit when combined with a domestic portfolio (proxied by the S&P 500). While we find that emerging market ADRs are effective instruments for reducing portfolio risk, they do not improve portfolio performance as measured by the Sharpe ratio. Developed market ADRs do improve portfolio performance as measured by the Sharpe ratio. The asset allocation which maximizes the Sharpe ratio is 84 percent domestic stocks, 16 percent developed ADRs, and 0 percent emerging ADRs. Further, due to problems in defining an appropriate market index for ADRs, the Sharpe ratio is viewed to be the preferred performance measure. Other measures such as Jensen’s alpha and the Treynor measure are susceptible to being “gamed” to distort portfolio performance.     

The consumption based asset pricing model: A note on potential tests and applications

Breeden's demonstration that Merton's multi-beta capital asset pricing model can be collapsed into a single-beta model where betas are computed with respect to aggregate consumption is an important theoretical advance. Nonetheless, Breeden's model retains many of the empirical problems that beset Merton's earlier version. In general the consumption betas will be nonstationary, so that the state variables must be observable for the model to be estimated.     

The Credit Risk and Pricing of OTC Options

In the over-the-counter (OTC) markets, the options traded are always subject to credit risk. Therefore the counterparty’s credit risk is a striking factor when pricing options, whereas it is not considered in the classic Black-Scholes models. Based on the first passage time models, this paper develops the credit risk and valuation model for the European options in the OTC markets, incorporating a practical default trigger mechanism. The default probability and the pricing formulae of the OTC options are obtained by using partial differential equation (PDE) techniques, especially Green’s function.     

Forecasting risk,informed speculation,and financial innovation

Speculators who prey on hedgers can stifle financial innovation in the sense that new markets can fail. In this paper I analyze whether a profit maximizing exchange nonetheless chooses to open markets for speculative securities and if so, how to circumvent the problem of market failure. I find that the optimal financial innovation takes two forms. The first is a market structure consisting of hedge instruments, traded in low volume at stable asset prices. The second is a market structure consisting of speculative instruments, traded in greater volume at volatile asset prices. These strategies are derived within the same framework where the cost and the quality of the speculators' information set and the hedgers risk aversion ultimately determine which is the optimal one.     

A Reduced‐Form Model for Warrant Valuation

This paper studies warrant valuation using a reduced‐form model. Analogous to the credit risk literature, structural models require complete information about the asset value process and the firm’s liabilities. In contrast, reduced‐form models require only information about the firm’s stock price process. We introduce a reduced‐form model where the warrant holder is a price taker, and we relate our model to structural models appearing in the literature.     

A critique of the asset pricing theory's tests Part I: On past and potential testability of the theory

Testing the two-parameter asset pricing theory is difficult (and currently infeasible). Due to a mathematical equivalence between the individual return/‘beta’ linearity relation and the market portfolio's mean-variance efficiency, any valid test presupposes complete knowledge of the true market portfolio's composition. This implies, inter alia, that every individual asset must be included in a correct test. Errors of inference inducible by incomplete tests are discussed and some ambiguities in published tests are explained.     

Corporate portfolio management

Summary We solve the optimal portfolio problem in continuous time from the point of view of a corporation, acting on behalf of risk neutral shareholders. Our model fits for example the case of a commercial bank. Risk aversion is generated endogenously by financial frictions, and increases when the value of the firm’s assets decrease. We find a remarkably simple investment policy: invest a multiple of the firm’s equity into the risky asset, keep the rest as cash reserves, and distribute dividends when the value of the firm exceeds some threshold. As a consequence, the firm locally behaves as a Von Neumann-Morgenstern investor with constant relative risk aversion.We thank three anonymous referees for their comments.