Showing papers on "Stochastic discount factor published in 1999"

Resurrecting the (C)Capm: A Cross-Sectional Test When Risk Premia Wre Time-Varying

Abstract: This paper explores the ability of theoretically based asset pricing models such as the CAPM and the consumption CAPM-referred to jointly as the (C)CAPM-to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumption CAPM, using aggregate consumption data, is able to account for the difference in returns between low book-to-market and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects.

Essentials of Stochastic Finance: Facts, Models, Theory

Abstract: This important book provides information necessary for those dealing with stochastic calculus and pricing in the models of financial markets operating under uncertainty; introduces the reader to the main concepts, notions and results of stochastic financial mathematics; and develops applications of these results to various kinds of calculations required in financial engineering. It also answers the requests of teachers of financial mathematics and engineering by making a bias towards probabilistic and statistical ideas and the methods of stochastic calculus in the analysis of market risks.

Inter-Generational Equity and the Rate of Discount in Long-Term Social Investment

Abstract: The importance of the correct choice of discount rate for social (or indeed individual) investments hardly needs elaboration. In the social context, the discount rate is, at least in part, an expression of concerns about equity between the present and future generations and among future generations. I say, in part, because it also expresses both an expectation of the rates of return available to future generations in alternative uses of capital and an expectation of the growth of income of the representative individual.

A critique of the stochastic discount factor methodology

Abstract: In this paper, we point out that the widely used stochastic discount factor ~SDF! methodology ignores a fully specified model for asset returns. As a result, it suffers from two potential problems when asset returns follow a linear factor model. The first problem is that the risk premium estimate from the SDF methodology is unreliable. The second problem is that the specification test under the SDF methodology has very low power in detecting misspecified models. Traditional methodologies typically incorporate a fully specified model for asset returns, and they can perform substantially better than the SDF methodology. ASSET PRICING THEORIES, such as those of Sharpe ~1964!, Lintner ~1965!, Black ~1972!, Merton ~1973!, Ross ~1976!, and Breeden ~1979!, show that the expected return on a financial asset is a linear function of its covariances ~or betas! with some systematic risk factors. This implication has been tested extensively in the finance literature by the so-called “traditional methodologies.” In the traditional methodologies, a data-generating process is first proposed for the returns, and then the restrictions imposed by an asset pricing model are tested as parametric constraints on the return-generating process. The approach taken by the traditional methodologies has a potential problem, which is that when the proposed return-generating process is misspecified the test results could be misleading. Therefore, in applying the traditional methodologies, researchers typically have to justify that the proposed data-generating process provides a good description of the returns. For example, when the proposed return-generating process is a factor model, one would like the model to have high R 2 in explaining the returns on the test assets, especially when the test assets are well-diversified portfolios. As many of the earlier theories are special cases of the stochastic discount factor ~SDF! model, recent empirical asset pricing studies have been focused on testing the pricing restrictions in terms of the SDF model, rather

Can Costs of Consumption Adjustment Explain Asset Pricing Puzzles

Abstract: We investigate Grossman and Laroque's (1990) conjecture that costs of adjusting consumption can account, in part, for the empirical failure of the consumptionbased capital asset pricing model (CCAPM). We incorporate small fixed costs of consumption adjustment into a CCAPM with heterogeneous agents. We find that undetectably small consumption adjustment costs can account for much of the discrepancy between the observed variance of nondurable aggregate consumption growth and the predictions of the CCAPM, and can partially reconcile nondurable consumption data with the observed equity premium. We conclude that the CCAPM's implications are nonrobust to extremely small adjustment costs. THE CONSUMPTION-BASED CAPITAL ASSET PRICING MODELS (CCAPMs)1 of Lucas (1978), Breeden (1979), and Grossman and Shiller (1982) have difficulty matching the high volatility of equity returns and the high mean equity premium found in U.S. data. First, the variance of the CCAPM asset pricing kernel is too low to generate plausible equity-return volatility. More precisely, Hansen and Jagannathan (1991) and Cochrane and Hansen (1992) show that, for any conjectured pricing kernel mean, the variance of the kernel is too low to satisfy the Hansen-Jagannathan bounds without implausibly high risk aversion or substantial habit formation.2 Second, the covariance between the CCAPM asset pricing kernel and excess equity returns is too low to generate a plausible equity premium. More precisely, let us define EP' as follows:

When are Options Overpriced? The Black-Scholes Model and Alternative Characterisations of the Pricing Kernel

Abstract: An important determinant of option prices is the elasticity of the pricing kernel used to price all claims in the economy. In this paper, we first show that for a given forward price of the underlying asset, option prices are higher when the elasticity of the pricing kernel is declining than when it is constant. We then investigate the implications of the elasticity of the pricing kernel for the stochastic process followed by the underlying asset. Given that the underlying information process follows a geometric Brownian motion, we demonstrate that constant elasticity of the pricing kernel is equivalent to a Brownian motion for the forward price of the underlying asset, so that the Black-Scholes formula correctly prices options on the asset. In contrast, declining elasticity implies that the forward price process is no longer a Brownian motion: it has higher volatility and exhibits autocorrelation. In this case, the Black-Scholes formula underprices all options.

Nonparametric Pricing of Multivariate Contingent Claims

Abstract: This paper develops and implements a methodology for pricing multivariate contingent claims (MVCC s) based on semiparametric estimation of the multivariate risk-neutral density function.This methodology generates MVCC prices which are consistent with current market prices of univariate contingent claims.This method allows for completely general marginal risk-neutral densities and is compatible with all univariate risk-neutral density estimation techniques. The univariate risk-neutral densities are related by their risk-neutral correlation, which is estimated using time-series data on asset returns and an empirical pricing kernel (Rosenberg and Engle, 1999). This permits the multivariate risk-neutral density to be identified without requiring observation of multivariate contingent claims prices. The semiparametric MVCC pricing technique is used for valuation of one-month options on the better of two equity index returns. Option contracts with payoffs dependent on are four equity indexpairs are considered: S&P500 - CAC40, S&P500 - NK225, S&P500 - FTSE100, and S&P500 - DAX30. Five marginal risk-neutral densities (S&P500, CAC40, NK225, FTSE100, and DAX30) are estimated semiparametrically using a cross-section of contemporaneously measured equity index option prices in each market. A bivariate risk-neutral Plackett (1965) density is constructed using the given marginals and risk-neutral correlation derived using an empirical pricing kernel and the historical joint density of the index returns. Price differences from a lognormal pricing formulausing historical and risk-neutral return moments are found to be significant.

Estimating the discount rate policy reaction function of the monetary authority

Abstract: This paper estimates a policy rule that explains the sign and the magnitude of the Federal Reserve's (Fed's) discount rate changes. It sets out a two-sided Type II Tobit model and develops a procedure for its estimation, considering the discrete and censored nature of the changes. The results suggest that the Fed has conducted discount rate policy counter-cyclically to influence output and to curb inflation, and that the Fed's response to policy indicators varies over monetary regimes. Furthermore, consistency is found between the model prediction of the discount rate change and a classification based on whether the change is technical or non-technical. Copyright © 1999 John Wiley & Sons, Ltd.

Extracting risk-neutral densities from option prices using mixture binomial trees

Abstract: Since the stock market crash in October of 1987, prices of index options deviate significantly from Black-Scholes theory. This fact is prominently documented in the literature as the volatility smile (M. Rubinstein 1994). The pricing error is a sign that the assumptions of the model do not capture all relevant information embedded in option prices. As response to this problem, previous research has relaxed some of the underlying assumptions in order to arrive at more realistic prices. Examples are changes in the data generating process of the underlying security, e.g., jump diffusion or constant elasticity of variance models. We reverse this direction of thought: we take recorded option prices as given and estimate the implied pricing kernel that is consistent with current market valuations. To be flexible in the shape of the risk-neutral density and to allow probabilities to be non-Gaussian, we use the concept of mixture distributions. We apply our methodology to a recent dataset of options on the S&P 500 index future traded on the Chicago Mercantile Exchange. The data spans the year 1998 and contains settlement prices for 22497 American-style futures options.

Price Elasticity of Demand and an Optimal Cash Discount Rate in Credit Policy

Abstract: While the provision of a cash discount is equivalent to a reduction in price, the role of price elasticity of demand in determining credit terms has been neglected in the extant literature. In this paper, this role is investigated and it is shown that the optimal cash discount rate is affected by the price elasticity of demand for the firm's product. The comparative effects on the optimal cash discount rate with respect to exogenous changes in the fraction of credit sales paid after taking cash discount, the cost of short-term funds and the bad debt loss ratio are investigated. A trade-off between the time value gain and the price elasticity of demand is established. We find that firms which sell in locations having different price elasticities for their products, and/or which face various costs of short-term funds in different locations, should vary their cash discount terms accordingly.

An Interpretation of SDF Based Performance Measures

Abstract: This note discusses stochastic discount factor (SDF) measures of mutual fund performance. It shows that the most common SDF performance measures can be interpreted as Jensen's alphas.

An Interpretation of SDF Based Performance Measures

Abstract: This note discusses stochastic discount factor (SDF) measures of mutual fund performance. It shows that the most common SDF performance measures can be interpreted as Jensen's "alphas". JEL Classification Numbers: G11, G12, G23

Financial Discount Rates in Project Appraisal

Abstract: In the financial appraisal of a project, the cashflow statements are constructed from two points of view: the Total Investment (TI) Point of View and the Equity Point of View. One of the most important issues is the estimation of the correct financial discount rates for the two points of view. In the presence of taxes, the benefit of the tax shield from the interest deduction may be excluded or included in the free cashflow (FCF) of the project. Depending on whether the tax shield is included or excluded, the formulas for the weighted average cost of capital (WACC) will be different. In this paper, using some basic ideas of valuation from corporate finance, the estimation of the financial discount rates for cashflows in perpetuity and single-period cashflows will be illustrated with simple numerical examples.

Minimum-Variance Kernels and Economic Risk Premia

Abstract: This paper offers a novel way of testing whether prespecified risk variables command significant risk premia. Specifically, we construct portfolios of securities to mimick the variation in the chosen risk variables, and we estimate the conditional and unconditional expected returns on these portfolios in excess of the risk-free rate. We also test for the ability of these hedging portfolios to price the returns on a large collection of assets. Our approach has several advantages over more traditional approachs that model asset returns as linear functions of a given set of explicit factors. First, the risk premia that we estimate do not depend on the appropriate specification of either an asset-pricing model or a stochastic process for asset returns. Second, while we allow for time variation in the conditional risk premia associated with economic risks, our estimates of the unconditional premia do not require explicit modeling of such time variation. Third, we can introduce conditioning information effectively to expand the set of asset returns under scrutiny and improve the ability of the hedging portfolio returns to track the economic risks. Fourth, we are able to impose the no-arbitrage positivity restriction on the pricing kernel, a requirement missing from the standard formulation of multi-beta models.

A Note on Formulating and Corroborating Discount Rates for Small Firms

Abstract: This article addresses the issue of formulating discount rates for small firms. The formulation of discount rates for small firms is most common in lost profit analysis and business valuation. This paper is divided into three sections. The first section in an overview of the more common methodologies for formulating discount rates. These methodologies include: using market rates for publicly traded securities, the capital asset pricing model, and the build-up method. The second section discusses the corroboration of the formulated discount rate via the use of market data. The final section is an illustrative example of corroborating a formulated discount rate using the methodology presented in the foregoing section.

Net Discount Rate and Below-Market Discount Rate: Two Methods in Forensic Economics

Abstract: This paper compares the below-market and net discount rate methods These are widely used to estimate damage awards in tort cases involving earnings loss Although nested in the same valuation model, they use information differently, require different procedures, and are fundamentally different methods The below-market method requires explicit forecasts of future earnings, which are then discounted On the other hand, the net discount rate method dispenses with the need to identify the stream of future earnings; instead, it combines growth and discounting into a single operation via a historical net discount rate

Resurrecting the (C)CAPM: a cross-sectional test when risk premia are time-varying

Abstract: This paper explores the ability of theoretically based asset pricing models such as the CAPM and the consumption CAPM-referred to jointly as the (C)CAPM - to explain the cross-section of average stock returns. Unlike many previous empirical tests of the (C)CAPM, we specify the pricing kernel as a conditional linear factor model, as would be expected if risk premia vary over time. Central to our approach is the use of a conditioning variable which proxies for fluctuations in the log consumption-aggregate wealth ratio and is likely to be important for summarizing conditional expectations of excess returns. We demonstrate that such conditional factor models are able to explain a substantial fraction of the cross-sectional variation in portfolio returns. These models perform much better than unconditional (C)CAPM specifications, and about as well as the three-factor Fama-French model on portfolios sorted by size and book-to-market ratios. This specification of the linear conditional consumption CAPM, using aggregate consumption data, is able to account for the difference in returns between low book-to-market and high book-to-market firms and exhibits little evidence of residual size or book-to-market effects.

Infinite-horizon optimal hedging under cone constraints

Abstract: We address the issue of hedging in infinite horizon markets with a type of con­ straints that the set of feasible portfolio holdings forms a convex cone. We show that the minimum cost of hedging a liability stream is equal to its largest present value with respect to admissible stochastic discount factors, thus can be deter­ mined without finding an optimal hedging strategy. We solve for an optimal hedg­ ing strategy by solving a sequence of independent one-period hedging problems. We apply the results to a variety of trading restrictions and also show how the admissible stochastic discount factors can be characterized.

Dynamics of Open Economy Models: What Is the Role of the Discount Factor?

Abstract: This paper examines the dynamic implications of the use of an endogenous discount factor in small open economy models. We first present a stochastic dynamic model of a small open economy with an endogenous discount factor. Then, we examine the same model with a fixed discount factor. We calibrate both models for a representative small open economy and then simulate them to examine the moment implications to help understand the impact of the preference formulation on model dynamics. We study the quantitative responses of the model variables to shocks in technology and real interest rates. Our results suggest that while the use of an endogenous discount factor helps researchers to define a stable stochastic steady state, the dynamic implications of the two models can be quite similar depending on the parameters of the model.

Environmental economics and cost–benefit analysis: the choice of an appropriate discount rate

Abstract: Notwithstanding earlier approbation from economists on the use of the discounting technique, the past twenty or thirty years have witnessed a growing acceptance of the use of this technique in cost–benefit analysis. Nevertheless, there is no general agreement on the type of discount rate to be employed, nor whether it would be more appropriate to employ a (lower) social discount rate, especially in the case of long–term projects or those which are assessed to have significant environmental impacts. Furthermore, in recent years, the earlier debate against the use of the discounting technique has re–emerged in somewhat different form. Against this background, this paper seeks to explain the different types of market discount rates available - namely, the consumption rate of interest, the investment rate of interest and the accounting rate of interest - and explores the argument for employing a (lower) social discount rate. Thereafter, attention is focused on the more recent debate against the use of the discounting technique in general. Finally, an attempt is made to assess alternative approaches to the conventional discounting technique: a zero discount rate, the internal rate of return and the use of so–called quasi–discount rates. The latter is found to offer a more pragmatic approach to the use of the discounting technique, and is considered more appropriate for cost–benefit analysis involving projects which have significant environmental impacts.