Exchange Rates and the Conversion of Currency‐Specific Risk Premia

How do the risk factors that drive asset prices influence exchange rates? Are the parameters of asset price processes relevant for specifying exchange rate processes? Most international asset pricing models focus on the analysis of asset returns given exchange rate processes. Little work has been done on the analysis of exchange rates dependent on asset returns. This paper uses an international stochastic discount factor (SDF) framework to analyse the interplay between asset prices and exchange rates. So far, this approach has only been implemented in international term structure models. We find that exchange rates serve to convert currency‐specific discount factors and currency‐specific prices of risk – a result linked to the international arbitrage pricing theory (IAPT). Our empirical investigation of exchange rates and stock markets of four countries presents evidence for the conversion of currency‐specific risk premia by exchange rates.     

Pricing growth-rate risk

We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S. We also consider a reference growth process G that may represent the growth in the payoff of a single asset or of the macroeconomy. Both S and G are modeled conveniently as multiplicative functionals of a multidimensional Brownian motion. We consider the pricing implications of parametrized family of growth processes G ^ε , with G ⁰=G, as ε is made small. This parametrization defines a direction of growth-rate risk exposure that is priced using the stochastic discount factor S. By changing the investment horizon, we trace a term structure of risk prices that shows how the valuation of risky cash flows depends on the investment horizon. Using methods of Hansen and Scheinkman (Econometrica 77:177–234, 2009), we characterize the limiting behavior of the risk prices as the investment horizon is made arbitrarily long.     

Financial Intermediaries and the Cross‐Section of Asset Returns

Financial intermediaries trade frequently in many markets using sophisticated models. Their marginal value of wealth should therefore provide a more informative stochastic discount factor (SDF) than that of a representative consumer. Guided by theory, we use shocks to the leverage of securities broker‐dealers to construct an intermediary SDF. Intuitively, deteriorating funding conditions are associated with deleveraging and high marginal value of wealth. Our single‐factor model prices size, book‐to‐market, momentum, and bond portfolios with an R² of 77% and an average annual pricing error of 1%—performing as well as standard multifactor benchmarks designed to price these assets.     

Commentary: Discount Rates in Disarray – Evidence on Flawed Goodwill Impairment Testing

Carlin and Finch (2009) compare the reported goodwill impairment discount rates to their own ‘independent’ estimate for a sample of 105 Australian firms. On the basis of this comparison they claim (but do not show) that the discretion in determining the discount rate ‘could be used opportunistically’ and ‘fundamental questions must be asked about the quality of reported earnings … produced in conformity with the IFRS regime’. This commentary points out that the research design does not permit the assessment of either of these claims.     

A Model of International Asset Pricing with a Constraint on the Foreign Equity Ownership

This paper derives a closed-form valuation model in a two-country world in which the domestic investors are constrained to own at most a fraction, δ, of the number of shares outstanding of the foreign firms. When the “δ constraint” is binding, two different prices rule in the foreign securities market, reflecting the premium offered by the domestic investors over the price under no constraints and the discount demanded by the foreign investors. The premium is shown to be a multiple of the discount, the multiple being the ratio of the aggregate risk aversion of the domestic and foreign investors. Given the aggregate risk-aversion parameters, the equilibrium premium and discount are determined by the severity of the δ constraint and the “pure” foreign market risk.     

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.     

Discount rate changes,stock market returns,volatility, and trading volume: Evidence from intraday data and implications for market efficiency

We examine the effect of discount rate changes on stock market returns, volatility, and trading volume using intraday data. Equity returns generally respond negatively and significantly to the unexpected announcements; however, the effect of expected changes on equity returns is insignificant. Furthermore, our results indicate that equity prices respond to announcements within the trading period/hour after the information release. An indication of a return reversal is too small to cover the full transaction costs. Unexpected discount rate changes also contribute to higher market volatility although the volatility is short-lived. Similarly, unexpected changes in discount rates induce larger trading volume while expected changes do not. Abnormal trading volume occurs only in period t. Our results also support the notion that unexpected changes in the discount rates impact market returns irrespective of the Federal Reserve operating procedures.     

New bond pricing models with applications to Japanese data

In this paper, the cross-sectional bond pricing model for individual bonds Kariya (1993) proposed by formulating stochastic discount function (term structure) is first applied to Japanese Government bond (JG-bond) data. The model performs very well as it stands. Second, we generalize the cross-sectional model to two types of time-dependent Markov models (TDM's) with the term structure of discount rates of each bond att being dependent on the one att−1, and apply them to the same data to find significantly improved results over those of the cross-sectional model. In fact, almost all the differences between actual prices and model values are less than 0.5 yen in each month over 12 years, implying that the error rate is less than 0.5%. On the basis of our analysis, we propose a TDM as a model for JG-bond trading.     

The Beta Dilemma in Emerging Markets

In principle, emerging markets analysts employ the same analytical framework when estimating the value of businesses as their counterparts in developed economies: they forecast future cash flows and discount those to the present with appropriate costs of capital that are estimated using the Capital Asset Pricing Model (CAPM) framework. But in practice, emerging market analysts have a more complicated job because the task of estimating costs of equity in emerging markets is more difficult. Whereas developed economies have an abundance of historical data on overall stock market movements, industry share price behavior, and many individual share price histories, emerging market economies often do not. There may be no comparable local firms that are publicly traded—or if there are, their CAPM betas may be unreliable. And if analysts instead use the beta of a U.S. competitor as a surrogate for the emerging market beta, they face the question of whether domestic betas are equivalent across borders. As a consequence, appraisers of emerging market companies confront a “beta dilemma.” Part of this is a data problem stemming from shorter share price histories in emerging markets and the absence of publicly traded companies in some industries. In such cases, analysts may be inclined to use industry betas calculated with U.S. share prices as a substitute. But this creates an equivalence problem—the possibility, as confirmed by the author's research, that domestic U.S. and emerging market betas are not statistically equivalent for most industries. The author proposes a solution to this problem that involves grouping emerging markets into a single, distinctive asset class that allows for reliable calculations of industry betas. He also suggests ways of testing emerging market industry betas to determine whether they are statistically comparable.     

Assessing Specification Errors in Stochastic Discount Factor Models

In this article we develop alternative ways to compare asset pricing models when it is understood that their implied stochastic discount factors do not price all portfolios correctly. Unlike comparisons based on ${\chi }^2$ statistics associated with null hypotheses that models are correct, our measures of model performance do not reward variability of discount factor proxies. One of our measures is designed to exploit fully the implications of arbitrage-free pricing of derivative claims. We demonstrate empirically the usefulness of our methods in assessing some alternative stochastic factor models that have been proposed in asset pricing literature.     

Mean Reversion in Net Discount Ratios: A Study in the Context of Fractionally Integrated Models

This article introduces a new alternative to the ongoing debate about stationarity and mean reversion of the net discount ratio. Modeling the net discount ratio as a fractionally integrated (I(d)) process, we apply recently developed frequency domain estimation procedures and find evidence that the net discount ratio is an I(d) process with 1/2 ≤d < 1. Although nonstationary, such series behave like stationary processes in one interesting respect; they are mean‐reverting. We present results from a simulation experiment suggesting that the finding of a nonstationary, but mean‐reverting net discount ratio generally supports the validity of current practice in estimating economic damages in personal injury litigation. Moreover, if recognized and accounted for, the presence of long memory in the net discount ratio even offers the potential to significantly improve forecasts of the present value of future earnings.     

Option pricing under regime switching

Abstract

This paper develops a family of option pricing models when the underlying stock price dynamic is modelled by a regime switching process in which prices remain in one volatility regime for a random amount of time before switching over into a new regime. Our family includes the regime switching models of Hamilton (Hamilton J 1989 Econometrica 57 357–84), in which volatility influences returns. In addition, our models allow for feedback effects from returns to volatilities. Our family also includes GARCH option models as a special limiting case. Our models are more general than GARCH models in that our variance updating schemes do not only depend on levels of volatility and asset innovations, but also allow for a second factor that is orthogonal to asset innovations. The underlying processes in our family capture the asymmetric response of volatility to good and bad news and thus permit negative (or positive) correlation between returns and volatility. We provide the theory for pricing options under such processes, present an analytical solution for the special case where returns provide no feedback to volatility levels, and develop an efficient algorithm for the computation of American option prices for the general case.     

Time-varying long-run mean of commodity prices and the modeling of futures term structures

The exploration of the mean-reversion of commodity prices is important for inventory management, inflation forecasting and contingent claim pricing. Bessembinder et al. [J. Finance, 1995, 50, 361–375] document the mean-reversion of commodity spot prices using futures term structure data; however, mean-reversion to a constant level is rejected in nearly all studies using historical spot price time series. This indicates that the spot prices revert to a stochastic long-run mean. Recognizing this, I propose a reduced-form model with the stochastic long-run mean as a separate factor. This model fits the futures dynamics better than do classical models such as the Gibson–Schwartz [J. Finance, 1990, 45, 959–976] model and the Casassus–Collin-Dufresne [J. Finance, 2005, 60, 2283–2331] model with a constant interest rate. An application for option pricing is also presented in this paper.     

Handling Valuation Models

Valuation models are useful tools, but they need to be handled with care. When taking the form of mathematical formulas, they can easily be made to convey a false sense of precision. In particular, selective choice of long‐term growth rates and discount rates can be used to justify almost any desired valuation. The author shows how relatively simple valuation models can be applied by active investors in a way that honors the fundamentalist dictum of building valuations on the foundation of “what we know” and avoiding speculation about long‐term growth rates. The article also emphasizes the role of accounting in discovering what we know, and shows how to use accounting results in a way that not only minimizes speculation about growth rates and discount rates, but actually challenges the speculation about those rates that is implicit in current stock prices. Accounting‐based valuation models are “reverse‐engineered” to discover the forecasts of future operating performance that are effectively built into current prices, so the plausibility of such forecasts can be evaluated with fundamental analysis. In this sense, valuation models are used not so much to discover the “right” price as to identify, and then subject to critical examination, the market's current expectations about future performance.     

Flexible Prices and the Business Cycle

Business cycles models with flexible prices face two major empirical challenges. One regards observed output dynamics: the positive, short run, autocorrelation in GNP growth, and the hump‐shaped, trend‐reverting output response to transitory shocks ( Cogley and Nason 1995 ). The other regards the alleged persistent decline in employment following a positive technology shock ( Galí 1999 ). No determinate model with flexible prices has so far been able to address all of the Cogley Nason–Galí challenges. We show that the standard RBC model can do so if it contains a signal extraction problem involving permanent and temporary supply shocks.     

AN EMPIRICAL TEST OF AN EX-ANTE MODEL OF THE DETERMINATION OF STOCK RETURN VOLATILITY

The assumption that changing expected cash flows and discount factors affect a security's return is at the foundation of many financial models. This study examines empirically the hypothesis that expected stock return variability is a function of cash flow and discount rate uncertainty. Maximum likelihood estimation techniques and expectational data are employed. Strong, positive relationships are found, verifying the foundations of the ex-ante models with ex-ante data and providing a better understanding of security markets by explaining, in part, the causes of expected stock price variability.     

Prediction of Individual Bond Prices via a Dynamic Bond Pricing Model: Application to Japanese Government Bond Price Data

In this paper, we propose a dynamic bond pricing model and report the usefulness of our bond pricing model based on analysis of Japanese Government bond price data. We extend the concept of the time dependent Markov (TDM) model proposed by Kariya and Tsuda (Financial Engineering and the Japanese Markets, Kluwer Academic Publishers, Dordrecht, The Netherlands, Vol. 1, pp. 1–20) to a dynamic model, which can obtain information for future bond prices. A main feature of the extended model is that the whole stochastic process of the random cash-flow discount functions of each individual bond has a time series structure. We express the dynamic structure for the models by using a Bayesian state space representation. The state space approach integrates cross-sectional and time series aspects of individual bond prices. From the empirical results, we find useful evidence that our model performs well for the prediction of the patterns of the term structure of the individual bond returns.