• Selected
• Entire List

Abstract:
Traditional approaches to valuing equities have largely focused on the Dividend Discount Model. It may be hard to reliably estimate dividend processes in small samples and market participants focus primarily on earnings and other accounting information in analyzing stocks. For these reasons we try to value stocks using earnings and book value. Building on the seminal work of Miller and Modigliani (1961) and Ohlson (1990, 1995) we develop a Generalized Earnings Model of stock valuation which uses earnings and book values. This is a general no-arbitrage model which uses stochastic pricing kernels. The model can be implemented by assuming the driving variables follow affine processes which allows tractable calculations. We apply the model to several individual stocks.

Abstract:
In theory, an investor can make infinite profits by taking unlimited positions in an arbitrage. In reality, however, investors must satisfy margin requirements which completely change the economics of arbitrage. We derive the optimal investment policy for a risk-averse investor in a market where there are arbitrage opportunities. We show that is is often optimal to underinvest in the arbitrage by taking a smaller position than margin constraints allow. In some cases, it is actually optimal for an investor to walk away from a pure arbitrage opportunity. Even when the optimal policy is followed, the arbitrage strategy may underperform the riskless asset to have an unimpressive Sharpe ratio. Furthermore, the arbitrage portfolio typically experiences losses at some point before the final convergence date. These results have important implications for the role of arbitrageurs in financial markets.

Arbitrage, margin requirements, optimal portfolio

Abstract:
While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores time-varying risk premiums and betas. We develop a model to consistently value cashflows with changing risk-free rates, predictable risk premiums and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large mis-valuations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time-variation in risk-free rates and factor loadings.

present value, term structure of discount rates, time-varying beta, time-varying risk premium, capital budgeting

Abstract:
While many studies document that the market risk premium is predictable and that betas are not constant, the dividend discount model ignores time-varying risk premiums and betas. We develop a model to consistently value cashflows with changing risk-free rates, predictable risk premiums and conditional betas in the context of a conditional CAPM. Practical valuation is accomplished with an analytic term structure of discount rates, with different discount rates applied to expected cashflows at different horizons. Using constant discount rates can produce large mis-valuations, which, in portfolio data, are mostly driven at short horizons by market risk premiums and at long horizons by time-variation in risk-free rates and factor loadings.

Abstract:
While many studies document that the market risk premium is predictable and that betas are not constant, the standard dividend discount model ignores these effects. This paper shows how to value cashflows with changing risk-free rates, predictable risk premiums and time-varying betas, by calculating a series of discount rates which take into account these effects. Using a constant discount rate can produce large misvaluations in portfolio data, which are mostly driven at long horizons by variation in risk-free rates and factor loadings.

present value, discount rates, term structure of expected returns, time-varying beta, time-varying risk premium, capital budgeting

Abstract:
This paper studies the market price of credit risk incorporated into one of the most important credit spreads in the financial markets: interest rate swap spreads. Our approach consists of jointly modeling the swap and Treasury term structures using a general five-factor affine credit framework and estimating the parameters by maximum likelihood. We solve for the implied special financing rate for Treasury bonds and find that the liquidity component of on-the-run bond prices can be significant. We also find that credit premia in swap spreads are positive on average. These premia, however, vary significantly over time and were actually negative for much of the 1990s.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
This paper studies the market price of credit risk incorporated into one of the most important credit spreads in the financial markets: interest-rate swap spreads. Our approach consists of jointly modeling the swap and Treasury term structures using a four-factor ane credit framework and estimating the parameters by maximum likelihood. We solve for the implied special financing rate for Treasury bonds and find that the liquidity component of on-the-run bond prices can be very significant. We show that most of the variation in swap spreads is driven by changes in the liquidity of Treasury bonds rather than changes in default risk. We find that there are positive credit premia in swap spreads on average. These premia, however, vary significantly over time and were negative for much of the 1990s. Since the hedge-fund crisis of 1998, credit premia have become positive and are currently at historical high.

Abstract:
Black (1986) and Summers (1986) suggest that there is noise in stock prices in a sense that the price of a stock can be randomly different from its intrinsic value. Such noise can arise from economic models (e.g., Grossman and Stiglitz (1980) and De Long, Shleifer, Summers, and and Robert J.Waldmann (1990)), market microstructure (e.g., Stambaugh 1983) and Roll (1983)), among other sources.

In this paper, we show that when there is noise in the price of a stock, its expected return conditional on the price or the price-dividend ratio decreases with the price or the price dividend-ratio. These higher expected returns associated with lower price or price-dividend ratios are not compensation for risk, but are generated because a stock with a low price or a price-ratio is more likely to have a negative price noise thus to be undervalued.

Fama and French (1992) use the matrix of expected returns conditional on size-value deciles as a demonstration of size and value effects. This matrix can be computed in closed form using our model and, for plausible parameters, is similar to its empirical counterpart (Table V of Fama and French). In our model, small and value stocks have slightly higher betas and positive alphas. Our study suggests that noise creates the size and value effect.

noise, size effect, value effect

Abstract:
We characterize the joint dynamics of dividends, expected returns, stochastic volatility, and prices. In particular, with a given dividend process, one of the processes of the expected return, the stock volatility, or the price-dividend ratio fully determines the other two. For example, together with dividends, the stock volatility process fully determines the dynamics of the expected return and the price-dividend ratio. By parameterizing one or more of expected returns, volatility, or prices, common empirical specifications place strong, and sometimes counter-factual, restrictions on the dynamics of the other variables. Our relations are useful for understanding the risk-return trade-off, as well as characterizing the predictability of stock returns.

Abstract:
We characterize the joint dynamics of dividends, expected returns, stochastic volatility, and prices. In particular, with a given dividend process, one of the processes of the expected return, the stock volatility, or the price-dividend ratio fully determines the other two. For example, together with cashflows, the stock volatility process fully determines the dynamics of the expected return and the price-dividend ratio. By parameterizing one or more of expected returns, volatility, or prices, common empirical specifications place strong, and sometimes counter-factual, restrictions on the dynamics of the other variables. Our relations are useful for understanding the risk-return trade-off, as well as characterizing the predictability of stock returns.

risk-return trade-off, risk premium,stochastic volatility, predictability

Abstract:
This paper studies the optimal investment strategy of an investor who can access not only the bond and the stock markets, but also the derivatives market. We consider the investment situation where, in addition to the usual diffusive price shocks, the stock market experiences sudden price jumps and stochastic volatility. The dynamic portfolio problem involving derivatives is solved in closed-form. Our results show that derivatives are important in providing access to the risk and return tradeoffs associated with the volatility and jump risks. Moreover, as a vehicle to the volatility risk, derivatives are used by non-myopic investors to exploit the time-varying opportunity set; and as a vehicle to the jump risk, derivatives are used by investors to disentangle their simultaneous exposure to the diffusive and jump risks in the stock market. In addition, derivatives investing also affects investors' stock position because of the interaction between the two markets. Finally, calibrating our model to the S&P 500 index and options markets, we find sizable portfolio improvement for taking advantage of derivatives.

Abstract:
Recently much progress has been made in developing optimal portfolio choice models accomodating time-varying opportunity sets, but unless investors are unreasonably risk averse, optimal holdings include unreasonably large equity positions. One reason is that most studies assume investors behave as expected utility maximizers with power utility. In this article, we provide a formal treatment of both static and dynamic portfolio choice using the Disappointment Aversion preferences of Gul (1991). While different from the Kahneman-Tversky (1979) loss aversion utility, these preferences imply asymmetric aversion to gains versus losses and are consistent with the tendency of some people to like lottery-type gambles but dislike stock in-vestments. By calibrating a number of data generating processes to actual US data on stock and bond returns, we find very reasonable portfolios for moderately disappointment averse investors with utility functions exhibiting low curvature. Disappointment aversion preferences affect intertemporal hedging demands and the state dependence of asset allocation in such a way as to not be replicable by standard expected utility functions with higher curvature. Furthermore, it is easy to reconcile the large equity premium observed in the data with disappointment aversion utility of low curvature and reasonable disappointment aversion.

Abstract:
Recently much progress has been made in developing optimal portfolio choice models accomodating time-varying opportunity sets, but unless investors are unreasonably risk averse, optimal holdings include unreasonably large equity positions. One reason is that most studies assume investors behave as expected utility maximizers with power utility. In this article, we provide a formal treatment of both static and dynamic portfolio choice using the Disappointment Aversion preferences of Gul (1991). While different from the Kahneman-Tversky (1979) loss aversion utility, these preferences imply asymmetric aversion to gains versus losses and are consistent with the tendency of some people to like lottery-type gambles but dislike stock investments. By calibrating a number of data generating processes to actual US data on stock and bond returns, we find very reasonable portfolios for moderately disappointment averse investors with utility functions exhibiting low curvature. Disappointment aversion preferences affect intertemporal hedging demands and the state dependence of asset allocation in such a way as to not be replicable by standard expected utility functions with higher curvature. Furthermore, it is easy to reconcile the large equity premium observed in the data with disappointment aversion utility of low curvature and reasonable disappointment.

Abstract:
We investigate the effects of information and diversification on cost of capital in a noisy rational expectations model. Assuming a factor structure for risky asset payoffs and two classes of investors, informed and uninformed, we show that in large economies the APT (Ross, 1976) holds and i) information from private signals about idiosyncratic shocks has no effect on cost of capital and ii) information from private signals about systematic factors affects cost of capital only through factor risk premiums; there is no effect on factor loadings. These results imply that there are no cross-sectional effects of information on cost of capital within large economies.

information, diversification, cost of capital

Abstract:
We examine the asymptotic efficiency of using individual stocks or portfolios as base assets to test cross-sectional asset pricing models. The literature has argued that creating portfolios reduces idiosyncratic volatility and enables factor loadings, and consequently risk premia, to be estimated more precisely. We show analytically and find empirically that the more efficient estimates of betas from creating portfolios do not lead to lower asymptotic variances of factor risk premia estimates. Instead, the standard errors of factor risk premia estimates are determined by the cross-sectional distribution of factor loadings and residual risk. Creating portfolios shrinks the dispersion of betas and leads to higher asymptotic standard errors of risk premia estimates.

Specifying Base Assets, Cross-Sectional Regression, Estimating Risk Premia

Abstract:
We develop a model of a firm owned by shareholders and administered by managers who may be either honest or dishonest. When managers have an informational advantage but shareholders retain control, dishonest managers can make false reports that distort investment and thereby reduce firm cash flows. When dishonest managers have privileged access to both information and control, firm value is further reduced and profits are diminished especially in the worst states of the world. Ineffective corporate governance combined with corruption (dishonesty) thus increases firms' exposure to systematic risk. In a cross-country empirical test of the model, we find that corruption substantially increases firm betas, particularly in countries with weak shareholder rights. Moving from the level of corruption in Canada to that in South Korea raises industry-adjusted betas by 0.35.

Abstract:
In this study, we examine the relation between implied cost of capital and expected returns under an assumption that expected returns are stochastic, a property supported by theory and empirical evidence. We demonstrate that implied cost of capital differs from expected return, on average, by a function encompassing volatilities of, as well as correlation between, expected returns and cash flows, growth in cash flows, and leverage. These results provide alternative explanations for findings from empirical studies employing implied cost of capital on the magnitude of the market risk premium; relations between cost of capital, growth, leverage, and idiosyncratic risks; predictability of future returns, and characteristics of the firm's information environment.

expected return, implied cost of capital, discount rate

Abstract:
In this paper, we study the asset pricing implication of imprecise knowledge about rare events. Modeling rare events as jumps in the aggregate endowment, we explicitly solve the equilibrium asset prices in a pure-exchange economy with a representative agent who is averse not only to risk but also to model uncertainty with respect to rare events. Our results show that there are three components in the equity premium: the diffusive-risk premium, the jump-risk premium, and the "rare event premium." While the first two premia are generated by risk aversion, the last one is driven exclusively by uncertainty aversion. To disentangle the "rare event premium" from the standard risk-based premia, we examine the equilibrium prices of options with varying degree of moneyness. We consider models with different levels of uncertainty aversion - including the one with zero uncertainty aversion, and calibrate all models to the same level of equity premium. Although observationally equivalent with respect to the equity market, these models provide distinctly different predictions on the option market. Without incorporating uncertainty aversion, the standard model cannot explain the extent of the premia implicit in options, particularly the prevalent "smirk" patterns documented in the index options market. In contrast, the models incorporating uncertainty aversion can generate significant premia for at-the-money option prices, as well as pronounced "smirk" patterns for options with different degrees of moneyness.

Abstract:
This paper solves explicitly a dynamic choice problem for a class of stochastic volatility models. The explicit solution is used to show that intuitions on static choice problems do not apply in a dynamic choice setting. For example, even though the risk premium of the risky asset in the problem is strictly positive, a more risk-averse agent may hold more risky assets, and a risk-averse agent may short (sometimes infinite amount of) a risky asset. I argue that these counter-intuitive results are due to rebalancing. The results suggest that it may be not appropriate to use stock holdings as a proxy for risk aversion.

dynamic choice, risk aversion, stochastic volatility

Abstract:
We study the consumption-investment problem of an agent with constant relative risk aversion (CRRA) preferences who possesses private information about the future prospects of a stock. We examine the value of the information to the agent by comparing the utility equivalent with and without the information of the agent. The value of private of information to the agent depends linearly on the wealth of agents and decreases with both the propensity to intermediate consumption and the risk aversion. Agents with low coefficients of relative risk aversion value private information more highly. Highly risk averse informed agents consume a greater fraction of their wealth when they are informed than when they are uninformed, but the opposite is true of agents with low degrees of risk aversion. Consistent with the empirical literature, the optimal portfolio holdings of informed agents are correlated with expected returns on the risky asset.

Information, portfolio choice

Abstract:
This paper studies the valuation of assets with debt tax shields when debt policy is a general time-dependent function of the asset's unlevered cash flows, value, and history. In a continuous-time setting, it shows that the value of a project's debt tax shield satisfies a partial differential equation, which simplifies to an easily solved ordinary differential equation for most plausible debt policies. A large class of cases exhibits closed-form solutions for the value of a levered asset, the value of its tax shield, and the appropriate tax-adjusted cost of capital for discounting unlevered cash flows.

Abstract:
This paper studies the valuation of assets with debt tax shields when debt policy is a general time-dependent function of the asset's unlevered cash flows, value, and history. In a continuous-time setting, it shows that the value of a project's debt tax shield satisfies a partial differential equation, which simplifies to an easily solved ordinary differential equation for most plausible debt policies. A large class of cases exhibits closed-form solutions for the value of a levered asset, the value of its tax shield, and the appropriate tax-adjusted cost of capital for discounting unlevered cash flows.

debt policy, corporate taxes, discount rates, weighted cost of capital

Abstract:
We show how to use conditioning information optimally to construct a sharper unconditional Hansen-Jagannathan (1991) bound. The approach in this paper is different from that of Gallant, Hansen and Tauchen (1990), but both approaches yield the same bound when the conditional moments are known. Unlike Gallant, Hansen and Tauchen, our approach is robust to misspecification of the first and second conditional moments. Potential applications include testing dynamic asset pricing models, studying the predictability of asset returns, diagnosing the accuracy of competing models for the first and second conditional moments of asset returns, dynamic asset allocation and mutual fund performance measurement. The illustration in this article starts with the familiar Hansen-Singleton (1983) setup of an autoregressive model for consumption growth and bond and stock returns. Our innovation is to add time-varying volatility to the model. Both an unconstrained version and a version with the restrictions of the standard consumption-based asset pricing model imposed serve as the data-generating processes to illustrate the behavior of the bounds. In the process, we discover and explore an interesting empirical phenomenon: asymmetric volatility in consumption growth.

Abstract:
We show how to use conditioning information optimally to construct a sharper unconditional Hansen-Jagannathan (1991) bound. The approach in this paper is different from that of Gallant, Hansen and Tauchen (1990), but both approaches yield the same bound when the conditional moments are known. Unlike Gallant, Hansen and Tauchen, our approach is robust to misspecification of the first and second conditional moments. Potential applications include testing dynamic asset pricing models, studying the predictability of asset returns, diagnosing the accuracy of competing models for the first and second conditional moments of asset returns, dynamic asset allocation and mutual fund performance measurement. The illustration in this article starts with the familiar Hansen-Singleton (1983) setup of an autoregressive model for consumption growth and bond and stock returns. Our innovation is to add time-varying volatility to the model. Both an unconstrained version and a version with the restrictions of the standard consumption-based asset pricing model imposed serve as the data-generating processes to illustrate the behavior of the bounds. In the process, we discover and explore an interesting empirical phenomenon: asymmetric volatility in consumption growth.

Abstract:
Many firms have stockholders who face severe restrictions on their ability to sell their shares and diversify the risk of their personal wealth. We study the costs of these liquidity restrictions on stockholders using a continuous-time portfolio choice framework. These restrictions have major effects on the optimal investment and consumption strategies because of the need to hedge the illiquid stock position and smooth consumption in anticipation of the eventual lapse of the restrictions. These results provide a number of important insights about the effects of illiquidity in financial markets.

Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.

Abstract:
Major events often trigger abrupt changes in stock prices and volatility. We study the implications of jumps in prices and volatility on investment strategies. Using the event-risk framework of Duffie, Pan, and Singleton (2000), we provide analytical solutions to the optimal portfolio problem. Event risk dramatically affects the optimal strategy. An investor facing event risk is less willing to take leveraged or short positions. The investor acts as if some portion of his wealth may become illiquid and the optimal strategy blends both dynamic and buy-and-hold strategies. Jumps in prices and volatility both have important effects.

Abstract:
Major events often trigger abrupt changes in stock prices and volatility. We study the implications of jumps in prices and volatility on investment strategies. Using the event-risk framework of Duffie, Pan, and Singleton (2000), we provide analytical solutions to the optimal portfolio problem. Event risk dramatically affects the optimal strategy. An investor facing event risk is less willing to take leveraged or short positions. The investor acts as if some portion of his wealth may become illiquid and the optimal strategy blends both dynamic and buy-and-hold strategies. Jumps in prices and volatility both have important effects.

Abstract:
We define risky arbitrages as self-financing trading strategies that have a strictly positive market price but a zero expected cumulative payoff. A continuous time cointegrated system is used to model risky arbitrages as arising from a mean-reverting mispricing component. We derive the optimal trading strategy in closed-form and show that the standard textbook arbitrage strategy is not optimal. In a calibration exercise, we show that the optimal strategy makes a sizeable difference in economic terms.

cointegrated asset prices, optimal portfolio choice, risky arbitrage

Abstract:
We examine the term structure of yield spreads between floating-rate and fixed-rate notes of the same credit quality and maturity. Floating-fixed spreads are theoretically characterized in some practical cases and quantified in a simple model in terms of maturity, credit quality, yield volatility, yield-spread volatility, correlation between changes in yield spreads and default-free yields, and other determining variables. We show that if the issuer's default risk is risk-neutrally independent of interest rates, the sign of floating-fixed spreads is determined by the term structure of the risk-free forward rate.