[In this article, I explicitly solve dynamic portfolio choice problems, up to the solution of an ordinary differential equation (ODE), when the asset returns are quadratic and the agent has a constant relative risk aversion (CRRA) coefficient. My solution includes as special cases many existing explicit solutions of dynamic portfolio choice problems. I also present three applications that are not in the literature. Application 1 is the bond portfolio selection problem when bond returns are described by "quadratic term structure models." Application 2 is the stock portfolio selection problem when stock return volatility is stochastic as in Heston model. Application 3 is a bond and stock portfolio selection problem when the interest rate is stochastic and stock returns display stochastic volatility.]

[Convergence trades exploit temporary mispricing by simultaneously buying relatively underpriced assets and selling short relatively overpriced assets. This paper studies optimal convergence trades under both recurring and nonrecurring arbitrage opportunities represented by continuing and "stopped" cointegrated price processes and considers both fixed and stochastic (Poisson) horizons. Conventional long-short delta neutral strategies are generally suboptimal and it can be optimal to simultaneously go long (or short) in two mispriced assets. Optimal portfolio holdings critically depend on whether the risky asset position is liquidated when prices converge. Our theoretical results are illustrated on pairs of Chinese bank shares traded on both the Hong Kong and China stock exchanges.]

Gallant, Hansen, and Tauchen (1990) show how to use conditioning information optimally to construct a sharper unconditional variance bound (the GHT bound) on pricing kernels. The literature predominantly resorts to a simple but suboptimal procedure that scales returns with predictive instruments and computes standard bounds using the original and scaled returns. This article provides a formal bridge between the two approaches. We propose an optimally scaled bound that coincides with the GHT bound when the first and second conditional moments are known. When these moments are misspecified, our optimally scaled bound yields a valid lower bound for the standard deviation of pricing kernels, whereas the GHT bound does not. We illustrate the behavior of the bounds using a number of linear and nonlinear models for consumption growth and bond and stock returns. We also illustrate how the optimally scaled bound can be used as a diagnostic for the specification of the first two conditional moments of asset returns.

We derive the optimal investment policy of a risk-averse investor in a market where there is a textbook arbitrage opportunity, but where liabilities must be secured by collateral. We find that it is often optimal to underinvest in the arbitrage by taking a smaller position than collateral constraints allow. Even when the optimal policy is followed, the arbitrage portfolio typically experiences losses before the final convergence date. In fact, its initial performance may be indistinguishable from that of a conventional portfolio with a poor track record. These results have important implications for the role of arbitrageurs in financial markets.

In this article, I explicitly solve dynamic portfolio choice problems, up to the solution of an ordinary differential equation (ODE), when the asset returns are quadratic and the agent has a constant relative risk aversion (CRRA) coefficient. My solution includes as special cases many existing explicit solutions of dynamic portfolio choice problems. I also present three applications that are not in the literature. Application 1 is the bond portfolio selection problem when bond returns are described by “quadratic term structure models.” Application 2 is the stock portfolio selection problem when stock return volatility is stochastic as in Heston model. Application 3 is a bond and stock portfolio selection problem when the interest rate is stochastic and stock returns display stochastic volatility. (JEL G11)

This article studies 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. The equilibrium equity premium has three components: the diffusive- and jump-risk premiums, both driven by risk aversion; and the "rare-event premium," driven exclusively by uncertainty aversion. To disentangle the rare-event premiums from the standard risk-based premiums, we examine the equilibrium prices of options across moneyness or, equivalently, across varying sensitivities to rare events. We find that uncertainty aversion toward rare events plays an important role in explaining the pricing differentials among options across moneyness, particularly the prevalent "smirk" patterns documented in the index options market.

Gallant, Hansen, and Tauchen (1990) show how to use conditioning information optimally to construct a sharper unconditional variance bound (the GHT bound) on pricing kernels. The literature predominantly resorts to a simple but suboptimal procedure that scales returns with predictive instruments and computes standard bounds using the original and scaled returns. This article provides a formal bridge between the two approaches. We propose an optimally scaled bound that coincides with the GHT bound when the first and second conditional moments are known. When these moments are misspecified, our optimally scaled bound yields a valid lower bound for the standard deviation of pricing kernels, whereas the GHT bound does not. We illustrate the behavior of the bounds using a number of linear and nonlinear models for consumption growth and bond and stock returns. We also illustrate how the optimally scaled bound can be used as a diagnostic for the specification of the first two conditional moments of asset returns. Copyright 2004, Oxford University Press.

We derive the optimal investment policy of a risk-averse investor in a market where there is a textbook arbitrage opportunity, but where liabilities must be secured by collateral. We find that it is often optimal to underinvest in the arbitrage by taking a smaller position than collateral constraints allow. Even when the optimal policy is followed, the arbitrage portfolio typically experiences losses before the final convergence date. In fact, its initial performance may be indistinguishable from that of a conventional portfolio with a poor track record. These results have important implications for the role of arbitrageurs in financial markets.

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; predictability of future returns; and the relations between cost of capital and a host of firm characteristics, such as growth, leverage, idiosyncratic risk and the firm’s information environment.