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Convex Analysisの二,三の進展について

We model dividend and consumption growth rates as containing a small long-run predictable component and economic uncertainty (i.e., growth rate volatility) as being time-varying. The magnitudes of the predictable variation and changing volatility in growth rates, as in the data, are quite small. These growth rate dynamics, for which we provide empirical support, in conjunction with plausible parameter configurations of the Epstein and Zin (1989) preferences can explain key observed asset markets phenomena. In particular, we show that the model can justify the observed equity premium, the low risk free rate, and the ex-post volatilities of the market return, real risk free rate, and the price-dividend ratio. As in the data, the model also implies that dividend yields predict returns and that market return volatility is stochastic. The main economic insight we capture is that news about growth rates significantly alter agent's perceptions regarding long run expected growth rates and growth rate uncertainty--in equilibrium, this leads to a large equity risk premium, low risk free interest rate, and large market volatility.

Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles

This article solves a realistically calibrated life cycle model of consumption and portfolio choice with non-tradable labor income and borrowing constraints. Since labor income substitutes for riskless asset holdings, the optimal share invested in equities is roughly decreasing over life. We compute a measure of the importance of human capital for investment behavior. We find that ignoring labor income generates large utility costs, while the cost of ignoring only its risk is an order of magnitude smaller, except when we allow for a disastrous labor income shock. Moreover, we study the implications of introducing endogenous borrowing constraints in this incomplete-markets setting. Copyright 2005, Oxford University Press.

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Consumption and Portfolio Choice over the Life Cycle

This paper presents an approximate analytical solution to the optimal consumption and portfolio choice problem of an infinitely lived investor with Epstein-Zin-Weil utility who faces a constant riskless interest rate and a time-varying equity premium. When the model is calibrated to U. S. stock market data, it implies that intertemporal hedging motives greatly increase, and may even double, the average demand for stocks by investors whose risk-aversion coefficients exceed one. The optimal portfolio policy also involves timing the stock market. Failure to time or to hedge can cause large welfare losses relative to the optimal policy.

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Consumption and Portfolio Decisions when Expected Returns are Time Varying

Convex Analysis: (pms-28)

This paper studies the consumption and portfolio selection problem of an agent who is liquidity constrained and has uninsurable income risk. The paper investigates how the optimal consumption and asset allocation policies deviate from the case where the financial market is perfect, i.e., the case where there are no liquidity constraints and uninsurable income risk. In particular, the paper shows that, for a given level of financial wealth and labor income, optimal consumption is smaller and the optimal level of risk taking is lower in the case where the agent is liquidity constrained and has uninsurable income risk than in the case where the financial market is perfect. The paper also discusses how the agent assesses the value of lifetime labor income and relates this evaluation to optimal consumption and asset allocation policies.

Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach

Standard literature concludes that transaction costs only have a second-order effect on liquidity premia. We show that this conclusion depends crucially on the assumption of a constant investment opportunity set. In a regime-switching model in which the investment opportunity set varies over time, we explicitly characterize the optimal consumption and investment strategy. In contrast to the standard literature, we find that transaction costs can have a first-order effect on liquidity premia. However, with reasonably calibrated parameters, the presence of transaction costs still cannot fully explain the equity premium puzzle. TRANSACTION COSTS ARE PREVALENT in almost all financial markets. Extensive research has been conducted on the optimal consumption and investment policy in the presence of transaction costs since the seminal work of Constantinides (1979, 1986). The presence of transaction costs significantly changes optimal consumption and investment strategies. For example, in the presence of transaction costs, continuous trade incurs infinite transaction costs, and thus even a small transaction cost can dramatically decrease the frequency of trade. However, most studies find that the utility loss due to the presence of transaction costs is small. In particular, Constantinides (1986) finds that the liquidity premium (i.e., the maximum expected return an investor is willing to exchange for zero transaction cost) is small relative to the transaction cost, even for a suboptimal trading strategy, and hence concludes that transaction costs only have a second-order effect for asset pricing. Indeed, in this framework it seems unlikely that transaction costs can have an important role in explaining the cross-sectional patterns of expected returns, the equity premium puzzle, or the small stock risk premia. This finding contrasts with many empirical studies that highlight the importance of transaction costs or related measures such as turnover in influencing the cross-sectional patterns of expected returns. 1

/pdf/liquidity-premia-and-transaction-costs-11b40o4ljx.pdf

Liquidity Premia and Transaction Costs

A comparison of numerical and analytic approximate solutions to an intertemporal consumption choice problem

Although transaction costs can alter optimal trading strategies significantly, standard literature (e.g., Constantinides (1986) among others) concludes that they only have a second-order effect on liquidity premia (i.e., the maximum expected return an investor is willing to exchange for a zero transaction cost). We show that this conclusion depends crucially on the assumption of a constant investment opportunity set. In a regime-switching setting where the investment opportunity set (such as expected return, volatility, and liquidity) varies stochastically, we explicitly characterize the optimal trading strategy in terms of two coupled ordinary differential equations with free boundaries; we prove a verification theorem for the obtained solution; and we provide an extensive analysis of the optimal trading strategy and liquidity premium. We find that contrary to the standard finding, transaction costs can have a first-order effect on liquidity premia. This result follows from a simple but fundamental intuition that if the investment opportunity set changes stochastically, the optimal stock investment target in the no-transaction-cost case also changes stochastically and an investor optimally rebalances more often to avoid being too far away from the moving target, which in turn results in the transaction cost having a greater effect. This result suggests that the presence of transaction costs can produce a significantly larger portion of the observed high risk premium than the literature on portfolio choice with a constant opportunity set and transaction costs indicates. However, we show that with reasonably calibrated parameters, the presence of transaction costs alone still cannot fully explain the magnitude of the equity premium puzzle, even when the investment opportunity set varies stochastically. Our new results follow from a simple but fundamental intuition that if the investment opportunity set changes stochastically, the optimal stock investment target in the absence of transaction costs also changes stochastically and as market conditions change an investor rebalances more often to avoid being too far away from the target if transaction cost rate is small and thus the relative impact of the transaction cost increases. This fundamental intuition also applies to the case where the investment opportunity set varies with a continuous state variable. Therefore jumps in the fundamental parameters in our model are not critical for our results and are employed only for tractability. Our model also has important implications for the resolution of the Equity-Premium Puzzle. We show that concerns over a potential liquidity crash, no matter how unlikely it is, can dramatically reduce investment in stock even when the current market is perfectly liquid and the expected excess return is high. Intuitively, an investor who has to liquidate her (leveraged) stock position in order to consume could risk insolvency when the market for the stock is illiquid. Thus, the sheer possibility of an unpredictable liquidity crash, no matter how small the probability is, would make leverage suboptimal no matter how high the equity premium is or how liquid the market is in normal circumstances. This suggests that the existence of liquidity risk may largely explain the Equity-Premium Puzzle. In contrast to the existing literature, this liquidity risk explanation does not require high risk aversion (e.g., Mehra and Prescott (1985)) or the separation of the risk aversion and the intertemporal rate of substitution (e.g., Epstein and Zin (1989)) or habit formation (e.g., Constantinides (1990)).

https://papers.ssrn.com/sol3/Delivery.cfm/SSRN_ID891784_code106088.pdf?abstractid=687602&mirid=1&type=2

Liquidity Premia and Transactions Costs

In this paper we propose an approach to investigate a model of consumption and investment with a mandatory retirement date and early retirement option; we analyze properties of the optimal strategy and thereby contribute to understanding the interaction between retirement, consumption, and portfolio decisions in the presence of both the important features of retirement. In particular, we provide a characterization of the threshold of wealth as a function of time, and we show that it is strictly decreasing near the mandatory retirement date. The threshold is similar to the early exercise boundary of an American option in the sense that if the agent’s wealth is above or equal to the threshold level, then the agent immediately retires. We also provide comparative static analysis.

Hyeng Keun Koo

Papers

Consumption and Portfolio Selection with Labor Income: A Continuous Time Approach

Liquidity Premia and Transaction Costs

A comparison of numerical and analytic approximate solutions to an intertemporal consumption choice problem

Liquidity Premia and Transactions Costs

Optimal Consumption and Portfolio Selection with Early Retirement Option