Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability, Wealth Shocks and State-Dependent Transaction Costs

The seminal work of Constantinides (1986) documents how, when the risky return is calibrated to the U.S. market return, the impact of transaction costs on per-annum liquidity premia is an order of magnitude smaller than the cost rate itself. A number of recent papers have formed portfolios sorted on liquidity measures and found a spread in expected per-annum return that is definitely not an order of magnitude smaller than the transaction cost spread: the expected per-annum return spread is found to be around 6-7% per annum. Our paper bridges the gap between Constantinides' theoretical result and the empirical magnitude of the liquidity premium by examining dynamic portfolio choice with transaction costs in a variety of more elaborate settings that move the problem closer to the one solved by real-world investors. In particular, we allow returns to be predictable and transaction costs to be stochastic, and we introduce wealth shocks, both stationary multiplicative and labor income. With predictable returns, we also allow the wealth shocks and transaction costs to be state dependent. We find that adding these real world complications to the canonical problem can cause transactions costs to produce per-annum liquidity premia that are no longer an order of magnitude smaller than the rate, but are instead the same order of magnitude. For example, predictable returns and i.i.d. labor income growth causes the liquidity premium for an agent with a wealth to monthly labor income ratio of 0 or 10 to be 1.68\% and 1.20\% respectively; these are 21-fold and 15-fold increases, respectively, relative to that in the standard i.i.d. return case. We conclude that the effect of proportional transaction costs on the standard consumption and portfolio allocation problem with i.i.d. returns can be materially altered by reasonable perturbations that bring the problem closer to the one investors are actually solving.

Labor Income Dynamics at Business-Cycle Frequencies: Implications for Portfolio Choice

A large recent literature has focused on multiperiod portfolio choice with labor income, and while the models are elaborate along several dimensions, they all assume that the joint distribution of shocks to labor income and asset returns is i.i.d.. Calibrating this joint distribution to U.S. data, these papers obtain three results not found empirically for U.S. households: young agents choose a higher stock allocation than old agents; young agents choose a higher stock allocation when poor than when rich; and, young agents always hold some stock. This paper asks whether allowing the conditional joint distribution to depend on the business cycle can allow the model to generate equity holdings that better match those of U.S. households, while keeping the unconditional distribution the same as in the data. Calibrating the business-cycle variation in the first two moments of labor income growth to U.S. data leads to large reductions in stock holdings by young agents with low wealth-income ratios. The reductions are so large that young, poor agents now hold less stock than both young, rich agents and old agents, and also hold no stock a large fraction of the time. Our results suggest that the predictability of labor-income growth at a business-cycle frequency plays an important role in a young agent's decision-making about her portfolio's stock holding.

Bankruptcy-Prior Discharge Within Six Years as Bar to Wage Earner\u27s Extension Plan

Appellant, a debtor, sought confirmation of a wage earners\u27 extension plan pursuant to Chapter XIII of the Bankruptcy Act. Section 656 prohibits confirmation of a plan under Chapter XIII if the debtor would have been denied an ordinary discharge in bankruptcy had he been seeking one. A discharge within six years prior to the date of filing constitutes a bar to such discharge. The referee, finding that the debtor had obtained a discharge within six years, dismissed the proceedings. On appeal from the district court\u27s affirmance, held, affirmed. Since a wage earner\u27s extension plan clearly contemplates a discharge of debts, confirmation is barred under sections 656a and 14c(5) by a prior discharge within six years. In re Schlageter, 319 F.2d 821 (3d Cir. 1963)

Using Samples of Unequal Length in Generalized Method of Moments Estimation

Many applications in financial economics use data series with different starting or ending dates. This paper describes estimation methods, based on the generalized method of moments (GMM), which make use of all available data for each moment condition. We introduce two asymptotically equivalent estimators that are consistent, asymptotically normal, and more efficient asymptotically than standard GMM. We apply these methods to estimating predictive regressions in international data and show that the use of the full sample affects point estimates and standard errors for both assets with data available for the full period and assets with data available for a subset of the period. Monte Carlo experiments demonstrate that reductions hold for small-sample standard errors as well as asymptotic ones. These methods are extended to more general patterns of missing data, and are shown to be more efficient than estimators that ignore intervals of the data, and thus more efficient than standard GMM

Multiple Risky Assets, Transaction Costs and Return Predictability: Implications for Portfolio Choice

Our paper contributes to the dynamic portfolio choice and transaction cost literatures by considering a multiperiod CRRA individual who faces transaction costs and who has access to multiple risky assets, all with predictable returns. We numerically solve the individual’s multiperiod problem in the presence of transaction costs and predictability. In particular, we characterize the investor’s optimal portfolio choice with proportional and fixed transaction costs, and with return predictability similar to that observed for the U.S. stock market. We also perform some comparative statics to better understand the nature of the no-trade region with more than one risky asset. Throughout our focus is on the case with two risky assets. We also perform some utility comparisons. The calibration exercise reveals some interesting results about the relative attractiveness of the three equity portfolios calibrated. With proportional transaction costs and i.i.d. returns, we numerically find the rebalancing rule to be a no-trade region for the portfolio weights with rebalancing to the boundary. With zero correlation, the no-trade region is a rectangle irrespective of the investor’s age. When the correlation of the risky assets is non-zero, the no-trade region becomes a parallelogram. With positive correlation, the parallelogram distorts the associated rectangle in such a way as to take advantage of the associated substitutability across the two assets that the positive correlation induces. The converse is true for negative correlation. Turning to the allocations with return predictability, our numerical results strongly suggest that it is the conditional return correlation that determines the nature of the distortion to the no-trade parallelogram. Irrespective of the investor’s age, the distortion always mirrors the no-trade parallelogram distortion that we find in the i.i.d. case for return correlation of the same sign. The no-trade region is always larger late in life than early in life. However, the difference in no-trade area between early and late in life is less pronounced when returns are predictable, consistent with intuition that the benefits from rebalancing today are more short-lived when returns are predictable than in the i.i.d. case

Multiple Risky Assets, Transaction Costs and Return Predictability: Implications for Portfolio Choice

Our paper contributes to the dynamic portfolio choice and transaction cost literatures by considering a multiperiod CRRA individual who faces transaction costs and who has access to multiple risky assets, all with predictable returns. We numerically solve the individual’s multiperiod problem in the presence of transaction costs and predictability. In particular, we characterize the investor’s optimal portfolio choice with proportional and fixed transaction costs, and with return predictability similar to that observed for the U.S. stock market. We also perform some comparative statics to better understand the nature of the no-trade region with more than one risky asset. Throughout our focus is on the case with two risky assets. We also perform some utility comparisons. The calibration exercise reveals some interesting results about the relative attractiveness of the three equity portfolios calibrated

Multiple Risky Assets, Transaction Costs and Return Predictability: Implications for Portfolio Choice

Our paper contributes to the dynamic portfolio choice and transaction cost literatures by considering a multiperiod CRRA individual who faces transaction costs and who has access to multiple risky assets, all with predictable returns. We numerically solve the individual’s multiperiod problem in the presence of transaction costs and predictability. In particular, we characterize the investor’s optimal portfolio choice with proportional and fixed transaction costs, and with return predictability similar to that observed for the U.S. stock market. We also perform some comparative statistics to better understand the nature of the no-trade region with more than one risky asset. Throughout our focus is on the case with two risky assets. We also perform some utility comparisons. The calibration exercise reveals some interesting results about the relative attractiveness of the three equity portfolios calibrated. With proportional transaction costs and i.i.d. returns, we numerically find the rebalancing rule to be a no-trade region for the portfolio weights with rebalancing to the boundary. With zero correlation, the no-trade region is a rectangle irrespective of the investor’s age. When the correlation of the risky assets is non-zero, the no-trade region becomes a parallelogram. With positive correlation, the parallelogram distorts the associated rectangle in such a way as to take advantage of the associated substitutability across the two assets that the positive correlation induces. The converse is true for negative correlation. Turning to the allocations with return predictability, our numerical results strongly suggest that it is the conditional return correlation that determines the nature of the distortion to the no-trade parallelogram. Irrespective of the investor’s age, the distortion always mirrors the no-trade parallelogram distortion that we find in the i.i.d. case for return correlation of the same sign. The no-trade region is always larger late in life than early in life. However, the difference in no-trade area between early and late in life is less pronounced when returns are predictable, consistent with intuition that the benefits from rebalancing today are more short-lived when returns are predictable than in the i.i.d. case

Labor Income Dynamics at Business-cycle Frequencies:Implications for Portfolio Choice

A large recent literature has focused on multiperiod portfolio choice with labor income, and while the models are elaborate along several dimensions, they all assume that the joint distribution of shocks to labor income and asset returns is i.i.d.. Calibrating this joint distribution to U.S. data, these papers obtain three results not found empirically for U.S. households: young agents choose a higher stock allocation than old agents; young agents choose a higher stock allocation when poor than when rich; and, young agents always hold some stock. This paper asks whether allowing the conditional joint distribution to depend on the business cycle can allow the model to generate equity holdings that better match those of U.S. households, while keeping the unconditional distribution the same as in the data. Calibrating the business-cycle variation in the first two moments of labor income growth to U.S. data leads to large reductions in stock holdings by young agents with low wealth-income ratios. The reductions are so large that young, poor agents now hold less stock than both young, rich agents and old agents, and also hold no stock a large fraction of the time. Our results suggest that the predictability of labor-income growth at a business-cycle frequency plays an important role in a young agent’s decision-making about her portfolio’s stock holding

Explaining the Magnitude of Liquidity Premia: The Roles of Return Predictability, Wealth Shocks and State-dependent Transaction Costs

The seminal work of Constantinides (1986) documents how, when the risky return is calibrated to the U.S. market return, the impact of transaction costs on per-annum liquidity premia is an order of magnitude smaller than the cost rate itself. A number of recent papers have formed portfolios sorted on liquidity measures and found a spread in expected per-annum return that is definitely not an order of magnitude smaller than the transaction cost spread: the expected per-annum return spread is found to be around 6-7% per annum. Our paper bridges the gap between Constantinides’ theoretical result and the empirical magnitude of the liquidity premium by examining dynamic portfolio choice with transaction costs in a variety of more elaborate settings that move the problem closer to the one solved by real-world investors. In particular, we allow returns to be predictable and transaction costs to be stochastic, and we introduce wealth shocks, both stationary multiplicative and labor income. With predictable returns, we also allow the wealth shocks and transaction costs to be state dependent. We find that adding these real world complications to the canonical problem can cause transactions costs to produce per-annum liquidity premia that are no longer an order of magnitude smaller than the rate, but are instead the same order of magnitude. For example, predictable returns and i.i.d. labor income growth causes the liquidity premium for an agent with a wealth to monthly labor income ratio of 0 or 10 to be 1.68% and 1.20% respectively; these are 21-fold and 15-fold increases, respectively, relative to that in the standard i.i.d. return case. We conclude that the effect of proportional transaction costs on the standard consumption and portfolio allocation problem with i.i.d. returns can be materially altered by reasonable perturbations that bring the problem closer to the one investors are actually solving

Using Samples of Unequal Length in Generalized Method of Moments Estimation

Many applications in financial economics use data series with different starting or ending dates. This paper describes an estimation method, based on the generalized method of moments (GMM), which makes use of all available data for each moment condition. We introduce two asymptotically equivalent estimators that are consistent, symptotically normal, and more efficient asymptotically than standard GMM. We illustrate these estimators in an application to mutual fund performance evaluation. Both estimators are extended to general patterns of missing data, and shown to be more efficient than estimators that ignore intervals of the data, and thus more efficient than standard GMM