Harold H. Zhang

Optimal Consumption and Investment with Capital Gains Taxes

This article characterizes optimal dynamic consumption and portfolio decisions in the presence of capital gains taxes and short-sale restrictions. The optimal decisions are a function of the investors age, initial portfolio holdings, and tax basis. Our results capture the trade-off between the diversification benefits and tax costs of trading over an investors lifetime. The incentive to rediversify the portfolio is inversely related to the size of the embedded gain and investors age. Contrary to standard financial advice, the optimal equity holding increases well into an investors lifetime in our model due to the forgiveness of capital gains taxes at death. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Volume, Volatility, and Leverage: A Dynamic Analysis

This paper uses dynamic impulse response analysis to investigate the interrelationships among stock price volatility, trading volume, and the leverage effect. Dynamic impulse response analysis is a technique for analyzing the multistep ahead characteristics of a nonparametric estimate of the one-step conditional density of a strictly stationary process. The technique is the generalization to a nonlinear process of Sims-style impulse response analysis for lienar models. In this paper, we refine the technique and apply it to a long panel of daily observations on the price and trading volume of four stocks actively traded on the NYSE: Boeing, Coca Cola, IBM, and MMM.

Stock Returns and the Volatility of Liquidity

This paper offers a rational explanation for the puzzling empirical fact that stock returns decrease with an increase in the volatility of liquidity. We model liquidity as a stochastic price impact process and define the liquidity premium as the additional return necessary to compensate a multiperiod investor for the adverse price impact of trading. The model demonstrates that a fully rational, utility maximizing, risk-averse investor can take advantage of time-varying liquidity by adapting his trades to the state of liquidity. We provide new empirical evidence supportive of the model.

Diversification and Capital Gains Taxes with Multiple Risky Assets

We examine the impact of capital gains taxes upon the structure of an investors optimal portfolio in the presence of multiple risky assets. Our numerical solutions suggest that the diversification benefits of reducing the exposure to a highly volatile concentrated position significantly outweigh the tax costs of selling, even for elderly investors. The presence of multiple risky assets in which the investor earns a substantial risk premium strongly increases the diversification incentive. We also contrast the impact of capital gains taxes and traditional transaction costs on rebalancing decisions and show that it can be optimal for the investor to reduce his overall equity exposure by selling underweighted assets with relatively small capital gains. Finally, we discuss the general qualitative features of the optimal investment policy in a broader context. Both our numerical and qualitative analyses show how the realization decision on one asset depends upon the embedded gains on other assets.

ENDOGENOUS SHORT-SALE CONSTRAINT, STOCK PRICES AND OUTPUT CYCLES

This study examines the effect of short-sale constraints on a stock market, in particular, on stock prices, trading volume, and the relationship between stock price movements and output cycles. The economic model features incomplete markets and heterogeneous agents. The short-sale constraint is endogenously determined in the economy and is a function of agents’ risk aversion, time preference, and exogenous driving forces. The dynamic model is solved using a policy function iteration algorithm. We find that, for an array of reasonable time-preference parameters and risk-aversion coefficients, the short sale limits range from 27 to 45% of total outstanding shares. Imposing short-sale constraints causes stock prices to move upward. Trading volume is high when some agents have a large amount of stock holdings but incur a negative shock on their nonfinancial income and is low when some agents have few stock holdings and also incur a negative shock to their nonfinancial income. Stock prices are found to be countercyclical and the expected stock returns are procyclical. These countercyclical stock-price movements are shown to be related to the imposition of a short-sale constraint.

Overparameterization in the seminonparametric density estimation

Abstract The seminonparametric (SNP) density estimation proposed by Gallant and Nychka (1987) and Gallant and Tauchen (1989) has been applied in many econometric analyses. In this paper, we show that the information matrix may become singular when an SNP model is overparameterized. This singularity problem may occur even when a model selection criterion penalizes the size of a model, and thus cause problems in the sieves expansion model selection process. We propose to use the likelihood ratio test to safeguard against such overparameterization.

Explaining Bond Returns in Heterogeneous Agent Models: The Importance of Higher Order Moments

This paper examines the higher-order moments and nonlinear dynamic properties of discount bond returns in an equilibrium heterogeneous agent economy with incomplete markets and borrowing constraints. We find that while it is possible for the economic model to match the mean and variance of the observed bond returns by choosing the parameters such that the borrowing constraint is binding sufficiently often, the implied higher-order moments are at odds with the data. To match the higher-order moments, one needs a model in which the borrowing constraint is binding at times but not too often. In this case, one does not match the first two moments. Using the seminonparametric density estimation and the nonlinear impulse response analysis, we find that our economic model can mimic the asymmetric effect of return shocks on conditional volatility as documented for the real bond returns. However, the economic model has difficulty replicating the dynamic properties observed in the data when the parameter values are chosen to match the first two moments of the observed bond returns.

Capital Gains Taxes and the Risk-Return Tradeoff

We derive cross-sectional implications of a capital gains tax rate change on the risk-return tradeoff on stock investment and show that stocks with higher accrued capital gains experience a larger risk-return tradeoff improvement after a capital gains tax rate cut. Stocks with higher dividend yields experience a larger increase (decrease) in the risk-return tradeoff when the dividend tax penalty effect dominates (is dominated by) the effect of reduced dividend yield associated with the capital gains tax cut. Studying both the Tax Relief Act of 1997 and the Revenue Act of 1978, we find stocks with higher accrued capital gains experienced larger increases in the expected return, the systematic risk, and the risk-return tradeoff after the capital gains tax cut. Stocks with higher dividend yields experienced larger decreases in the risk-return tradeoff, suggesting that the reduction in dividend yield associated with the capital gains tax cut may have dominated the dividend tax penalty effect.

Comment on ‘Household Portfolio Choices in Taxable and Tax-Deferred Accounts: Another Puzzle?’

Using an arbitrage approach, Black (1980) and Tepper (1981) conclude that the optimal corporate pension policy is for companies to fully fund their pension plans, borrowing on corporate account if necessary, and investing the pension fund entirely in taxable bonds. The implications of the Black-Tepper arbitrage results for optimal asset location for individual investors were first discussed in Dammon et al. (1999). They demonstrate in their numerical analysis that the investor should optimally hold taxable bonds in his tax-deferred account and stocks in his taxable account, borrowing if necessary to achieve the optimal overall risk exposure. When the investor faces a binding borrowing constraint, he may hold some stock in his tax-deferred account, but only if his taxable account is entirely invested in equity. This optimal asset location policy was later formally derived by both Huang (2000) and Dammon et al. (2004) using the Black-Tepper arbitrage approach. Studies by Shoven (1999), Shoven and Sialm (2002), and Poterba et al. (2000) provide an alternative view. They argue that because many actively managed mutual funds distribute a large fraction of capital gains each year it can be optimal to hold equity in the tax-deferred account and tax-exempt bonds in the taxable account. However, Dammon et al. (2004) demonstrate that holding equity in the taxdeferred account, and tax-exempt bonds in the taxable account, is optimal only if the form of equity holding is highly tax-inefficient and significantly outperforms a tax-efficient index fund. Given the well-documented evidence on the underperformance of actively managed mutual funds, Dammon et al. (2004) conclude that investors would be better off holding index funds (or individual stocks) in the taxable account and taxable bonds in the tax-deferred account.