Optimal Dynamic Portfolio Choice Research Articles

Wealth Effect on Portfolio Allocation in Incomplete Markets

This paper provides a novel five-component decomposition of optimal dynamic portfolio choice. It reveals the simultaneous impacts from market incompleteness and wealth-dependent utilities. The decomposition leads to implementation via either closed-form solutions or Monte Carlo simulations. With a nonrandom but time-varying interest rate, we can explicitly solve for the optimal policy under the wealth-dependent HARA utility. It is a combination of a bond holding scheme and the corresponding simpler CRRA strategy. Under incomplete markets with a stochastic volatility model estimated on US equity data, wealth-dependence introduces sophisticated cycle-dependence for optimal policy and hysteresis effect in Sharpe ratio.

Dynamic portfolio selection with market impact costs

This paper concerns optimal dynamic portfolio choice with quadratic utility when there are market impact costs. The optimal policy is difficult to characterize, so we look instead for sub-optimal policies. Our proposed suboptimal policy solves a tractable dynamic portfolio choice problem where the cost of trading is captured in the objective instead of the price dynamics. A multiple time scale asymptotic expansion shows that our proposed policy has sensible structural properties, while numerical experiments show promising performance and robustness properties.

Optimal Dynamic Portfolio Choice with Multiple Decentralized Agents

Optimal Dynamic Portfolio Choice with Multiple Decentralized Agents

Investing when Volatility Fluctuates

We examine how the evidence of the time-varying volatility in stock returns affects optimal dynamic portfolio choice of investors with long horizons. As return volatility shows a relatively small correlation with realized return, its time-variation is expected to cause little, if any, hedging demand (in the sense of Merton (1973)). However, we find that, once transaction costs are taken into account in portfolio rebalancing, the time-varying monthly return volatility produces significant horizon effect with stock allocations despite the negligible hedging demand. The driving force of this surprising result is newly identified in our study, and differs from the hedging demand documented in earlier studies (e.g., Brennan, Schwartz, and Lagnado (1997) and Barberis (2000)). Moreover, the horizon effect is found to be state-dependent, and could be either positive or strikingly negative, depending on the current value of return volatility. This leads to a reduced sensitivity of the initial optimal stock allocation to current return volatility as a function of the expected portfolio holding period. It also suggests that how much an investor values the knowledge of the true current return volatility depends on the investment horizons and transaction costs.

Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities

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.

Learning about Predictability: The Effects of Parameter Uncertainty on Dynamic Asset Allocation

ABSTRACTThis paper examines the effects of uncertainty about the stock return predictability on optimal dynamic portfolio choice in a continuous time setting for a longhorizon investor. Uncertainty about the predictive relation affects the optimal portfolio choice through dynamic learning, and leads to a state‐dependent relation between the optimal portfolio choice and the investment horizon. There is substantial market timing in the optimal hedge demands, which is caused by stochastic covariance between stock return and dynamic learning. The opportunity cost of ignoring predictability or learning is found to be quite substantial.

Losing Money on Arbitrage: Optimal Dynamic Portfolio Choice in Markets with Arbitrage Opportunities

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.