Abstract: This paper derives in closed form the optimal dynamic portfolio policy when trading is costly and security returns are predictable by signals with different mean-reversion speeds. The optimal updated portfolio is a linear combination of the existing portfolio, the optimal portfolio absent trading costs, and the optimal portfolio based on future expected returns and transaction costs. Predictors with slower mean reversion (alpha decay) get more weight since they lead to a favorable positioning both now and in the future. We implement the optimal policy for commodity futures and show that the resulting portfolio has superior returns net of trading costs relative to more naive benchmarks. Finally, we derive natural equilibrium implications, including that demand shocks with faster mean reversion command a higher return premium
We derive an explicit solution to a continuous time dynamic portfolio problem assuming investors maximize their welfare from a consumption stream in an incomplete market where returns to the securities are predictable but costly to trade. The solution is phrased in terms of a risk-sensitive Riccati equation. We show that the optimal trading strategy is to target a portfolio that is the optimal solution to a frictionless (or 'no-cost') dynamic portfolio problem but where the returns to the assets have been adjusted for costs; that is they have been expressed on a net rather than gross basis. The legacy portfolio (the inherited undesirable positions) are then traded away in line with a backward-looking optimal execution problem. We show that the utility gradient is a stochastic discount factor that prices the assets net returns. Thus we are able to generalise some of the results of the martingale approach to dynamic portfolio theory to market with frictions.
We propose a simple approach to dynamic multi-period portfolio choice with transaction costs that is tractable in settings with a large number of securities, realistic return dynamics with multiple risk factors, many predictor variables, and stochastic volatility. We obtain a closed-form solution for an optimal trading rule when the problem is restricted to a broad class of strategies we define as 'linearity generating strategies' (LGS). When restricted to this class, the non-linear dynamic optimization problem reduces to a deterministic linear-quadratic optimization problem in the parameters of the trading strategies. We show that the LGS approach dominates several alternatives in realistic settings, and in particular when the covariance structure and transaction costs are stochastic.
We consider a class of dynamic portfolio optimization problems that allow for models of return predictability, transaction costs, and stochastic volatility. Determining the dynamic optimal portfolio in this general setting is almost always intractable. We propose a multiscale asymptotic expansion when the volatility process is characterized by its time scales of fluctuation. The analysis of the nonlinear Hamilton- Jacobi-Bellman PDE is a singular perturbation problem when volatility is fast mean-reverting; and it is a regular perturbation when the volatility is slowly varying. These analyses can be combined for multifactor multiscale stochastic volatility model. We present formal derivations of asymptotic approximations and demonstrate how the proposed algorithms improve our Profit & Loss using Monte Carlo simulations.
We examine the interplay between event risk, transaction costs and predictability on the dynamic asset allocation of an investor with discrete trading opportunities. The model is calibrated to the U.S. stock market and a Gauss-Hermite quadrature approach is used to solve the investor's dynamic optimization problem. Numerical scenarios are examined to show the impact of event risk on asset allocations, hedging demands, no-trading regions, and certainty equivalent returns. It is found that event risk shrinks hedging demand. Neglecting event risk can also lead to sizeable certainty equivalent return losses.
This monograph collects in one place the basic definitions, a careful description of the model, and discussion of how convex optimization can be used in multi-period trading, all in a common notation and framework.
Academic finance has had a remarkable impact on many financial services. Yet long-term investors have received curiously little guidance from academic financial economists. Mean-variance analysis, developed almost fifty years ago, has provided a basic paradigm for portfolio choice. This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead. However, many investors—-both individuals and institutions such as charitable foundations or universities—-seek to finance a stream of consumption over a long lifetime. In addition, mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption. At the theoretical level, it is well understood that the solution to a long-term portfolio choice problem can be very different from the solution to a short-term problem. Long-term investors care about intertemporal shocks to investment opportunities and labor income as well as shocks to wealth itself, and they may use financial assets to hedge their intertemporal risks. This should be important in practice because there is a great deal of empirical evidence that investment opportunities—-both interest rates and risk premia on bonds and stocks—-vary through time. Yet this insight has had little influence on investment practice because it is hard to solve for optimal portfolios in intertemporal models. This book seeks to develop the intertemporal approach into an empirical paradigm that can compete with the standard mean-variance analysis. The book shows that long-term inflation-indexed bonds are the riskless asset for long-term investors, it explains the conditions under which stocks are safer assets for long-term than for short-term investors, and it shows how labor income influences portfolio choice. These results shed new light on the rules of thumb used by financial planners. The book explains recent advances in both analytical and numerical methods, and shows how they can be used to understand the portfolio choice problems of long-term investors.
This comprehensive reference delivers a toolkit for harvesting market rewards from a wide range of investments. Written by a world-renowned industry expert, the reference discusses how to forecast returns under different parameters. Expected returns of major asset classes, investment strategies, and the effects of underlying risk factors such as growth, inflation, liquidity, and different risk perspectives, are also explained. Judging expected returns requires balancing historical returns with both theoretical considerations and current market conditions. Expected Returns provides extensive empirical evidence, surveys of risk-based and behavioral theories, and practical insights.
