A Multi-period Portfolio Selection in a Large Financial Market

A Multi-period Portfolio Selection in a Large Financial Market
Author: N'Golo Koné
Publisher:
Total Pages:
Release: 2020
Genre:
ISBN:

This paper addresses a multi-period portfolio selection problem when the number of assets in the financial market is large. Using an exponential utility function, the optimal solution is shown to be a function of the inverse of the covariance matrix of asset returns. Nonetheless, when the number of assets grows, this inverse becomes unreliable, yielding a selected portfolio that is far from the optimal one. We propose two solutions to this problem. First, we penalize the norm of the portfolio weights in the dynamic problem and show that the selected strategy is asymptotically efficient. Second, we penalize the norm of the difference of successive portfolio weights in the dynamic problem to guarantee that the optimal portfolio composition does not fluctuate widely between periods. This second method helps investors to avoid high trading costs in the financial market by selecting stable strategies over time. Extensive simulations and empirical results confirm that our procedures considerably improve the performance of the dynamic portfolio.

Portfolio and Consumption Decisions Under Mean-Revering Returns

Portfolio and Consumption Decisions Under Mean-Revering Returns
Author: Jessica A. Wachter
Publisher:
Total Pages: 36
Release: 2011
Genre:
ISBN:

This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and of the behavior of the approximate log-linear solution. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of investment horizon is extended to that of an investor who consumes at multiple points in time.

Multi-Period Trading Via Convex Optimization

Multi-Period Trading Via Convex Optimization
Author: Stephen Boyd
Publisher:
Total Pages: 92
Release: 2017-07-28
Genre: Mathematics
ISBN: 9781680833287

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.

Optimal Consumption and Portfolio Allocation Under Mean-Reverting Returns

Optimal Consumption and Portfolio Allocation Under Mean-Reverting Returns
Author: Jessica A. Wachter
Publisher:
Total Pages: 31
Release: 2011
Genre:
ISBN:

This paper solves, in closed form, the optimal portfolio choice problem for an investor with utility over consumption under mean-reverting returns. Previous solutions either require approximations, numerical methods, or the assumption that the investor does not consume over his lifetime. This paper breaks the impasse by assuming that markets are complete. The solution leads to a new understanding of hedging demand and the behavior of approximate log-linear solutions. The portfolio allocation takes the form of a weighted average and is shown to be analogous to duration for coupon bonds. Through this analogy, the notion of investment horizon is extended to that of an investor who consumes at multiple points in time.

Consumption and Portfolio Decisions when Expected Returns are Time Varying

Consumption and Portfolio Decisions when Expected Returns are Time Varying
Author: John Y. Campbell
Publisher:
Total Pages: 88
Release: 1996
Genre: Consumption (Economics)
ISBN:

This paper proposes and implements a new approach to a classic unsolved problem in financial economics: the optimal consumption and portfolio choice problem of a long-lived investor facing time-varying investment opportunities. The investor is assumed to be infinitely-lived, to have recursive Epstein-Zin-Weil utility, and to choose in discrete time between a riskless asset with a constant return, and a risky asset with constant return variance whose expected log return follows and AR(1) process. The paper approximates the choice problem by log-linearizing the budget constraint and Euler equations, and derives an analytical solution to the approximate problem. When the model is calibrated to US 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.

Discrete Choice Methods with Simulation

Discrete Choice Methods with Simulation
Author: Kenneth Train
Publisher: Cambridge University Press
Total Pages: 399
Release: 2009-07-06
Genre: Business & Economics
ISBN: 0521766559

This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.

Multiperiod Portfolio Choice Under Loss Aversion with Dynamic Reference Point in Serially Correlated Market

Multiperiod Portfolio Choice Under Loss Aversion with Dynamic Reference Point in Serially Correlated Market
Author: Jianjun Gao
Publisher:
Total Pages: 0
Release: 2023
Genre:
ISBN:

In this paper, we investigate a novel multiperiod portfolio decision model for loss-averse investors with dynamically adapted reference points in a market with serially correlated returns. We demonstrate that the optimal policy is a piecewise linear function of the deviation between current wealth and reference level, and its slopes are a path-dependent function of the historical returns, in sharp contrast to the constant slopes generated by the simplified model that ignores the diminishing sensitivity and assumes independent returns. We show that this new feature significantly changes the typical V-shape pattern of the risky position, resulting in a more complicated nonlinear functional mapping. Our research highlights the potential dangers of relying on the simplified model and provides valuable insights for investors and practitioners to develop effective portfolio strategies under realistic market conditions. Additionally, our simulation analysis indicates that the predictability of returns combined with a small degree of diminishing sensitivity may enhance the disposition effect. Lastly, we prove that the new policy also fits to solve the multiperiod mean-Conditional-Value-at-Risk (CVaR) portfolio optimization problem with correlated returns, further broadening the application of our findings.

Portfolio Choice with Stochastic Interest Rates and Learning About Stock Return Predictability

Portfolio Choice with Stochastic Interest Rates and Learning About Stock Return Predictability
Author: Marcos Escobar
Publisher:
Total Pages: 35
Release: 2014
Genre:
ISBN:

The problem of optimal wealth allocation is solved under the assumptions that interest rates are stochastic and stock returns are predictable with observed and unobserved factors. The stock risk premium is taken to be an affine function of the predictive variables and the stock return volatility is assumed to depend on the observed factor. The latent factor is estimated based on the observations. It is shown that the stock return predictability can significantly impact the optimal bond portfolio. The welfare loss from ignoring learning can be considerable.