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.

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.

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.

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.

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.

Financial Markets Theory

Financial Markets Theory
Author: Emilio Barucci
Publisher: Springer
Total Pages: 843
Release: 2017-06-08
Genre: Mathematics
ISBN: 1447173228

This work, now in a thoroughly revised second edition, presents the economic foundations of financial markets theory from a mathematically rigorous standpoint and offers a self-contained critical discussion based on empirical results. It is the only textbook on the subject to include more than two hundred exercises, with detailed solutions to selected exercises. Financial Markets Theory covers classical asset pricing theory in great detail, including utility theory, equilibrium theory, portfolio selection, mean-variance portfolio theory, CAPM, CCAPM, APT, and the Modigliani-Miller theorem. Starting from an analysis of the empirical evidence on the theory, the authors provide a discussion of the relevant literature, pointing out the main advances in classical asset pricing theory and the new approaches designed to address asset pricing puzzles and open problems (e.g., behavioral finance). Later chapters in the book contain more advanced material, including on the role of information in financial markets, non-classical preferences, noise traders and market microstructure. This textbook is aimed at graduate students in mathematical finance and financial economics, but also serves as a useful reference for practitioners working in insurance, banking, investment funds and financial consultancy. Introducing necessary tools from microeconomic theory, this book is highly accessible and completely self-contained. Advance praise for the second edition: "Financial Markets Theory is comprehensive, rigorous, and yet highly accessible. With their second edition, Barucci and Fontana have set an even higher standard!"Darrell Duffie, Dean Witter Distinguished Professor of Finance, Graduate School of Business, Stanford University "This comprehensive book is a great self-contained source for studying most major theoretical aspects of financial economics. What makes the book particularly useful is that it provides a lot of intuition, detailed discussions of empirical implications, a very thorough survey of the related literature, and many completely solved exercises. The second edition covers more ground and provides many more proofs, and it will be a handy addition to the library of every student or researcher in the field."Jaksa Cvitanic, Richard N. Merkin Professor of Mathematical Finance, Caltech "The second edition of Financial Markets Theory by Barucci and Fontana is a superb achievement that knits together all aspects of modern finance theory, including financial markets microstructure, in a consistent and self-contained framework. Many exercises, together with their detailed solutions, make this book indispensable for serious students in finance."Michel Crouhy, Head of Research and Development, NATIXIS

Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives

Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives
Author: Jean-Pierre Fouque
Publisher: Cambridge University Press
Total Pages: 456
Release: 2011-09-29
Genre: Mathematics
ISBN: 113950245X

Building upon the ideas introduced in their previous book, Derivatives in Financial Markets with Stochastic Volatility, the authors study the pricing and hedging of financial derivatives under stochastic volatility in equity, interest-rate, and credit markets. They present and analyze multiscale stochastic volatility models and asymptotic approximations. These can be used in equity markets, for instance, to link the prices of path-dependent exotic instruments to market implied volatilities. The methods are also used for interest rate and credit derivatives. Other applications considered include variance-reduction techniques, portfolio optimization, forward-looking estimation of CAPM 'beta', and the Heston model and generalizations of it. 'Off-the-shelf' formulas and calibration tools are provided to ease the transition for practitioners who adopt this new method. The attention to detail and explicit presentation make this also an excellent text for a graduate course in financial and applied mathematics.