Consumption-portfolio Choice with Preferences for Cash

Consumption-portfolio Choice with Preferences for Cash
Author: Holger Kraft
Publisher:
Total Pages:
Release: 2017
Genre:
ISBN:

This paper studies a consumption-portfolio problem where money enters the agent's utility function. We solve the corresponding Hamilton-Jacobi-Bellman equation and provide closed-form solutions for the optimal consumption and portfolio strategy both in an infinite- and finite-horizon setting. For the infinite-horizon problem, the optimal stock demand is one particular root of a polynomial. In the finite-horizon case, the optimal stock demand is given by the inverse of the solution to an ordinary differential equation that can be solved explicitly. We also prove verification results showing that the solution to the Bellman equation is indeed the value function of the problem. From an economic point of view, we find that in the finite-horizon case the optimal stock demand is typically decreasing in age, which is in line with rules of thumb given by financial advisers and also with recent empirical evidence.

Portfolio and Consumption Choice with Stochastic Investment Opportunities and Habit Formation in Preferences

Portfolio and Consumption Choice with Stochastic Investment Opportunities and Habit Formation in Preferences
Author: Claus Munk
Publisher:
Total Pages: 43
Release: 2002
Genre:
ISBN:

We study the dynamic consumption and portfolio choice of an investor who has habit formation in preferences and access to a complete financial market. For general, possibly non-Markov, dynamics of market prices, we provide an exact characterization of the optimal behavior in terms of two relatively simple and intuitively interpretable stochastic processes. We study in more detail the optimal strategies in two concrete examples of time-varying investment opportunities. Firstly, we derive a closed-form solution of the optimal consumption and portfolio choice with mean-reverting stock returns. Secondly, with Cox-Ingersoll-Ross interest rate dynamics we can express the optimal strategies in terms of the solution to a partial differential equation, which has an explicit solution for time-additive preferences, but not with habit formation. Our numerical examples show that, while hedging demands for various assets are affected differently by habit persistence, the main effect on relative asset allocations stems from the fact that some assets (bonds and cash) are better investment objects than others (stocks) when it comes to ensuring that future consumption will not fall below the habit level. The implications of habit persistence in models with labor income are also addressed.

Lifetime Consumption-Portfolio Choice Under Trading Constraints, Recursive Preferences and Nontradeable Income

Lifetime Consumption-Portfolio Choice Under Trading Constraints, Recursive Preferences and Nontradeable Income
Author: Mark D. Schroder
Publisher:
Total Pages: 40
Release: 2003
Genre:
ISBN:

We consider the lifetime consumption-portfolio problem in a competitive securities market with essentially arbitrary continuous price dynamics, a possibly nontradeable income stream, and convex constraints on the vector of market values of financial positions. (The setting extends Schroder and Skiadas, 2002, where the endowment is assumed tradeable and constraints are imposed in terms of wealth proportions.) For any utility function with a supergradient density, we develop the first-order conditions of optimality, a side-product being the characterization of a constrained notion of state-pricing. The methodology is applied to generalized continuous-time recursive utility, allowing for first and second-order risk-aversion that can depend on the risk source, reflecting the source's quot;ambiguity.quot; Within this class, we isolate a more tractable formulation in which preferences exhibit no wealth effects (an example being time-additive expected discounted exponential utility), and there is unrestricted trading in a money market and a suitably defined consol bond. In this case, we derive closed-form solutions for the optimal consumption and trading strategy in terms of the solution to a single constrained backward stochastic differential equation (BSDE), which in a Markovian setting maps to a PDE. Methodologically, we develop the utility gradient approach, but for the wealth-invariant case we also verify the solution using the dynamic programming approach, without having to assume a Markovian structure. Finally, we present a class of parametric examples in which the PDE characterizing the solution simplifies to a system of ordinary differential equations (of the Riccati type).

Strategic Asset Allocation

Strategic Asset Allocation
Author: John Y. Campbell
Publisher: OUP Oxford
Total Pages: 272
Release: 2002-01-03
Genre: Business & Economics
ISBN: 019160691X

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.

Portfolio Theory and the Demand for Money

Portfolio Theory and the Demand for Money
Author: Neil Thompson
Publisher: Springer
Total Pages: 223
Release: 2016-07-27
Genre: Business & Economics
ISBN: 1349228273

The book is an in-depth review of the theory and empirics of the demand for money and other financial assets. The different theoretical approaches to the portfolio choice problem are described, together with an up-to-date survey of the results obtained from empirical studies of asset choice behaviour. Both single-equation studies and the more complete multi-asset portfolio models, are analysed.

Investors and Markets

Investors and Markets
Author: William F. Sharpe
Publisher: Princeton University Press
Total Pages: 232
Release: 2011-01-01
Genre: Business & Economics
ISBN: 1400830184

In Investors and Markets, Nobel Prize-winning financial economist William Sharpe shows that investment professionals cannot make good portfolio choices unless they understand the determinants of asset prices. But until now asset-price analysis has largely been inaccessible to everyone except PhDs in financial economics. In this book, Sharpe changes that by setting out his state-of-the-art approach to asset pricing in a nonmathematical form that will be comprehensible to a broad range of investment professionals, including investment advisors, money managers, and financial analysts. Bridging the gap between the best financial theory and investment practice, Investors and Markets will help investment professionals make better portfolio choices by being smarter about asset prices. Based on Sharpe's Princeton Lectures in Finance, Investors and Markets presents a method of analyzing asset prices that accounts for the real behavior of investors. Sharpe makes this technique accessible through a new, one-of-a-kind computer program (available for free on his Web site, at http://www.stanford.edu/~wfsharpe/apsim/index.html) that enables users to create virtual markets, setting the starting conditions and then allowing trading until equilibrium is reached and trading stops. Program users can then analyze the final portfolios and asset prices, see expected returns, and measure risk. In addition to popularizing the most sophisticated form of asset-price analysis, Investors and Markets summarizes much of Sharpe's most important previous work and reflects a lifetime of thinking about investing by one of the leading minds in financial economics. Any serious investment professional will benefit from Sharpe's unique insights.

Handbook of Computational Finance

Handbook of Computational Finance
Author: Jin-Chuan Duan
Publisher: Springer Science & Business Media
Total Pages: 791
Release: 2011-10-25
Genre: Business & Economics
ISBN: 3642172547

Any financial asset that is openly traded has a market price. Except for extreme market conditions, market price may be more or less than a “fair” value. Fair value is likely to be some complicated function of the current intrinsic value of tangible or intangible assets underlying the claim and our assessment of the characteristics of the underlying assets with respect to the expected rate of growth, future dividends, volatility, and other relevant market factors. Some of these factors that affect the price can be measured at the time of a transaction with reasonably high accuracy. Most factors, however, relate to expectations about the future and to subjective issues, such as current management, corporate policies and market environment, that could affect the future financial performance of the underlying assets. Models are thus needed to describe the stochastic factors and environment, and their implementations inevitably require computational finance tools.

Portfolio Selection Using Multi-Objective Optimisation

Portfolio Selection Using Multi-Objective Optimisation
Author: Saurabh Agarwal
Publisher: Springer
Total Pages: 240
Release: 2017-08-21
Genre: Business & Economics
ISBN: 3319544160

This book explores the risk-return paradox in portfolio selection by incorporating multi-objective criteria. Empirical research is presented on the development of alternate portfolio models and their relative performance in the risk/return framework to provide solutions to multi-objective optimization. Next to outlining techniques for undertaking individual investor’s profiling and portfolio programming, it also offers a new and practical approach for multi-objective portfolio optimization. This book will be of interest to Foreign Institutional Investors (FIIs), Mutual Funds, investors, and researchers and students in the field.