This supplemental appendix accompanies "Optimal Investment with Transaction Costs and Stochastic Volatility Part II: Finite Horizon" by the same authors, available at:"http://ssrn.com/abstract=2659918" http://ssrn.com/abstract=2659918. In this appendix we prove the verification theorem that the value function is a viscosity solution of the HJB equation.
In this companion paper to “Optimal Investment with Transaction Costs and Stochastic Volatility Part I: Infinite Horizon”, "http://ssrn.com/abstract=2374150" http://ssrn.com/abstract=2374150, we give an accuracy proof for the finite time optimal investment and consumption problem under fast mean-reverting stochastic volatility of a joint asymptotic expansion in a time scale parameter and the small transaction cost. The supplemental appendix accompanies this paper is, available at "http://ssrn.com/abstract=3234374" http://ssrn.com/abstract=3234374, in which we prove the verification theorem that the value function is a viscosity solution of the HJB equation.
Two major financial market complexities are transaction costs and uncertain volatility, and we analyze their joint impact on the problem of portfolio optimization. When volatility is constant, the transaction costs optimal investment problem has a long history, especially in the use of asymptotic approximations when the cost is small. Under stochastic volatility, but with no transaction costs, the Merton problem under general utility functions can also be analyzed with asymptotic methods. Here, we look at the long-run growth rate problem when both complexities are present, using separation of time scales approximations. This leads to perturbation analysis of an eigenvalue problem. We find the first term in the asymptotic expansion in the time scale parameter, of the optimal long-term growth rate, and of the optimal strategy, for fixed small transaction costs.The Companion piece for this paper are available at the following URL: "http://ssrn.com/abstract=2659918" http://ssrn.com/abstract=2659918.
At the height of the Great Depression a number of leading U.S. economists advanced a proposal for monetary reform that became known as the Chicago Plan. It envisaged the separation of the monetary and credit functions of the banking system, by requiring 100% reserve backing for deposits. Irving Fisher (1936) claimed the following advantages for this plan: (1) Much better control of a major source of business cycle fluctuations, sudden increases and contractions of bank credit and of the supply of bank-created money. (2) Complete elimination of bank runs. (3) Dramatic reduction of the (net) public debt. (4) Dramatic reduction of private debt, as money creation no longer requires simultaneous debt creation. We study these claims by embedding a comprehensive and carefully calibrated model of the banking system in a DSGE model of the U.S. economy. We find support for all four of Fisher's claims. Furthermore, output gains approach 10 percent, and steady state inflation can drop to zero without posing problems for the conduct of monetary policy.
How to prevent runs on open-end mutual funds? In recent years, markets have observed an innovation that changed the way open-end funds are priced. Alternative pricing rules (known as swing pricing) adjust funds’ net asset values to pass on funds’ trading costs to transacting shareholders. Using unique data on investor transactions in U.K. corporate bond funds, we show that swing pricing eliminates the first-mover advantage arising from the traditional pricing rule and significantly reduces redemptions during stress periods. The positive impact of alternative pricing rules on fund flows reverses in calm periods when costs associated with higher tracking error dominate the pricing effect.
Stocks and bonds? Real estate? Hedge funds? Private equity? If you think those are the things to focus on in building an investment portfolio, Andrew Ang has accumulated a body of research that will prove otherwise. In this book, Ang upends the conventional wisdom about asset allocation by showing that what matters aren't asset class labels but the bundles of overlapping risks they represent.
An introduction to the theory and methods of empirical asset pricing, integrating classical foundations with recent developments. This book offers a comprehensive advanced introduction to asset pricing, the study of models for the prices and returns of various securities. The focus is empirical, emphasizing how the models relate to the data. The book offers a uniquely integrated treatment, combining classical foundations with more recent developments in the literature and relating some of the material to applications in investment management. It covers the theory of empirical asset pricing, the main empirical methods, and a range of applied topics. The book introduces the theory of empirical asset pricing through three main paradigms: mean variance analysis, stochastic discount factors, and beta pricing models. It describes empirical methods, beginning with the generalized method of moments (GMM) and viewing other methods as special cases of GMM; offers a comprehensive review of fund performance evaluation; and presents selected applied topics, including a substantial chapter on predictability in asset markets that covers predicting the level of returns, volatility and higher moments, and predicting cross-sectional differences in returns. Other chapters cover production-based asset pricing, long-run risk models, the Campbell-Shiller approximation, the debate on covariance versus characteristics, and the relation of volatility to the cross-section of stock returns. An extensive reference section captures the current state of the field. The book is intended for use by graduate students in finance and economics; it can also serve as a reference for professionals.
This classic textbook in the field, now completely revised and updated, provides a bridge between theory and practice. Appropriate for the second course in Finance for MBA students and the first course in Finance for doctoral students, the text prepares students for the complex world of modern financial scholarship and practice. It presents a unified treatment of finance combining theory, empirical evidence and applications.
