Modern Portfolio Theory, Part One
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Managing Volatility Risk
Managing Volatility Risk Innovation of Financial Derivatives, Stochastic Models and Their Analytical Implementation Chenxu Li Submitted in partial fulfillment of the Requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences COLUMBIA UNIVERSITY 2010 c 2010 Chenxu Li All Rights Reserved ABSTRACT Managing Volatility Risk Innovation of Financial Derivatives, Stochastic Models and Their Analytical Implementation Chenxu Li This dissertation investigates two timely topics in mathematical finance. In partic- ular, we study the valuation, hedging and implementation of actively traded volatil- ity derivatives including the recently introduced timer option and the CBOE (the Chicago Board Options Exchange) option on VIX (the Chicago Board Options Ex- change volatility index). In the first part of this dissertation, we investigate the pric- ing, hedging and implementation of timer options under Heston’s (1993) stochastic volatility model. The valuation problem is formulated as a first-passage-time problem through a no-arbitrage argument. By employing stochastic analysis and various ana- lytical tools, such as partial differential equation, Laplace and Fourier transforms, we derive a Black-Scholes-Merton type formula for pricing timer options. This work mo- tivates some theoretical study of Bessel processes and Feller diffusions as well as their numerical implementation. In the second part, we analyze the valuation of options on VIX under Gatheral’s double mean-reverting stochastic volatility model, which is able to consistently price options on S&P 500 (the Standard and Poor’s 500 index), VIX and realized variance (also well known as historical variance calculated by the variance of the asset’s daily return). -
Hedging Volatility Risk
Journal of Banking & Finance 30 (2006) 811–821 www.elsevier.com/locate/jbf Hedging volatility risk Menachem Brenner a,*, Ernest Y. Ou b, Jin E. Zhang c a Stern School of Business, New York University, New York, NY 10012, USA b Archeus Capital Management, New York, NY 10017, USA c School of Business and School of Economics and Finance, The University of Hong Kong, Pokfulam Road, Hong Kong Received 11 April 2005; accepted 5 July 2005 Available online 9 December 2005 Abstract Volatility risk plays an important role in the management of portfolios of derivative assets as well as portfolios of basic assets. This risk is currently managed by volatility ‘‘swaps’’ or futures. How- ever, this risk could be managed more efficiently using options on volatility that were proposed in the past but were never introduced mainly due to the lack of a cost efficient tradable underlying asset. The objective of this paper is to introduce a new volatility instrument, an option on a straddle, which can be used to hedge volatility risk. The design and valuation of such an instrument are the basic ingredients of a successful financial product. In order to value these options, we combine the approaches of compound options and stochastic volatility. Our numerical results show that the straddle option is a powerful instrument to hedge volatility risk. An additional benefit of such an innovation is that it will provide a direct estimate of the market price for volatility risk. Ó 2005 Elsevier B.V. All rights reserved. JEL classification: G12; G13 Keywords: Volatility options; Compound options; Stochastic volatility; Risk management; Volatility index * Corresponding author. -
An Overview of the Empirical Asset Pricing Approach By
AN OVERVIEW OF THE EMPIRICAL ASSET PRICING APPROACH BY Dr. GBAGU EJIROGHENE EMMANUEL TABLE OF CONTENT Introduction 1 Historical Background of Asset Pricing Theory 2-3 Model and Theory of Asset Pricing 4 Capital Asset Pricing Model (CAPM): 4 Capital Asset Pricing Model Formula 4 Example of Capital Asset Pricing Model Application 5 Capital Asset Pricing Model Assumptions 6 Advantages associated with the use of the Capital Asset Pricing Model 7 Hitches of Capital Pricing Model (CAPM) 8 The Arbitrage Pricing Theory (APT): 9 The Arbitrage Pricing Theory (APT) Formula 10 Example of the Arbitrage Pricing Theory Application 10 Assumptions of the Arbitrage Pricing Theory 11 Advantages associated with the use of the Arbitrage Pricing Theory 12 Hitches associated with the use of the Arbitrage Pricing Theory (APT) 13 Actualization 14 Conclusion 15 Reference 16 INTRODUCTION This paper takes a critical examination of what Asset Pricing is all about. It critically takes an overview of its historical background, the model and Theory-Capital Asset Pricing Model and Arbitrary Pricing Theory as well as those who introduced/propounded them. This paper critically examines how securities are priced, how their returns are calculated and the various approaches in calculating their returns. In this Paper, two approaches of asset Pricing namely Capital Asset Pricing Model (CAPM) as well as the Arbitrage Pricing Theory (APT) are examined looking at their assumptions, advantages, hitches as well as their practical computation using their formulae in their examination as well as their computation. This paper goes a step further to look at the importance Asset Pricing to Accountants, Financial Managers and other (the individual investor). -
Post-Modern Portfolio Theory Supports Diversification in an Investment Portfolio to Measure Investment's Performance
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Rasiah, Devinaga Article Post-modern portfolio theory supports diversification in an investment portfolio to measure investment's performance Journal of Finance and Investment Analysis Provided in Cooperation with: Scienpress Ltd, London Suggested Citation: Rasiah, Devinaga (2012) : Post-modern portfolio theory supports diversification in an investment portfolio to measure investment's performance, Journal of Finance and Investment Analysis, ISSN 2241-0996, International Scientific Press, Vol. 1, Iss. 1, pp. 69-91 This Version is available at: http://hdl.handle.net/10419/58003 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend -
Portfolio Management Under Transaction Costs
Portfolio management under transaction costs: Model development and Swedish evidence Umeå School of Business Umeå University SE-901 87 Umeå Sweden Studies in Business Administration, Series B, No. 56. ISSN 0346-8291 ISBN 91-7305-986-2 Print & Media, Umeå University © 2005 Rickard Olsson All rights reserved. Except for the quotation of short passages for the purposes of criticism and review, no part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior consent of the author. Portfolio management under transaction costs: Model development and Swedish evidence Rickard Olsson Master of Science Umeå Studies in Business Administration No. 56 Umeå School of Business Umeå University Abstract Portfolio performance evaluations indicate that managed stock portfolios on average underperform relevant benchmarks. Transaction costs arise inevitably when stocks are bought and sold, but the majority of the research on portfolio management does not consider such costs, let alone transaction costs including price impact costs. The conjecture of the thesis is that transaction cost control improves portfolio performance. The research questions addressed are: Do transaction costs matter in portfolio management? and Could transaction cost control improve portfolio performance? The questions are studied within the context of mean-variance (MV) and index fund management. The treatment of transaction costs includes price impact costs and is throughout based on the premises that the trading is uninformed, immediate, and conducted in an open electronic limit order book system. These premises characterize a considerable amount of all trading in stocks. -
MODERN PORTFOLIO THEORY: FOUNDATIONS, ANALYSIS, and NEW DEVELOPMENTS Table of Contents
MODERN PORTFOLIO THEORY: FOUNDATIONS, ANALYSIS, AND NEW DEVELOPMENTS Table of Contents Preface Chapter 1 Introduction (This chapter contains three Figures) 1.1 The Portfolio Management Process 1.2 The Security Analyst's Job 1.3 Portfolio Analysis 1.3A Basic Assumptions 1.3B Reconsidering The Assumptions 1.4 Portfolio Selection 1.5 Mathematics Segregated to Appendices 1.6 Topics To Be Discussed Appendix - Various Rates of Return A1.1 The Holding Period Return A1.2 After-Tax Returns A1.3 Continuously Compounded Return PART 1: PROBABILITY FOUNDATIONS Chapter 2 Assessing Risk (This chapter contains six Numerical Examples) 2.1 Mathematical Expectation 2.2 What is Risk? 2.3 Expected Return 2.4 Risk of a Security 2.5 Covariance of Returns 2.6 Correlation of Returns 2.7 Using Historical Returns 2.8 Data Input Requirements 2.9 Portfolio Weights 2.10 A Portfolio’s Expected Return 2.11 Portfolio Risk 2.12 Summary of Conventions and Formulas MODERN PORTFOLIO THEORY - Table of Contents – Page 1 Chapter 3 Risk and Diversification: An Overview (This chapter contains ten Figures and three Tables of real numbers) 3.1 Reconsidering Risk 3.1A Symmetric Probability Distributions 3.1B Fundamental Security Analysis 3.2 Utility Theory 3.2A Numerical Example 3.2B Indifference Curves 3.3 Risk-Return Space 3.4 Diversification 3.4A Diversification Illustrated 3.4B Risky A + Risky B = Riskless Portfolio 3.4C Graphical Analysis 3.5 Conclusions PART 2: UTILITY FOUNDATIONS Chapter 4 Single-Period Utility Analysis (This chapter contains sixteen Figures, four Tables -
An Exploitable Anomaly in the Ukrainian Stock Market?
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Caporale, Guglielmo Maria; Gil-Alana, Luis; Plastun, Alex Working Paper The weekend effect: An exploitable anomaly in the Ukrainian stock market? DIW Discussion Papers, No. 1458 Provided in Cooperation with: German Institute for Economic Research (DIW Berlin) Suggested Citation: Caporale, Guglielmo Maria; Gil-Alana, Luis; Plastun, Alex (2015) : The weekend effect: An exploitable anomaly in the Ukrainian stock market?, DIW Discussion Papers, No. 1458, Deutsches Institut für Wirtschaftsforschung (DIW), Berlin This Version is available at: http://hdl.handle.net/10419/107690 Standard-Nutzungsbedingungen: Terms of use: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Documents in EconStor may be saved and copied for your Zwecken und zum Privatgebrauch gespeichert und kopiert werden. personal and scholarly purposes. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle You are not to copy documents for public or commercial Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich purposes, to exhibit the documents publicly, to make them machen, vertreiben oder anderweitig nutzen. publicly available on the internet, or to distribute or otherwise use the documents in public. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, If the documents have been made available under an Open gelten abweichend -
The Cross-Section of Volatility and Expected Returns
THE JOURNAL OF FINANCE • VOL. LXI, NO. 1 • FEBRUARY 2006 The Cross-Section of Volatility and Expected Returns ANDREW ANG, ROBERT J. HODRICK, YUHANG XING, and XIAOYAN ZHANG∗ ABSTRACT We examine the pricing of aggregate volatility risk in the cross-section of stock returns. Consistent with theory, we find that stocks with high sensitivities to innovations in aggregate volatility have low average returns. Stocks with high idiosyncratic volatility relative to the Fama and French (1993, Journal of Financial Economics 25, 2349) model have abysmally low average returns. This phenomenon cannot be explained by exposure to aggregate volatility risk. Size, book-to-market, momentum, and liquidity effects cannot account for either the low average returns earned by stocks with high exposure to systematic volatility risk or for the low average returns of stocks with high idiosyncratic volatility. IT IS WELL KNOWN THAT THE VOLATILITY OF STOCK RETURNS varies over time. While con- siderable research has examined the time-series relation between the volatility of the market and the expected return on the market (see, among others, Camp- bell and Hentschel (1992) and Glosten, Jagannathan, and Runkle (1993)), the question of how aggregate volatility affects the cross-section of expected stock returns has received less attention. Time-varying market volatility induces changes in the investment opportunity set by changing the expectation of fu- ture market returns, or by changing the risk-return trade-off. If the volatility of the market return is a systematic risk factor, the arbitrage pricing theory or a factor model predicts that aggregate volatility should also be priced in the cross-section of stocks. -
Investor Sentiment, Post-Earnings Announcement Drift, and Accruals
Investor Sentiment, Post-Earnings Announcement Drift, and Accruals Joshua Livnat New York University Quantitative Management Associates Christine Petrovits College of William & Mary We examine whether stock price reactions to earnings surprises and accruals vary systematically with investor sentiment. Using quarterly drift tests and monthly trading strategy tests, we find that holding good news firms (and low accrual firms) following pessimistic sentiment periods earns higher abnormal returns than holding good news firms (and low accrual firms) following optimistic sentiment periods. We also document that abnormal returns in the short-window around earnings announcements for good news firms are higher during periods of low sentiment. Overall, our results indicate that investor sentiment influences the source of excess returns from accounting-based trading strategies. Keywords: Investor Sentiment, Post-Earnings Announcement Drift, Accruals, Anomalies INTRODUCTION We investigate whether investor sentiment influences the immediate and long-run market reactions to earnings surprises and accruals. Investor sentiment broadly represents the mood of investors at any given time. Relying on behavioral finance theories, several studies examine how waves of investor sentiment affect assets prices (e.g., Brown and Cliff, 2005; Baker and Wurgler, 2006; Lemmon and Portniaguina, 2006). The general result from this literature is that following periods of low (high) investor sentiment, subsequent market returns are relatively high (low), suggesting that stocks are underpriced (overpriced) in low (high) sentiment states but that prices eventually revert to fundamental values. Because a common explanation for post-earnings announcement drift is that investors initially underreact to the earnings news and a common explanation for the accruals anomaly is that investors initially overreact to accruals, it is possible that investor sentiment plays a role in how these two accounting anomalies unfold. -
Momentum – the Premier Market Anomaly
Momentum – The Premier Market Anomaly Fama/French (2008): Momentum is "the center stage anomaly of recent years…an anomaly that is above suspicion…the premier market anomaly." This paper will share a simple example of the power of momentum, and more specifically, the power of combining relative strength momentum with absolute momentum. Absolute momentum is often referred to as trend following or time-series momentum. We highly recommend those who want to go further in depth to pick up Gary Antonacci’s book, Dual Momentum Investing: An Innovative Strategy for Higher Returns with Lower Risk1. We will start by creating a benchmark global equity portfolio that is equally allocated to US large cap stocks, US small cap stocks, and International stocks2. The benchmark portfolio is rebalanced monthly. Our analysis period is 1972–2014 which includes three substantial bear markets (1973-1974, 2000-2002, and 2008-2009) along with one of the most prolific bull market runs in recent history from 1982–1999. 1 Gary Antonacci is not affiliated with Lorintine Capital. Lorintine Capital does not receive any compensation for mentioning his book nor is it an endorsement. We provide his book as a third-party reference for those interested in learning more about momentum and the concepts presented in this paper. 2 Historical data represents index data. You cannot invest directly in an index. Indexes do not include fees, expenses, or transaction costs. All examples are hypothetical. Past performance does not guarantee future results. 1 Since 1972 our benchmark portfolio has produced double digit annual returns with a Compound Annual Growth Rate (CAGR) of 10.85%, enough to grow $100 to $8,465.493. -
Do Equity Prices Reflect the Ultra-Low Interest Rate Environment?
27 FEBRUARY 2020 — N O . 1 Do equity prices reflect the ultra-low interest rate environment? Søren Lejsgaard Autrup Jonas Ladegaard Hensch The viewpoints and conclusions stated are the responsibility Principal Economist Economist of the individual contributors, and do not necessarily reflect ECONOMICS AND ECONOMICS AND the views of Danmarks Nationalbank. MONETARY POLICY MONETARY POLICY [email protected] [email protected] ECONOMIC MEMO — DANMARKS NATIONALBANK 27 FEBRUARY 2020 — N O . 1 Do equity prices reflect the ultra-low interest rate environment? The equity risk premium has Investors face a choice when deciding where to about doubled after the financial invest today: Get a certain return on bonds crisis, amid a sharp decline in offering very low or negative returns, or buy a interest rates and an unchanged risky equity and expect to get around 7 per cent per annum, but with downside and upside required return on equities. risks. Before the financial crisis of 2007-08, the trade-off looked different: The expected return The increase in the premium on equities was at the same level, but the entailed a lower pass-through of alternative looked much more favorable with monetary policy rates to the total bond yields around 4 per cent. In other words, financing costs of corporations. the equity risk premium, defined as the That may help to explain why additional return required as compensation for corporate investments have not investing in equities rather than risk-free assets rebounded faster and stronger (bonds), has about doubled to around 7 per after the financial crisis. cent. Still, bonds are in high demand and no major, global rotation between asset classes has taken place so far. -
Risk Management of Investments in Structured Credit Products
Risk Management of Investments in Structured Credit Products Background A growing number of FDIC-supervised institutions are experiencing deterioration in financial performance as a result of investments in structured credit products.1 The underlying collateral of certain structured credit products has performed poorly. As a result, the level of credit support for senior tranches has diminished, the volume and severity of credit rating downgrades have increased, liquidity has declined, prices are not transparent, and price volatility has increased. Consequently, an increasing number of financial institutions are recognizing other-than-temporary impairment (OTTI) charges and substantial fair value markdowns. Some institutions have invested in structured products in volumes representing concentrations of capital. In some cases, significant purchases were initiated after the credit market turmoil began and, in some cases, funding came from brokered deposits or other volatile funding sources. The FDIC is concerned that financial institutions are not appropriately identifying and controlling the risks inherent in complex structured credit products. Examiners are identifying weaknesses in management’s understanding of product risks, due diligence efforts, portfolio diversification standards, and application of proper accounting standards. Purpose This letter clarifies the application of existing supervisory guidance to structured credit products. Guidance referenced comes primarily from the 1998 “Supervisory Policy Statement on Investment Securities and End-User Derivatives Activities” (Policy Statement), and the “Uniform Agreement on the Classification of Assets and Appraisal of Securities” (Uniform Agreement).2 Topics addressed in this letter include investment suitability and due diligence, the use of external credit ratings, pricing and liquidity, and adverse classification of investment securities. FDIC-supervised institutions should revisit outstanding guidance and incorporate this document’s clarifications into existing policies and processes.