WACC and Vol (Valuation for Companies with Real Options)
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The Cost of Capital: an International Comparison
The Cost of Capital: An International Comparison The Cost of Capital: An International Comparison EXECUTIVE SUMMARY June 2006 June 2006 The Cost of Capital: An International Comparison EXECUTIVE SUMMARY Oxera Consulting Ltd Park Central 40/41 Park End Street Oxford OX1 1JD Telephone: +44(0) 1865 253 000 Fax: +44(0) 1865 251 172 www.oxera.com London Stock Exchange and the coat of arms device are registered trade marks plc June 2006 The Cost of Capital: An International Comparison is published by the City of London. The authors of this report are Leonie Bell, Luis Correia da Silva and Agris Preimanis of Oxera Consulting Ltd. This report is intended as a basis for discussion only. Whilst every effort has been made to ensure the accuracy and completeness of the material in this report, the authors, Oxera Consulting Ltd, the London Stock Exchange, and the City of London, give no warranty in that regard and accept no liability for any loss or damage incurred through the use of, or reliance upon, this report or the information contained herein. June 2006 © City of London PO Box 270, Guildhall London EC2P 2EJ www.cityoflondon.gov.uk/economicresearch Table of Contents Forewords ………………………………………………………………………………... 1 Executive Summary …………………………………………………………………….. 3 1. Introduction ………………………………………………………………………… 7 2. Overview of public equity and corporate debt markets in London and other financial centres …………………………………………………………………… 9 2.1 Equity markets ………………………………………………………………… 9 2.2 Corporate debt markets ………………………………………………………... 10 3. The cost of raising equity in London and other equity markets ……………… 12 3.1 Framework of analysis ……………………………………………………………….. 12 3.2 IPO costs in different markets ……………………………………………………… 17 3.3 Trading costs in the secondary market ……………………………………………. -
Implied Volatility Modeling
Implied Volatility Modeling Sarves Verma, Gunhan Mehmet Ertosun, Wei Wang, Benjamin Ambruster, Kay Giesecke I Introduction Although Black-Scholes formula is very popular among market practitioners, when applied to call and put options, it often reduces to a means of quoting options in terms of another parameter, the implied volatility. Further, the function σ BS TK ),(: ⎯⎯→ σ BS TK ),( t t ………………………………(1) is called the implied volatility surface. Two significant features of the surface is worth mentioning”: a) the non-flat profile of the surface which is often called the ‘smile’or the ‘skew’ suggests that the Black-Scholes formula is inefficient to price options b) the level of implied volatilities changes with time thus deforming it continuously. Since, the black- scholes model fails to model volatility, modeling implied volatility has become an active area of research. At present, volatility is modeled in primarily four different ways which are : a) The stochastic volatility model which assumes a stochastic nature of volatility [1]. The problem with this approach often lies in finding the market price of volatility risk which can’t be observed in the market. b) The deterministic volatility function (DVF) which assumes that volatility is a function of time alone and is completely deterministic [2,3]. This fails because as mentioned before the implied volatility surface changes with time continuously and is unpredictable at a given point of time. Ergo, the lattice model [2] & the Dupire approach [3] often fail[4] c) a factor based approach which assumes that implied volatility can be constructed by forming basis vectors. Further, one can use implied volatility as a mean reverting Ornstein-Ulhenbeck process for estimating implied volatility[5]. -
Uva-F-1274 Methods of Valuation for Mergers And
Graduate School of Business Administration UVA-F-1274 University of Virginia METHODS OF VALUATION FOR MERGERS AND ACQUISITIONS This note addresses the methods used to value companies in a merger and acquisitions (M&A) setting. It provides a detailed description of the discounted cash flow (DCF) approach and reviews other methods of valuation, such as book value, liquidation value, replacement cost, market value, trading multiples of peer firms, and comparable transaction multiples. Discounted Cash Flow Method Overview The discounted cash flow approach in an M&A setting attempts to determine the value of the company (or ‘enterprise’) by computing the present value of cash flows over the life of the company.1 Since a corporation is assumed to have infinite life, the analysis is broken into two parts: a forecast period and a terminal value. In the forecast period, explicit forecasts of free cash flow must be developed that incorporate the economic benefits and costs of the transaction. Ideally, the forecast period should equate with the interval in which the firm enjoys a competitive advantage (i.e., the circumstances where expected returns exceed required returns.) For most circumstances a forecast period of five or ten years is used. The value of the company derived from free cash flows arising after the forecast period is captured by a terminal value. Terminal value is estimated in the last year of the forecast period and capitalizes the present value of all future cash flows beyond the forecast period. The terminal region cash flows are projected under a steady state assumption that the firm enjoys no opportunities for abnormal growth or that expected returns equal required returns in this interval. -
Managed Futures and Long Volatility by Anders Kulp, Daniel Djupsjöbacka, Martin Estlander, Er Capital Management Research
Disclaimer: This article appeared in the AIMA Journal (Feb 2005), which is published by The Alternative Investment Management Association Limited (AIMA). No quotation or reproduction is permitted without the express written permission of The Alternative Investment Management Association Limited (AIMA) and the author. The content of this article does not necessarily reflect the opinions of the AIMA Membership and AIMA does not accept responsibility for any statements herein. Managed Futures and Long Volatility By Anders Kulp, Daniel Djupsjöbacka, Martin Estlander, er Capital Management Research Introduction and background The buyer of an option straddle pays the implied volatility to get exposure to realized volatility during the lifetime of the option straddle. Fung and Hsieh (1997b) found that the return of trend following strategies show option like characteristics, because the returns tend to be large and positive during the best and worst performing months of the world equity markets. Fung and Hsieh used lookback straddles to replicate a trend following strategy. However, the standard way to obtain exposure to volatility is to buy an at-the-money straddle. Here, we will use standard option straddles with a dynamic updating methodology and flexible maturity rollover rules to match the characteristics of a trend follower. The lookback straddle captures only one trend during its maturity, but with an effective systematic updating method the simple option straddle captures more than one trend. It is generally accepted that when implementing an options strategy, it is crucial to minimize trading, because the liquidity in the options markets are far from perfect. Compared to the lookback straddle model, the trading frequency for the simple straddle model is lower. -
White Paper Volatility: Instruments and Strategies
White Paper Volatility: Instruments and Strategies Clemens H. Glaffig Panathea Capital Partners GmbH & Co. KG, Freiburg, Germany July 30, 2019 This paper is for informational purposes only and is not intended to constitute an offer, advice, or recommendation in any way. Panathea assumes no responsibility for the content or completeness of the information contained in this document. Table of Contents 0. Introduction ......................................................................................................................................... 1 1. Ihe VIX Index .................................................................................................................................... 2 1.1 General Comments and Performance ......................................................................................... 2 What Does it mean to have a VIX of 20% .......................................................................... 2 A nerdy side note ................................................................................................................. 2 1.2 The Calculation of the VIX Index ............................................................................................. 4 1.3 Mathematical formalism: How to derive the VIX valuation formula ...................................... 5 1.4 VIX Futures .............................................................................................................................. 6 The Pricing of VIX Futures ................................................................................................ -
Futures & Options on the VIX® Index
Futures & Options on the VIX® Index Turn Volatility to Your Advantage U.S. Futures and Options The Cboe Volatility Index® (VIX® Index) is a leading measure of market expectations of near-term volatility conveyed by S&P 500 Index® (SPX) option prices. Since its introduction in 1993, the VIX® Index has been considered by many to be the world’s premier barometer of investor sentiment and market volatility. To learn more, visit cboe.com/VIX. VIX Futures and Options Strategies VIX futures and options have unique characteristics and behave differently than other financial-based commodity or equity products. Understanding these traits and their implications is important. VIX options and futures enable investors to trade volatility independent of the direction or the level of stock prices. Whether an investor’s outlook on the market is bullish, bearish or somewhere in-between, VIX futures and options can provide the ability to diversify a portfolio as well as hedge, mitigate or capitalize on broad market volatility. Portfolio Hedging One of the biggest risks to an equity portfolio is a broad market decline. The VIX Index has had a historically strong inverse relationship with the S&P 500® Index. Consequently, a long exposure to volatility may offset an adverse impact of falling stock prices. Market participants should consider the time frame and characteristics associated with VIX futures and options to determine the utility of such a hedge. Risk Premium Yield Over long periods, index options have tended to price in slightly more uncertainty than the market ultimately realizes. Specifically, the expected volatility implied by SPX option prices tends to trade at a premium relative to subsequent realized volatility in the S&P 500 Index. -
Option Prices Under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities∗
Option Prices under Bayesian Learning: Implied Volatility Dynamics and Predictive Densities∗ Massimo Guidolin† Allan Timmermann University of Virginia University of California, San Diego JEL codes: G12, D83. Abstract This paper shows that many of the empirical biases of the Black and Scholes option pricing model can be explained by Bayesian learning effects. In the context of an equilibrium model where dividend news evolve on a binomial lattice with unknown but recursively updated probabilities we derive closed-form pricing formulas for European options. Learning is found to generate asymmetric skews in the implied volatility surface and systematic patterns in the term structure of option prices. Data on S&P 500 index option prices is used to back out the parameters of the underlying learning process and to predict the evolution in the cross-section of option prices. The proposed model leads to lower out-of- sample forecast errors and smaller hedging errors than a variety of alternative option pricing models, including Black-Scholes and a GARCH model. ∗We wish to thank four anonymous referees for their extensive and thoughtful comments that greatly improved the paper. We also thank Alexander David, Jos´e Campa, Bernard Dumas, Wake Epps, Stewart Hodges, Claudio Michelacci, Enrique Sentana and seminar participants at Bocconi University, CEMFI, University of Copenhagen, Econometric Society World Congress in Seattle, August 2000, the North American Summer meetings of the Econometric Society in College Park, June 2001, the European Finance Association meetings in Barcelona, August 2001, Federal Reserve Bank of St. Louis, INSEAD, McGill, UCSD, Universit´edeMontreal,andUniversity of Virginia for discussions and helpful comments. -
The Cost of Capital: the Swiss Army Knife of Finance
The Cost of Capital: The Swiss Army Knife of Finance Aswath Damodaran April 2016 Abstract There is no number in finance that is used in more places or in more contexts than the cost of capital. In corporate finance, it is the hurdle rate on investments, an optimizing tool for capital structure and a divining rod for dividends. In valuation, it plays the role of discount rate in discounted cash flow valuation and as a control variable, when pricing assets. Notwithstanding its wide use, or perhaps because of it, the cost of capital is also widely misunderstood, misestimated and misused. In this paper, I look at what the cost of capital is trying to measure and how best to avoid the pitfalls that I see in practice. What is the cost of capital? If you asked a dozen investors, managers or analysts this question, you are likely to get a dozen different answers. Some will describe it as the cost of raising funding for a business, from debt and equity. Others will argue that it is the hurdle rate used by businesses to determine whether to invest in new projects. A few may use it as a metric that drives whether to return cash, and if yes, how much to return to investors in dividends and stock buybacks. Many will point to it as the discount rate that is used when valuing an entire business and some may characterize it as an optimizing tool for the deciding on the right mix of debt and equity for a company. They are all right and that is the reason the cost of capital is the Swiss Army knife of Finance, much used and oftentimes misused. -
The Impact of Implied Volatility Fluctuations on Vertical Spread Option Strategies: the Case of WTI Crude Oil Market
energies Article The Impact of Implied Volatility Fluctuations on Vertical Spread Option Strategies: The Case of WTI Crude Oil Market Bartosz Łamasz * and Natalia Iwaszczuk Faculty of Management, AGH University of Science and Technology, 30-059 Cracow, Poland; [email protected] * Correspondence: [email protected]; Tel.: +48-696-668-417 Received: 31 July 2020; Accepted: 7 October 2020; Published: 13 October 2020 Abstract: This paper aims to analyze the impact of implied volatility on the costs, break-even points (BEPs), and the final results of the vertical spread option strategies (vertical spreads). We considered two main groups of vertical spreads: with limited and unlimited profits. The strategy with limited profits was divided into net credit spread and net debit spread. The analysis takes into account West Texas Intermediate (WTI) crude oil options listed on New York Mercantile Exchange (NYMEX) from 17 November 2008 to 15 April 2020. Our findings suggest that the unlimited vertical spreads were executed with profits less frequently than the limited vertical spreads in each of the considered categories of implied volatility. Nonetheless, the advantage of unlimited strategies was observed for substantial oil price movements (above 10%) when the rates of return on these strategies were higher than for limited strategies. With small price movements (lower than 5%), the net credit spread strategies were by far the best choice and generated profits in the widest price ranges in each category of implied volatility. This study bridges the gap between option strategies trading, implied volatility and WTI crude oil market. The obtained results may be a source of information in hedging against oil price fluctuations. -
The Cost of Capital—Everything an Actuary Needs to Know
RECORD, Volume 25, No. 3* San Francisco Annual Meeting October 17-20, 1999 Session 32PD The Cost of Capital—Everything an Actuary Needs to Know Track: Financial Reporting Key Words: Financial Management, Financial Reporting, Risk-Based Capital Moderator: MICHAEL V. ECKMAN Panelists: MICHAEL V. ECKMAN FRANCIS DE REGNAUCOURT Recorder: MICHAEL V. ECKMAN Summary: This panel covers the determination and use of the cost of capital for both stock and mutual companies. Topics covered include: · How to measure the cost of capital · Use of cost of capital in choosing among options or setting an enterprise's direction · Should different costs of capital be used for different purposes? · Options for financing and the effect on cost · Maximizing return by proper mix of options · Example of an acquisition · Appropriate amount of capital · International perspective Mr. Michael V. Eckman: Francis de Regnaucourt works for Ernst and Young. He's a senior consulting actuary in the New York office. He has six years of experience in a bond rating agency, is a Chartered Financial Analyst, a Fellow of the CIA, and a self-described retired Canadian and actuary. I am the appointed actuary with ReliaStar Financial Corporation in Minneapolis. I have some experience in product pricing, valuation, and acquisitions. I will be focusing on the use and measurement of cost of capital in a stock life insurance and holding company. First, I will give my working definition of the cost of capital. Cost of capital is the burden a product, strategy, or enterprise must bear in order to hold required capital sufficient for risks assumed. -
VIX Futures As a Market Timing Indicator
Journal of Risk and Financial Management Article VIX Futures as a Market Timing Indicator Athanasios P. Fassas 1 and Nikolas Hourvouliades 2,* 1 Department of Accounting and Finance, University of Thessaly, Larissa 41110, Greece 2 Department of Business Studies, American College of Thessaloniki, Thessaloniki 55535, Greece * Correspondence: [email protected]; Tel.: +30-2310-398385 Received: 10 June 2019; Accepted: 28 June 2019; Published: 1 July 2019 Abstract: Our work relates to the literature supporting that the VIX also mirrors investor sentiment and, thus, contains useful information regarding future S&P500 returns. The objective of this empirical analysis is to verify if the shape of the volatility futures term structure has signaling effects regarding future equity price movements, as several investors believe. Our findings generally support the hypothesis that the VIX term structure can be employed as a contrarian market timing indicator. The empirical analysis of this study has important practical implications for financial market practitioners, as it shows that they can use the VIX futures term structure not only as a proxy of market expectations on forward volatility, but also as a stock market timing tool. Keywords: VIX futures; volatility term structure; future equity returns; S&P500 1. Introduction A fundamental principle of finance is the positive expected return-risk trade-off. In this paper, we examine the dynamic dependencies between future equity returns and the term structure of VIX futures, i.e., the curve that connects daily settlement prices of individual VIX futures contracts to maturities across time. This study extends the VIX futures-related literature by testing the market timing ability of the VIX futures term structure regarding future stock movements. -
Three Discount Methods for Valuing Projects and the Required Return on Equity
Three discount methods for valuing projects and the required return on equity Fecha de recepción: 26/04/2011 Fecha de aceptación: 29/08/2011 Marc B.J. Schauten Erasmus School of Economics [email protected] Abstract In this paper we discuss the required return on equity for a simple project with a finite life. To determine a project’s cost of equity, it is quite common to use Modigliani and Miller’s Proposition II (1963). However, if the assumptions of MM do not hold, Proposition II will lead to wrong required returns and project values. This paper gives an example of how the cost of equity should be determined in order to obtain correct valua- tions. The methods we apply are the Adjusted Present Value method, the Cash Flow to Equity method and the WACC me- thod. Keywords: Proposition II, net present value, APV, CFE, WACC. JEL classification: G12; G31; G32; H43 Contaduría y Administración 58 (1), enero-marzo 2013: 63-85 Marc B.J. Schauten Tres métodos de descuento para valuar proyectos y la tasa requerida de ren- dimiento para el capital accionario Resumen En este artículo analizamos el rendimiento requerido para el capital accionario en un pro- yecto simple con vida finita. Es muy común el uso de la Proposición II de Modigliani y Miller (1963) para determinar el costo del capital accionario de un proyecto. No obstante, si los supuestos de MM no se mantienen, la Proposición II llevará a rendimientos requeri- dos y valores del proyecto erróneos. Este trabajo brinda un ejemplo de cómo el costo del capital accionario puede determinarse de forma que se obtengan valuaciones correctas.