...1) Using Excel’s standard deviations function to calculate the variability of the stock returns of California REIT, Brown Group, and the Vanguard Index 500. Standard Deviation Vanguard 500 4.61% California REIT 9.23% Brown Group 8.17% Brown Group and California REIT stock returns both have large variability compared to the Vanguard 500. Brown Groups variability is substantially larger that of the Vanguard 500, and California REIT variability is even larger as it is double that of the Vanguard 500. While both Brown Group, and California REIT are more risky then the Vanguard 500, California REIT is the most risking of all as the variability of the stock return is the largest of the three. 2) To compare the two portfolio options Beta is offering portfolio 1 containing 99% of equity funds invested in Vanguard 500, and 1% in California REIT, and portfolio 2 containing 99% Vanguard 500, and 1% in Brown Group. Using Excel function’s to find standard deviations and Excel functions to find covariance. First we calculated the monthly return of portfoilio1, and portfolio 2. After doing that we used Excel function standard deviation to find the variance of each portfolio. Standard Deviation Portfolio 1 4.57% Portfolio 2 4.61% Looking at the two portfolios it is apparent that the portfolio containing Brown Group is riskier, because it adds more variability to the portfolio. This contradicts the answer in question...
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...Market Volatility: Measures and Results Gary E. Mullins, Ph.D. University of Wisconsin - Stevens Point | | IntroductionVirtually everyone who is interested in financial markets seems to agree on two things: that markets are now more volatile than ever, and that volatility causes many problems. Let's look at some recent and not-so-recent articles concerning volatility. This week turned out to be slower than expected on the IPO market, as intense volatility on U.S. exchanges prompted many companies to put off much-anticipated debuts. I am writing to you today to address my concerns about trading in a fast market, a current issue of extreme importance to me. I want to give you my perspective and let you know the steps we at Schwab are taking to support investors during this time of market volatility. In recent months, there has been a marked increase in price volatility and volume in many stocks, particularly of companies that sell products or services via the Internet (Internet issuers). In the above quotes, there are two implicit assumptions: that volatility is higher now than it has been in the past, and that this volatility is somehow bad. In the first article, it assumes that (obviously) increased volatility has caused firms to delay their Initial Public Offerings (IPO's). Next, Schwab believes that investors need special support because of the high volatility inherent in today's market. Finally, Barrett appears to be more concerned about volatility for Internet...
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...yield to maturity as risk-free rate. Data are from Yahoo Finance. 2) Calculating preliminary statistics Using the data, the daily log return was calculated Daily log return = ln (△close pricei+1/close pricei) We assumed that the stock price follows Geometric Brownian Motion with constant mean[pic] and standard deviation[pic]. Therefore, the return of the stock was assumed to be normally distributed with mean [pic] and standard deviation [pic]. So we picked up n-days samples of stock prices and estimated the annualized volatility as follows. Next, we calculated the recent historical volatility. Here, n denotes the number of observations (business day), Si denotes the stock price at the end of the i-th interval (i=0, 1, … , n), [pic] denotes the length of the time interval in years (For daily observations, 1/252(business day)) [pic][pic][pic] [pic] = [pic] Estimated daily volatility S = 0.01042889 Estimated annualized volatility [pic] = 0.1655535 Continuous dividend yield (calculated from the notification) q = 0.028 (Dividend payment= $0.57/share...
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...Taylor & Francis Group, LLC ISSN: 0747-4938 print/1532-4168 online DOI: 10.1080/07474930701853509 REALIZED VOLATILITY: A REVIEW Michael McAleer1 and Marcelo C. Medeiros2 2 School of Economics and Commerce, University of Western Australia Department of Economics, Pontifical Catholic University of Rio de Janeiro, Rio de Janeiro, Brasil 1 Downloaded At: 15:53 5 September 2008 This article reviews the exciting and rapidly expanding literature on realized volatility. After presenting a general univariate framework for estimating realized volatilities, a simple discrete time model is presented in order to motivate the main results. A continuous time specification provides the theoretical foundation for the main results in this literature. Cases with and without microstructure noise are considered, and it is shown how microstructure noise can cause severe problems in terms of consistent estimation of the daily realized volatility. Independent and dependent noise processes are examined. The most important methods for providing consistent estimators are presented, and a critical exposition of different techniques is given. The finite sample properties are discussed in comparison with their asymptotic properties. A multivariate model is presented to discuss estimation of the realized covariances. Various issues relating to modelling and forecasting realized volatilities are considered. The main empirical findings using univariate and multivariate methods are summarized. Keywords...
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...NBER WORKING PAPER SERIES FINANCIAL RISK MEASUREMENT FOR FINANCIAL RISK MANAGEMENT Torben G. Andersen Tim Bollerslev Peter F. Christoffersen Francis X. Diebold Working Paper 18084 http://www.nber.org/papers/w18084 NATIONAL BUREAU OF ECONOMIC RESEARCH 1050 Massachusetts Avenue Cambridge, MA 02138 May 2012 Forthcoming in Handbook of the Economics of Finance, Volume 2, North Holland, an imprint of Elsevier. For helpful comments we thank Hal Cole and Dongho Song. For research support, Andersen, Bollerslev and Diebold thank the National Science Foundation (U.S.), and Christoffersen thanks the Social Sciences and Humanities Research Council (Canada). We appreciate support from CREATES funded by the Danish National Science Foundation. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research. NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official NBER publications. © 2012 by Torben G. Andersen, Tim Bollerslev, Peter F. Christoffersen, and Francis X. Diebold. All rights reserved. Short sections of text, not to exceed two paragraphs, may be quoted without explicit permission provided that full credit, including © notice, is given to the source. Financial Risk Measurement for Financial Risk Management Torben G. Andersen, Tim Bollerslev, Peter F. Christoffersen, and...
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...0.1 = 0.05379/0.1 = 0.5379 N(d1) = 0.70467695 d2 = 0.5379 – 10%*√1 = 0.5379 – 0.1 = 0.4379 N(d2) = 0.66927061 e-rcT = e-0.04879*1 = 0.952381 C0 = 50*0.70467695 – 50*0.952381*0.66927061 = 35.2338475 – 31.8700306 = 3.3638 2. Solve the value of the above one-year American call using CBOE Options Toolbox [pic] 3. Noting the Greek values: How will the call value change for a. 1% change in interest rate [pic] b. $1 increases in the stock price [pic] c. Reduction of one-day in maturity [pic] 4. All options are European and the stock does not pay a dividend. Which option is relatively more expensive? Explain. (Hint: Compute implied volatility). a. S = $50, C (X=$60) =$14 [pic] b. S = $50, C (X=$65) =$10 [pic] Option (a) is relatively more expensive because the higher Implied...
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...(2002) 45–60 INSTITUTE O F PHYSICS PUBLISHING RE S E A R C H PA P E R quant.iop.org Dynamics of implied volatility surfaces Rama Cont1,3 and Jos´ da Fonseca2 e Centre de Math´ matiques Appliqu´ es, Ecole Polytechnique, F-91128 e e Palaiseau, France 2 Ecole Superieure d’Ingenierie Leonard de Vinci, F-92916 Paris La D´ fense, e France E-mail: Rama.Cont@polytechnique.fr and jose.da fonseca@devinci.fr Received 20 September 2001 Published 4 February 2002 Online at stacks.iop.org/Quant/2/45 1 Abstract The prices of index options at a given date are usually represented via the corresponding implied volatility surface, presenting skew/smile features and term structure which several models have attempted to reproduce. However, the implied volatility surface also changes dynamically over time in a way that is not taken into account by current modelling approaches, giving rise to ‘Vega’ risk in option portfolios. Using time series of option prices on the SP500 and FTSE indices, we study the deformation of this surface and show that it may be represented as a randomly fluctuating surface driven by a small number of orthogonal random factors. We identify and interpret the shape of each of these factors, study their dynamics and their correlation with the underlying index. Our approach is based on a Karhunen–Lo` ve e decomposition of the daily variations of implied volatilities obtained from market data. A simple factor model compatible with the empirical observations is proposed. We...
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...conditional heteroskedasticity, the implied volatility smile, and the variance risk premium Louis H. Ederington a,⇑, Wei Guan b a b Finance Division, Michael F. Price College of Business, University of Oklahoma, 205A Adams Hall, Norman, OK 73019, USA College of Business, University of South Florida St. Petersburg, 140 Seventh Avenue South, St. Petersburg, FL 33701, USA a r t i c l e i n f o a b s t r a c t This paper estimates how the shape of the implied volatility smile and the size of the variance risk premium relate to parameters of GARCH-type time-series models measuring how conditional volatility responds to return shocks. Markets in which return shocks lead to large increases in conditional volatility tend to have larger variance risk premia than markets in which the impact on conditional volatility is slight. Markets in which negative (positive) return shocks lead to larger increases in future volatility than positive (negative) return shocks tend to have downward (upward) sloping implied volatility smiles. Also, differences in how volatility responds to return shocks as measured by GARCH-type models explain much, but not all, of the variations in excess kurtosis and multi-period skewness across different markets. Ó 2013 Elsevier B.V. All rights reserved. Article history: Received 11 October 2012 Accepted 14 April 2013 Available online 17 May 2013 JEL classification: G13 G10 G12 Keywords: Implied volatility Volatility smile Variance risk premium GARCH Conditional...
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...O N R E G A R D I N G F O R W A R D - L O O K I N G S T A T E M E N T S , R I S K S A N D A S S U M P T I O N S This MD&A includes “forward-looking information” within the meaning of applicable securities laws and assumptions concerning, among other things our business, its operations and its financial performance and condition approved by management on the date of this MD&A. This forward-looking information and these assumptions include, but are not limited to, statements with respect to our objectives and strategies to achieve those objectives, as well as statements with respect to our beliefs, plans, expectations, anticipations, estimates or intentions. This forward-looking information also includes, but is not limited to, guidance and forecasts relating to revenue, adjusted operating profit, property, plant and equipment expenditures, cash income tax payments, free cash flow, dividend payments, expected growth in subscribers and the services to which they subscribe, the cost of acquiring subscribers and the deployment of new services, and all other statements that are not historical facts. The words “could”, “expect”, “may”, “anticipate”, “assume”, “believe”, “intend”, “estimate”, “plan”, “project”, “guidance”, and similar expressions are intended to identify statements containing forward-looking information, although not all forward-looking statements include such words. Conclusions, forecasts and projections set out in forward-looking information...
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...Ibrahim Nasser Khatatbeh May, 2013 Q1: Explain how the option pricing formula developed by black and scholes can be used for common stock and bond valuation. Include in your discussion the consequences of using variance applied over the option instead of actual variance. Its generally known that Black and Scholes model became a standard in option pricing methods , with almost everything from corporate liabilities and debt instruments can be viewed as option (except some complicated instruments), we can modify the fundamental formula in order to fit the specifications of the instrument that will be valued. An argument done by Black and Scholes which was based on the past proposition of Miller and Modigliani a well as assuming some ideal conditions, States that value of the firm is a sum of total value of debt plus the total value of common stock. As well as the fact that in the absence of taxes, the value of the firm is independent of its leverage and the change of debt has no effect on the firm value. V = E + Dm V: value of the firm. E: shareholders right (common stock values). Dm: market value of the debt. As the above equation impose that Equity (common stock values) can be viewed as a call option on the firm value (due to the shareholders limited liability and with consideration that firm debt can be represent as a zero-coupon bond), where exercising the option means that equity holders buy the firm at the face value of debt (which is in this case will be...
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...Article Rebuttal BCOM/275 1/27/2014 Article Rebuttal “A well-regulated militia, being necessary to the security of a free state, the right of the people to keep and bear arms, shall not be infringed” (U.S. Const., am 2). Since the ratification of the Bill of Rights, including the Second Amendment in 1791, our right to bear arms has been under attack. This article rebuttal will focus on an USA Today article titled “Epidemic: Guns kill twice as many kids as cancer does.” This article attempts to use biased statistics to provoke demand for further restrictions against our second amendment right. In the article, the author provides some staggering statistics which he uses to substantiate the claim “guns kill”. Here are a few; “guns still kill twice as many children and young people than cancer, five times as many than heart disease and fifteen times more than infection, according to the New England Journal of Medicine.” The article goes on to state “in 2010, 15,576 children and teenagers were injured by firearms – three times more than the number of U.S. soldiers injured in the war in Afghanistan, according to the defense fund.” On the surface, these statistics are alarming. Beyond the statistics, the article makes the claim “guns kill”. The remainder of this rebuttal will put into perspective the statistical claims on gun related deaths among youth, as well, debunk the implication “guns kill”. First, let’s place a level of perspective on the statistical...
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...for their invaluable direction, patience, and guidance throughout this entire process. Abstract The goal of this paper is to investigate the forecasting ability of the Dynamic Conditional Correlation Generalized Autoregressive Conditional Heteroskedasticity (DCC-GARCH). We estimate the DCC’s forecasting ability relative to unconditional volatility in three equity-based crashes: the S&L Crisis, the Dot-Com Boom/Crash, and the recent Credit Crisis. The assets we use are the S&P 500 index, 10-Year US Treasury bonds, Moody’s A Industrial bonds, and the Dollar/Yen exchange rate. Our results suggest that the choice of asset pair may be a determining factor in the forecasting ability of the DCC-GARCH model. I. Introduction Many of today’s key financial applications, including asset pricing, capital allocation, risk management, and portfolio hedging, are heavily dependent on accurate estimates and well-founded forecasts of asset return volatility and correlation between assets. Although volatility and correlation forecasting are both important, however, existing literature has dealt more closely with the performance of volatility models – only very recently has the issue of correlation estimation and forecasting begun to receive extensive investigation and analysis. The goal of this paper is to extend research that has been undertaken regarding the forecasting ability of one specific correlation model, the Dynamic...
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...Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support. Ernst 1. & whinney never issued an audit opinion on the financial statements of ZZZZ Best; however, Ernst & Whinney did issue a review report on the companys quarterly statements for the three months ending July 31, 1986. How does a review differ from an audit, particularly in terms of the level of assurance implied by the auditors report ? Ernst & Whinney resigned as ZZZZ Bests auditor on June 2, 1987, following a series of disturbing events that caused the firm to question the integrity of M inkow and his associates. First, Ernst & Whinney was alarmed by a Los Angeles Times article in mid-May 1987 that revealed Minkow had been i nvolved in a string of credit card forgeries as a teenager. Second, on May 28, 1987, ZZZZ Best issued a press release, without consulting or notifying Ernst & Whinney, that reported record profits and revenues. The purpose of this press release was to restore in vestors confidence in the companyconfidence t hat had been shaken by the damaging Los Angeles Times story. Third, and most important, on May 29, Ernst & Whinney auditors discovered evidence supporting allegations made several weeks earlier by a third party informant t hat ZZZZ Bests insurance restoration business was fictitious. The informant had contacted Ernst & Whinney in April 1987 and asked for $25...
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...INTRODUCTION a new business model. We do accept that the degree of change in the aerospace industrial system may be less evident at the technological pinnacle of this world — the high performance UCAV. But, even here, there are likely to be challenges to conventional attitudes and processes. We further conclude that despite movement on the collabo- rative front, Europe could still struggle to make headway in the market unless industry is able to embrace the new ways of doing business implied by the UAS transformation. This includes the need to encourage new entrants as well as adopting a full systems approach to the market, offering an integrated package of hardware and services to a range of civil and military customers. In this respect, the paper urges the rapid adoption and implementation of the June 2013 EU Roadmap for the integration of UAS operations into European airspace. The Revolution in Military Affairs — these days often known as military transformation — with its emphasis on network centric warfare and exotic weapons systems, has threat- ened a comparable revolution in defence industrial affairs. The proposition is that the fundamental changes in defence technology implied by military transformation will challenge the existing structure of defence companies, encourage new entrants and new combinations of players, especially from the wider civilian high technology community to enter the defence business. Yet a...
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...model for stock price dynamics and option pricing, which not only has the same analyticity as log-normal and Black-Scholes model, but can also capture and explain all the main puzzles and phenomenons arising from empirical stock and option markets which log-normal and Black-Scholes model fail to explain. In addition, this model and its parameters have clear economic interpretations. Large sample empirical calibration and tests are performed and show strong empirical consistency with our model’s assumption and implication. Immediate applications on risk management, equity and option evaluation and trading, etc are also presented. Keywords: Nonlinear model, Random walk, Stock price, Option pricing, Default risk, Realized volatility, Local volatility, Volatility skew, EGARCH. This paper is self-funded and self-motivated. The author is currently working as a quantitative analyst at J.P. Morgan Chase & Co. All errors belong to the author. Email: henry.na.pang@jpmchase.com or hdpang@gmail.com. ∗ 1 Electronic copy available at: http://ssrn.com/abstract=1374688 2 Huadong(Henry) Pang/J.P. Morgan Chase & Co. 1. Introduction The well-known log-normal model for stock price was first proposed by Louis Bachelier (1870-1946) and published in his doctoral thesis at 1900. His “theory of speculation” (Theorie de la Speculation, see Bachelier(1900)) was discounted by none other than Henri Poincare, observing that “Mr. Bachelier has evidenced an original and precise mind [but]...
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