An Effective Way for Teaching the Arbitrage Pricing Theory
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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). -
Understanding the Risks of Smart Beta and the Need for Smart Alpha
UNDERSTANDING THE RISKS OF SMART BETA, AND THE NEED FOR SMART ALPHA February 2015 UNCORRELATED ANSWERS® Key Ideas Richard Yasenchak, CFA Senior Managing Director, Head of Client Portfolio Management There has been a proliferation of smart-beta strategies the past several years. According to Morningstar, asset flows into smart-beta offerings have been considerable and there are now literally thousands of such products, all offering Phillip Whitman, PhD a systematic but ‘different’ equity exposure from that offered by traditional capitalization-weighted indices. During the five years ending December 31, 2014 assets under management (AUM) of smart-beta ETFs grew by 320%; for the same period, index funds experienced AUM growth of 235% (Figure 1 on the following page). Smart beta has also become the media darling of the financial press, who often position these strategies as the answer to every investor’s investing prayers. So what is smart beta; what are its risks; and why should it matter to investors? Is there an alternative strategy that might help investors meet their investing objectives over time? These questions and more will be answered in this paper. This page is intentionally left blank. Defining smart beta and its smart-beta strategies is that they do not hold the cap-weighted market index; instead they re-weight the index based on different intended use factors such as those mentioned previously, and are therefore not The intended use of smart-beta strategies is to mitigate exposure buy-and-hold strategies like a cap-weighted index. to undesirable risk factors or to gain a potential benefit by increasing exposure to desirable risk factors resulting from a Exposure risk tactical or strategic view on the market. -
Low-Beta Strategies
A Service of Leibniz-Informationszentrum econstor Wirtschaft Leibniz Information Centre Make Your Publications Visible. zbw for Economics Korn, Olaf; Kuntz, Laura-Chloé Working Paper Low-beta strategies CFR Working Paper, No. 15-17 [rev.] Provided in Cooperation with: Centre for Financial Research (CFR), University of Cologne Suggested Citation: Korn, Olaf; Kuntz, Laura-Chloé (2017) : Low-beta strategies, CFR Working Paper, No. 15-17 [rev.], University of Cologne, Centre for Financial Research (CFR), Cologne This Version is available at: http://hdl.handle.net/10419/158007 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 von diesen Nutzungsbedingungen die in der dort Content Licence (especially Creative Commons Licences), you genannten Lizenz gewährten -
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 -
Arbitrage Pricing Theory∗
ARBITRAGE PRICING THEORY∗ Gur Huberman Zhenyu Wang† August 15, 2005 Abstract Focusing on asset returns governed by a factor structure, the APT is a one-period model, in which preclusion of arbitrage over static portfolios of these assets leads to a linear relation between the expected return and its covariance with the factors. The APT, however, does not preclude arbitrage over dynamic portfolios. Consequently, applying the model to evaluate managed portfolios contradicts the no-arbitrage spirit of the model. An empirical test of the APT entails a procedure to identify features of the underlying factor structure rather than merely a collection of mean-variance efficient factor portfolios that satisfies the linear relation. Keywords: arbitrage; asset pricing model; factor model. ∗S. N. Durlauf and L. E. Blume, The New Palgrave Dictionary of Economics, forthcoming, Palgrave Macmillan, reproduced with permission of Palgrave Macmillan. This article is taken from the authors’ original manuscript and has not been reviewed or edited. The definitive published version of this extract may be found in the complete The New Palgrave Dictionary of Economics in print and online, forthcoming. †Huberman is at Columbia University. Wang is at the Federal Reserve Bank of New York and the McCombs School of Business in the University of Texas at Austin. The views stated here are those of the authors and do not necessarily reflect the views of the Federal Reserve Bank of New York or the Federal Reserve System. Introduction The Arbitrage Pricing Theory (APT) was developed primarily by Ross (1976a, 1976b). It is a one-period model in which every investor believes that the stochastic properties of returns of capital assets are consistent with a factor structure. -
A Financially Justifiable and Practically Implementable Approach to Coherent Stress Testing
———————— An EDHEC-Risk Institute Working Paper A Financially Justifiable and Practically Implementable Approach to Coherent Stress Testing September 2018 ———————— 1. Introduction and Motivation 5 2. Bayesian Nets for Stress Testing 10 3. What Constitutes a Stress Scenario 13 4. The Goal 15 5. Definition of the Variables 17 6. Notation 19 7. The Consistency and Continuity Requirements 21 8. Assumptions 23 9. Obtaining the Distribution of Representative Market Indices. 25 10. Limitations and Weaknesses of the Approach 29 11. From Representative to Granular Market Indices 31 12. Some Practical Examples 35 13. Simple Extensions and Generalisations 41 Portfolio weights 14. Conclusions 43 back to their original References weights, can be a 45 source of additional About EDHEC-Risk Institute performance. 48 EDHEC-Risk Institute Publications and Position Papers (2017-2019) 53 ›2 Printed in France, July 2019. Copyright› 2EDHEC 2019. The opinions expressed in this study are those of the authors and do not necessarily reflect those of EDHEC Business School. Abstract ———————— We present an approach to stress testing that is both practically implementable and solidly rooted in well-established financial theory. We present our results in a Bayesian-net context, but the approach can be extended to different settings. We show i) how the consistency and continuity conditions are satisfied; ii) how the result of a scenario can be consistently cascaded from a small number of macrofinancial variables to the constituents of a granular portfolio; and iii) how an approximate but robust estimate of the likelihood of a given scenario can be estimated. This is particularly important for regulatory and capital-adequacy applications. -
Expected Stock Returns and Volatility Kenneth R
University of Pennsylvania ScholarlyCommons Finance Papers Wharton Faculty Research 1987 Expected Stock Returns and Volatility Kenneth R. French G. William Schwert Robert F. Stambaugh University of Pennsylvania Follow this and additional works at: http://repository.upenn.edu/fnce_papers Part of the Finance Commons, and the Finance and Financial Management Commons Recommended Citation French, K. R., Schwert, G., & Stambaugh, R. F. (1987). Expected Stock Returns and Volatility. Journal of Financial Economics, 19 (1), 3-29. http://dx.doi.org/10.1016/0304-405X(87)90026-2 At the time of publication, author Robert F. Stambaugh was affiliated with the University of Chicago. Currently, he is a faculty member at the Wharton School at the University of Pennsylvania. This paper is posted at ScholarlyCommons. http://repository.upenn.edu/fnce_papers/363 For more information, please contact [email protected]. Expected Stock Returns and Volatility Abstract This paper examines the relation between stock returns and stock market volatility. We find ve idence that the expected market risk premium (the expected return on a stock portfolio minus the Treasury bill yield) is positively related to the predictable volatility of stock returns. There is also evidence that unexpected stock market returns are negatively related to the unexpected change in the volatility of stock returns. This negative relation provides indirect evidence of a positive relation between expected risk premiums and volatility. Disciplines Finance | Finance and Financial Management Comments At the time of publication, author Robert F. Stambaugh was affiliated with the University of Chicago. Currently, he is a faculty member at the Wharton School at the University of Pennsylvania. -
Understanding Alpha Versus Beta in High Yield Bond Investing
PERITUS ASSET MANAGEMENT, LLC Market Commentary Independent Credit Research – Leveraged Finance – July 2012 Understanding Alpha versus Beta in High Yield Bond Investing Investors have come to recognize that there is a secular change occurring in financial markets. After the 2008 meltdown, we have watched equities stage an impressive rally off the bottom, only to peter out. There is no conviction and valuations are once again stretched given the lack of growth as the world economy remains on shaky ground. In another one of our writings (“High Yield Bonds versus Equities”), we discussed our belief that U.S. businesses would plod along, but valuations would continue their march toward the lower end of their historical range. So far, this looks like the correct call. Europe still hasn’t been fixed, the China miracle is slowing and, perhaps, the commodity supercycle is also in the later innings. The amount of debt assumed by the developed world is unsustainable so deleveraging began a few years ago. These are not short or pleasant cycles and both governments and individuals will be grumpy participants in this event. It simply means that economic growth will be subdued for years to come. I have never really been able to understand economic growth rates that are significantly ahead of the population growth anyway…oh yeah, the productivity miracle. I have written chapter and verse on the history of financial markets and where returns have come from: yield. Anyone with access to the internet can verify that dividends, dividend growth and dividend re-investment are what have driven stock returns over the decades. -
Arbitrage and Price Revelation with Asymmetric Information And
Journal of Mathematical Economics 38 (2002) 393–410 Arbitrage and price revelation with asymmetric information and incomplete markets Bernard Cornet a,∗, Lionel De Boisdeffre a,b a CERMSEM, Université de Paris 1, 106–112 boulevard de l’Hˆopital, 75647 Paris Cedex 13, France b Cambridge University, Cambridge, UK Received 5 January 2002; received in revised form 7 September 2002; accepted 10 September 2002 Abstract This paper deals with the issue of arbitrage with differential information and incomplete financial markets, with a focus on information that no-arbitrage asset prices can reveal. Time and uncertainty are represented by two periods and a finite set S of states of nature, one of which will prevail at the second period. Agents may operate limited financial transfers across periods and states via finitely many nominal assets. Each agent i has a private information about which state will prevail at the second period; this information is represented by a subset Si of S. Agents receive no wrong information in the sense that the “true state” belongs to the “pooled information” set ∩iSi, hence assumed to be non-empty. Our analysis is two-fold. We first extend the classical symmetric information analysis to the asym- metric setting, via a concept of no-arbitrage price. Second, we study how such no-arbitrage prices convey information to agents in a decentralized way. The main difference between the symmetric and the asymmetric settings stems from the fact that a classical no-arbitrage asset price (common to every agent) always exists in the first case, but no longer in the asymmetric one, thus allowing arbitrage opportunities. -
Estimating Value at Risk
Estimating Value at Risk Eric Marsden <[email protected]> Do you know how risky your bank is? Learning objectives 1 Understand measures of financial risk, including Value at Risk 2 Understand the impact of correlated risks 3 Know how to use copulas to sample from a multivariate probability distribution, including correlation The information presented here is pedagogical in nature and does not constitute investment advice! Methods used here can also be applied to model natural hazards 2 / 41 Warmup. Before reading this material, we suggest you consult the following associated slides: ▷ Modelling correlations using Python ▷ Statistical modelling with Python Available from risk-engineering.org 3 / 41 Risk in finance There are 1011 stars in the galaxy. That used to be a huge number. But it’s only a hundred billion. It’s less than the national deficit! We used to call them astronomical numbers. ‘‘ Now we should call them economical numbers. — Richard Feynman 4 / 41 Terminology in finance Names of some instruments used in finance: ▷ A bond issued by a company or a government is just a loan • bond buyer lends money to bond issuer • issuer will return money plus some interest when the bond matures ▷ A stock gives you (a small fraction of) ownership in a “listed company” • a stock has a price, and can be bought and sold on the stock market ▷ A future is a promise to do a transaction at a later date • refers to some “underlying” product which will be bought or sold at a later time • example: farmer can sell her crop before harvest, -
Risk, Return, and Diversification a Reading Prepared by Pamela Peterson Drake
Risk, return, and diversification A reading prepared by Pamela Peterson Drake O U T L I N E 1. Introduction 2. Diversification and risk 3. Modern portfolio theory 4. Asset pricing models 5. Summary 1. Introduction As managers, we rarely consider investing in only one project at one time. Small businesses and large corporations alike can be viewed as a collection of different investments, made at different points in time. We refer to a collection of investments as a portfolio. While we usually think of a portfolio as a collection of securities (stocks and bonds), we can also think of a business in much the same way -- a portfolios of assets such as buildings, inventories, trademarks, patents, et cetera. As managers, we are concerned about the overall risk of the company's portfolio of assets. Suppose you invested in two assets, Thing One and Thing Two, having the following returns over the next year: Asset Return Thing One 20% Thing Two 8% Suppose we invest equal amounts, say $10,000, in each asset for one year. At the end of the year we will have $10,000 (1 + 0.20) = $12,000 from Thing One and $10,000 (1 + 0.08) = $10,800 from Thing Two, or a total value of $22,800 from our original $20,000 investment. The return on our portfolio is therefore: ⎛⎞$22,800-20,000 Return = ⎜⎟= 14% ⎝⎠$20,000 If instead, we invested $5,000 in Thing One and $15,000 in Thing Two, the value of our investment at the end of the year would be: Value of investment =$5,000 (1 + 0.20) + 15,000 (1 + 0.08) = $6,000 + 16,200 = $22,200 and the return on our portfolio would be: ⎛⎞$22,200-20,000 Return = ⎜⎟= 11% ⎝⎠$20,000 which we can also write as: Risk, return, and diversification, a reading prepared by Pamela Peterson Drake 1 ⎡⎤⎛⎞$5,000 ⎡ ⎛⎞$15,000 ⎤ Return = ⎢⎥⎜⎟(0.2) +=⎢ ⎜⎟(0.08) ⎥ 11% ⎣⎦⎝⎠$20,000 ⎣ ⎝⎠$20,000 ⎦ As you can see more immediately by the second calculation, the return on our portfolio is the weighted average of the returns on the assets in the portfolio, where the weights are the proportion invested in each asset. -
A Securitization-Based Model of Shadow Banking with Surplus Extraction and Credit Risk Transfer
A Securitization-based Model of Shadow Banking with Surplus Extraction and Credit Risk Transfer Patrizio Morganti∗ August, 2017 Abstract The paper provides a theoretical model that supports the search for yield motive of shadow banking and the traditional risk transfer view of securitization, which is consistent with the factual background that had characterized the U.S. financial system before the recent crisis. The shadow banking system is indeed an important provider of high-yield asset-backed securi- ties via the underlying securitized credit intermediation process. Investors' sentiment on future macroeconomic conditions affects the reservation prices related to the demand for securitized assets: high-willing payer (\optimistic") investors are attracted to these investment opportu- nities and offer to intermediaries a rent extraction incentive. When the outside wealth is high enough that securitization occurs, asset-backed securities are used by intermediaries to extract the highest feasible surplus from optimistic investors and to offload credit risk. Shadow banking is pro-cyclical and securitization allows risks to be spread among market participants coherently with their risk attitude. Keywords: securitization, shadow banking, credit risk transfer, surplus extraction JEL classification: E44, G21, G23 1 Introduction During the last four decades we witnessed to fundamental changes in financial techniques and financial regulation that have gradually transformed the \originate-to-hold" banking model into a \originate-to-distribute" model based on a securitized credit intermediation process relying upon i) securitization techniques, ii) securities financing transactions, and iii) mutual funds industry.1 ∗Tuscia University in Viterbo, Department of Economics and Engineering. E-mail: [email protected]. I am most grateful to Giuseppe Garofalo for his continuous guidance and support.