DOCSLIB.ORG

Using Modern Portfolio Theory to Identify Increased

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Using Modern Portfolio Theory to Identify Increased USING MODERN PORTFOLIO THEORY TO IDENTIFY INCREASED INVESTMENT RISKS IN PRIVATE BANKS A Project Presented to the Faculty of California State Polytechnic University, Pomona In Partial Fulfillment Of the Requirements for the Degree Master of Science In Economics By Roberto Martinez Suarez 2015 SIGNATURE PAGE PROJECT: USING MODERN PORTFOLIO THEORY TO IDENTIFY INCREASED INVESTMENT RISKS IN PRIVATE BANKS AUTHOR: Roberto Martinez Suarez DATE SUBMITTED: Fall 2015 Economics Department Dr. Bruce Brown Project Committee Chair Professor of Economics Dr. Carsten Lange _____________________________________________ Graduate Coordinator Professor of Economics ii ACKNOWLEDGEMENTS Foremost, I would like to express my sincere gratitude to my advisor Prof. Bruce Brown for his continuous support of my graduate studies and research, and for his patience, motivation, enthusiasm, and immense knowledge. His guidance has helped me in all the time of research and writing of this project. I cannot imagine having a better advisor and mentor. Besides my advisor, I would like to thank my other project committee member Prof. Carsten Lange. His encouragement, insightful comments, and hard questions have been truly appreciated. My sincere thanks also goes to Dr. Mohammad Safarzadeh for making economics at Cal Poly Pomona so difficult. This forced me to bring my “A” game. I thank my classmates Justin Niakamal and David Raymundo. They have offered me their guidance, assistance, and friendship throughout the previous two years. Last, but not the least, I would like to thank my family. I thank my parents Roberto Martinez and Emma Victoria Martinez for giving birth to me in the first place and for supporting me spiritually throughout my life. I thank my younger siblings Erika, Bayron, Alfred, and Denise who have been instrumental in my success as well. A shout-out to my girlfriend Erica Picazo for being very supportive and understanding. iii ABSTRACT In the wake of the Great Recession of 2009, it is little wonder that there has been growing interest in identifying optimal investment strategies that can avoid unnecessary risks while maximizing returns on investment. Despite its constraints, modern portfolio theory has emerged as a viable strategy for this purpose. This paper applies modern portfolio theory to identify indications of increased investment risks in private banks. This paper also explores how those investment risks can in turn affect private markets, particularly in view of potential penalty risks that private investors sometimes incur. An examination of portfolio returns for various levels of risk through an evaluation of a firm’s beta is followed by an analysis concerning the perspective of Warren Buffett on this issue. Finally, in the conclusion, the paper provides a summary of the research and important findings concerning the application of modern portfolio theory. iv TABLE OF CONTENTS Signature Page…………………………………………………………………………. ii Acknowledgements……………………………………………………………………. iii Abstract………………………………………………………………………………... iv List of Tables…………………………………………………………………………… vi List of Figures………………………………………………………………………….. vii Chapter1: Introduction………………………………………………………………… 1 Chapter 2: Review and Analysis……………………………………………………….. 2 Overview of Modern Portfolio Theory………………………………………… 2 Identifying Signs of Increased Investment Risks in Private Banks……………. 6 How Increased Investment Risk Affects Private Markets……………………... 23 Applicability of Beta to Increased Investment Risk in Private Banks…………. 25 Chapter 3: Conclusion………………………………………………………………….. 29 References……………………………………………………………………………… 31 Appendix: Due Diligence Required for Investments in Private Enterprises…………… 34 v LIST OF TABLES Table 1 Variables That Signal Potential Investment Crises……………………... 20 Table 2 Stock Selection Using Beta……………………………………………... 26 vi LIST OF FIGURES Figure 1 Share of the investment portfolio dedicated to credit investments: 2007-2011………………………………………………………………. 12 Figure 2 Portion of the securities portfolio classified as credit or spread investments in 2011…………………………………………………….. 14 Figure 3 Increase in credit portfolio assets and liquidity portfolio asset exposures……………………………………………………………….. 15 Figure 4 Minimizing unsystematic risk through portfolio diversification……….. 18 Figure 5 Efficient frontier for Google and Coca Cola stocks……………………. 19 vii CHAPTER 1 INTRODUCTION Today, there is a growing consensus among practitioners that it is possible to identify salient risks and improve returns on investment by applying modern portfolio theory. There is less agreement, though, concerning the optimal approaches to applying modern portfolio theory to identify increased investment risks in private banks and how those investment risks can affect private markets. To determine the facts, this paper uses modern portfolio theory to reveal signs of increased investment risks in private banks. This paper then explores how those investment risks effect private markets, especially in light of potential penalty risks that private investors sometimes incur. In addition, by appraising a firm’s beta, there can be an examination of portfolio returns for various levels of risk. Beta views risk solely from the perspective of market prices. Warren Buffett’s opinion on this matter is that some investors shun beta because it implies that a stock that has fallen sharply in value is more risky than it was before it fell. Finally, a summary of the research and important findings concerning the application of modern portfolio theory in this context are provided in the conclusion. 1 CHAPTER 2 REVIEW AND ANALYSIS Overview of Modern Portfolio Theory The recipient of the 1990 Nobel Prize winner in economics, Harry Markowitz, was responsible for developing modern portfolio theory as well as for participating in additional collaboration with other economists to fine-tune its tenets (Bai, Dow, & Newsom, 2008). A useful definition of modern portfolio theory is provided by Mangram (2013) who advises, “[Markowitz’s] innovative work established the underpinnings for Modern Portfolio Theory -- an investment framework for the selection and construction of investment portfolios based on the maximization of expected portfolio returns and simultaneous minimization of investment risk” (p. 59). The work by Markowitz was expanded upon in 1964 by William Sharpe whose research into financial asset price formation became known as the Capital Asset Pricing Model, or CAPM (Mangram, 2013). This expanded conceptualization of modern portfolio theory provides a useful framework for investment analysis that allows practitioners to select and develop investment portfolios that are founded on the optimization of expected returns of the portfolio and the simultaneous minimization of the associated risks of investment (Fabozzi, Gupta, & Markowitz, 2002). The expanded version of modern portfolio theory is frequently referred to as the mean-variance analysis in which the “mean” is used interchangeably with the average expected return and the “variance” applies to the indicated risk (Mangram, 2013). The mean-variance analytical approach has since emerged as a fundamental approach to optimizing investment portfolios (Campbell, 2000). There are some 2 constraints to modern portfolio theory as conceptualized by Markowitz. For example, Goetzmann and Wachter (1999) note, “As originally conceived, mean-variance calculates a set of portfolio weights across assets that result in the highest expected return for each given level of investor risk. While useful, the procedure is not without drawbacks” (p. 271). The main drawbacks to modern portfolio theory depend on the viewpoints of the investors, with some viewing some aspects of the model as being suboptimal while others consider other variables more salient for their purposes (Viezer, 1999). Along this same line, Campbell (2000) points out, “This approach usefully emphasizes the ability of diversification to reduce risk, but it ignores several critically important factors. Most notably, the analysis is static; it assumes that investors care only about risks to wealth one period ahead” (para. 2). However, Campbell goes on to explain that a number of institutional and individual investors are more interested in developing a long-term system of consumption. Moreover, there are also constraints to the mean-variance analytical approach. These include the manner in which financial wealth and income are treated (Bielski, 2005). Along this line, Campbell (2000) adds, “Mean-variance analysis treats financial wealth in isolation from income. Long-term investors typically receive a stream of income and use it, along with financial wealth, to support their consumption” (para. 2). Currently, mean-variance analysis is the foundation of modern portfolio selection and optimization (Leung, 2009). Notwithstanding these constraints, the research to date suggests that the risk factors associated with modern portfolio theory can be determined through the 3 application of different mathematical formulas and can be analyzed using the concept of diversification. Diversification seeks to optimize a weighted collection of investment assets that, in the aggregate, demonstrate lower risk factors compared to investments in any individual asset or asset class (Mangram, 2013). This concept is derived directly from the earlier work by Markowitz. As Mangram (2013) points out, “Diversification is, in fact, the core concept of modern portfolio theory and directly relies on the conventional wisdom of ‘never putting all your eggs
Load more

Recommended publications
  • Basel III: Post-Crisis Reforms
    Basel III: Post-Crisis Reforms Implementation Timeline Focus: Capital Definitions, Capital Focus: Capital Requirements Buffers and Liquidity Requirements Basel lll 2018 2019 2020 2021 2022 2023 2024 2025 2026 2027 1 January 2022 Full implementation of: 1. Revised standardised approach for credit risk; 2. Revised IRB framework; 1 January 3. Revised CVA framework; 1 January 1 January 1 January 1 January 1 January 2018 4. Revised operational risk framework; 2027 5. Revised market risk framework (Fundamental Review of 2023 2024 2025 2026 Full implementation of Leverage Trading Book); and Output 6. Leverage Ratio (revised exposure definition). Output Output Output Output Ratio (Existing exposure floor: Transitional implementation floor: 55% floor: 60% floor: 65% floor: 70% definition) Output floor: 50% 72.5% Capital Ratios 0% - 2.5% 0% - 2.5% Countercyclical 0% - 2.5% 2.5% Buffer 2.5% Conservation 2.5% Buffer 8% 6% Minimum Capital 4.5% Requirement Core Equity Tier 1 (CET 1) Tier 1 (T1) Total Capital (Tier 1 + Tier 2) Standardised Approach for Credit Risk New Categories of Revisions to the Existing Standardised Approach Exposures • Exposures to Banks • Exposure to Covered Bonds Bank exposures will be risk-weighted based on either the External Credit Risk Assessment Approach (ECRA) or Standardised Credit Risk Rated covered bonds will be risk Assessment Approach (SCRA). Banks are to apply ECRA where regulators do allow the use of external ratings for regulatory purposes and weighted based on issue SCRA for regulators that don’t. specific rating while risk weights for unrated covered bonds will • Exposures to Multilateral Development Banks (MDBs) be inferred from the issuer’s For exposures that do not fulfil the eligibility criteria, risk weights are to be determined by either SCRA or ECRA.
    [Show full text]
  • Personal Loans 101: Understanding Your Credit Risk Loans Have Some Risk for Both the Borrower and the Lender
    PERSONAL LOANS 101: Understanding YoUr credit risk Loans have some risk for both the borrower and the lender. The borrower takes on the responsibilities and terms of paying back the loan. The lender’s risk is the chance of non-payment. Consumers can choose from several types of loans. As a borrower, you need to understand the type of loan you are considering and its possible risk. This brochure provides information to help you make a smart choice before applying for a loan. 2 It is important to review your financial situation to see if you can handle another monthly payment before applying for a loan. Creating a budget will help you apply for the loan that best meets your present and future needs. For an interactive budget, visit www.afsaef.org/budgetplanner or www.afsaef.org/personalloans101. You will need to show the lender that you can repay what you borrow, with interest. After you have made a budget, consider these factors, which maY redUce or add risk to a Loan. 3 abiLitY to repaY the Loan Is the lender evaluating your ability to repay the loan based on facts such as your credit history, current and expected income, current expenses, debt-to- income ratio (your expenses compared to your income) and employment status? This assessment, often called underwriting, helps determine if you can make the monthly payment and raises your chances of getting a loan to fit your needs that you can afford to repay. It depends on you providing complete and correct information to the lender. Testing “your ability to repay” and appropriate “underwriting” reduces your risk when taking out any type of loan.
    [Show full text]
  • Manulife Asset Allocation Client Brochure
    Manulife Asset Allocation Portfolios Sophisticated Investment Solutions Made Simple 1 Getting The Big Decisions Right You want a simple yet Deciding how to invest is one of life’s big decisions – effective way to invest in fact it’s a series of decisions that can have a big and Manulife Asset impact on your financial future. Allocation Portfolios It can be complicated and overwhelming, leaving you feeling uncertain offer a solution that can and anxious. The result? Many investors end up chasing fads, trends and help you get it right. short-term thinking, which can interfere with your ability to achieve long-term financial goals. As an investor, you want to make the most of your investments. You want to feel confident you’re receiving value for your money and reputable, professional advice. Big life decisions “Am I making the right investment choices?” Disappointing returns “Should I change my investing strategy?” Confusion and guesswork “How can I choose the best investment for me?” Manulife Asset Allocation Portfolios are managed by Manulife Investment Management Limited (formerly named Manulife Asset Management Limited). Manulife Asset Allocation Portfolios are available in the InvestmentPlus Series of the Manulife GIF Select, MPIP Segregated Pools and Manulife Segregated Fund Education Saving Plan insurance contracts offered by The Manufacturers Life Insurance Company. 2 Why Invest? The goal is to offset inflation and grow your wealth, while planning for important financial goals. Retirement: Canadian Education Raising a Child Pension Plan (CPP) $66,000 $253,947 $735.21 Current cost of a four-year The average cost of raising a Current average monthly payout for post-secondary education1 child from birth to age 183 new beneficiaries.
    [Show full text]
  • 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).
    [Show full text]
  • Division of Investment Management No-Action Letter: Lazard Freres
    FEB 2 1996 Our Ref. No. 95-399 RESPONSE OF THE OFFICE OF CHIEF Lazard Freres Asset COUNSEL DIVISION OF INVESTMENT Management MAAGEMENT File No.80l-6568 Your letter dated July 20, 1995 requests our assurance that we would not recommend enforcement action to the Commission under the Investment Advisers Act of 1940 ("Advisers Act ") if Lazard Freres Asset Management ("LFAM"), a registered investment adviser, charges a performance fee to BPI Capital Management Corporation (BPI Capital) with respect to the performance of the BPI Global Opportunities Fund (the "Fund"). BPI Capital is an investment counsel and portfolio manager registered under the laws of the Province of Ontario and manages 16 publicly offered mutual funds. The Fund is an open- end fund organized under the laws of the Province of Ontario. The Fund has entered into a management agreement with BPI Capital under which BPI Capital is responsible for management of the Fund's ::civestment portfolio and day- to- day management of the Fund. unics of the Fund are offered to investors in the Provinces of Ontario, Manitoba, Saskatchewan, Alberta and British Columbia pursuant to prospectus exemptions under the laws and regulations of each of these Provinces. Under such prospectus exemptions, miLimum investment amounts are CAD $150,000 for investors in Oncario and Saskatchewan and CAD $97,000 for investors in Mani toba, Alberta and British Columbia. A lower minimum amount of CAD $25,000 is available to investors in British Columbia designated as "sophisticated purchasers." No units of the Fund have been offered to any investors residing in the United States and there is no intention to offer any units of the Fund to U.
    [Show full text]
  • 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
    [Show full text]
  • Investment Management Update
    Investment Management Update March 2012 CFTC Adopts Rule Amendments Affecting CPOs and CTAs Introduction • Eliminate an exemption available in Rule 4.7 under the CEA to commodity pools whose participants The Commodity Futures Trading Commission (CFTC) are “qualified eligible participants” from the recently adopted amendments to Part 4 of the regulations requirement to provide audited financial 1 statements in annual reports. implementing the Commodity Exchange Act (CEA). In • Incorporate by reference, rather than by full relevant part, Part 4 of the regulations sets forth the inclusion of its specific text, the accredited registration and compliance obligations for commodity pool investor standard set forth in Rule 502 of operators (CPOs) and commodity trading advisors (CTAs). Regulation D under the Securities Act of 1933, as First proposed in February 2011, the amendments implicate amended, into the definition of “qualified eligible several sections of Part 4, including Rule 4.5, upon which person” in Rule 4.7. many mutual funds and other registered investment • Adopt new Rule 4.27, which requires registered 2 CPOs and CTAs to annually file, respectively, Forms companies rely to avoid registering as a CPO. As adopted, CPO-PQR and CTA-PR with the National Futures revised Rule 4.5 will significantly narrow the relief from CPO Association (NFA). registration currently available for advisers to, and sponsors • Adopt a mandatory Risk Disclosure Statement for of, registered investment companies. Furthermore, since CPOs and CTAs addressing certain risks specific to many advisers to investment companies rely on a CTA swap transactions. registration exemption that is dependent upon the investment company’s ability to rely on Rule 4.5, the Amendments to Rule 4.5 amendments to Rule 4.5 will result in more advisers to Background registered investment companies having to register as CTAs.
    [Show full text]
  • The Portfolio Optimization Performance During Malaysia's
    Modern Applied Science; Vol. 14, No. 4; 2020 ISSN 1913-1844 E-ISSN 1913-1852 Published by Canadian Center of Science and Education The Portfolio Optimization Performance during Malaysia’s 2018 General Election by Using Noncooperative and Cooperative Game Theory Approach Muhammad Akram Ramadhan bin Ibrahim1, Pah Chin Hee1, Mohd Aminul Islam1 & Hafizah Bahaludin1 1Department of Computational and Theoretical Sciences Kulliyyah of Science International Islamic University Malaysia, 25200 Kuantan, Pahang, Malaysia Correspondence: Pah Chin Hee, Department of Computational and Theoretical Sciences, Kulliyyah of Science, International Islamic University Malaysia, 25200 Kuantan, Pahang, Malaysia. Received: February 10, 2020 Accepted: February 28, 2020 Online Published: March 4, 2020 doi:10.5539/mas.v14n4p1 URL: https://doi.org/10.5539/mas.v14n4p1 Abstract Game theory approach is used in this study that involves two types of games which are noncooperative and cooperative. Noncooperative game is used to get the equilibrium solutions from each payoff matrix. From the solutions, the values then be used as characteristic functions of Shapley value solution concept in cooperative game. In this paper, the sectors are divided into three groups where each sector will have three different stocks for the game. This study used the companies that listed in Bursa Malaysia and the prices of each stock listed in this research obtained from Datastream. The rate of return of stocks are considered as an input to get the payoff from each stock and its coalition sectors. The value of game for each sector is obtained using Shapley value solution concepts formula to find the optimal increase of the returns. The Shapley optimal portfolio, naive diversification portfolio and market portfolio performances have been calculated by using Sharpe ratio.
    [Show full text]
  • 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.
    [Show full text]
  • Revised Standards for Minimum Capital Requirements for Market Risk by the Basel Committee on Banking Supervision (“The Committee”)
    A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf Basel Committee on Banking Supervision STANDARDS Minimum capital requirements for market risk January 2016 A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf This publication is available on the BIS website (www.bis.org). © Bank for International Settlements 2015. All rights reserved. Brief excerpts may be reproduced or translated provided the source is stated. ISBN 978-92-9197-399-6 (print) ISBN 978-92-9197-416-0 (online) A revised version of this standard was published in January 2019. https://www.bis.org/bcbs/publ/d457.pdf Minimum capital requirements for Market Risk Contents Preamble ............................................................................................................................................................................................... 5 Minimum capital requirements for market risk ..................................................................................................................... 5 A. The boundary between the trading book and banking book and the scope of application of the minimum capital requirements for market risk ........................................................................................................... 5 1. Scope of application and methods of measuring market risk ...................................................................... 5 2. Definition of the trading book ..................................................................................................................................
    [Show full text]
  • The Cost of Equity Capital for Reits: an Examination of Three Asset-Pricing Models
    MIT Center for Real Estate September, 2000 The Cost of Equity Capital for REITs: An Examination of Three Asset-Pricing Models David N. Connors Matthew L. Jackman Thesis, 2000 © Massachusetts Institute of Technology, 2000. This paper, in whole or in part, may not be cited, reproduced, or used in any other way without the written permission of the authors. Comments are welcome and should be directed to the attention of the authors. MIT Center for Real Estate, 77 Massachusetts Avenue, Building W31-310, Cambridge, MA, 02139-4307 (617-253-4373). THE COST OF EQUITY CAPITAL FOR REITS: AN EXAMINATION OF THREE ASSET-PRICING MODELS by David Neil Connors B.S. Finance, 1991 Bentley College and Matthew Laurence Jackman B.S.B.A. Finance, 1996 University of North Carolinaat Charlotte Submitted to the Department of Urban Studies and Planning in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE IN REAL ESTATE DEVELOPMENT at the MASSACHUSETTS INSTITUTE OF TECHNOLOGY September 2000 © 2000 David N. Connors & Matthew L. Jackman. All Rights Reserved. The authors hereby grant to MIT permission to reproduce and to distribute publicly paper and electronic (\aopies of this thesis in whole or in part. Signature of Author: - T L- . v Department of Urban Studies and Planning August 1, 2000 Signature of Author: IN Department of Urban Studies and Planning August 1, 2000 Certified by: Blake Eagle Chairman, MIT Center for Real Estate Thesis Supervisor Certified by: / Jonathan Lewellen Professor of Finance, Sloan School of Management Thesis Supervisor
    [Show full text]
  • Credit Risk Models
    Lecture notes on risk management, public policy, and the financial system Credit risk models Allan M. Malz Columbia University Credit risk models Outline Overview of credit risk analytics Single-obligor credit risk models © 2020 Allan M. Malz Last updated: February 8, 2021 2/32 Credit risk models Overview of credit risk analytics Overview of credit risk analytics Credit risk metrics and models Intensity models and default time analytics Single-obligor credit risk models 3/32 Credit risk models Overview of credit risk analytics Credit risk metrics and models Key metrics of credit risk Probability of default πt defined over a time horizon t, e.g. one year Exposure at default: amount the lender can lose in default For a loan or bond, par value plus accrued interest For OTC derivatives, also driven by market value Net present value (NPV) 0 ( counterparty risk) S → But exposure at default 0 ≥ Recovery: creditor generally loses fraction of exposure R < 100 percent Loss given default (LGD) equals exposure minus recovery (a fraction 1 − R) Expected loss (EL) equals default probability × LGD or fraction πt × (1 − R) Credit risk management focuses on unexpected loss Credit Value-at-Risk related to a quantile of the credit return distribution Differs from market risk in excluding EL Credit VaR at confidence level of α defined as: 1 − α-quantile of credit loss distribution − EL 4/32 Credit risk models Overview of credit risk analytics Credit risk metrics and models Estimating default probabilities Risk-neutral default probabilities based on market
    [Show full text]