The theory and practice of investment management frank fabozzi harry markowitz

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The Theory and Practice of Investment Management Second Edition The Frank J Fabozzi Series Fixed Income Securities, Second Edition by Frank J Fabozzi Focus on Value: A Corporate and Investor Guide to Wealth Creation by James L Grant and James A Abate Handbook of Global Fixed Income Calculations by Dragomir Krgin Managing a Corporate Bond Portfolio by Leland E Crabbe and Frank J Fabozzi Real Options and Option-Embedded Securities by William T Moore Capital Budgeting: Theory and Practice by Pamela P Peterson and Frank J Fabozzi The Exchange-Traded Funds Manual by Gary L Gastineau Professional Perspectives on Fixed Income Portfolio Management, Volume edited by Frank J Fabozzi Investing in Emerging Fixed Income Markets edited by Frank J Fabozzi and Efstathia Pilarinu Handbook of Alternative Assets by Mark J P Anson The Global Money Markets by Frank J Fabozzi, Steven V Mann, and Moorad Choudhry The Handbook of Financial Instruments edited by Frank J Fabozzi Collateralized Debt Obligations: Structures and Analysis by Laurie S Goodman and Frank J Fabozzi Interest Rate, Term Structure, and Valuation Modeling edited by Frank J Fabozzi Investment Performance Measurement by Bruce J Feibel The Handbook of Equity Style Management edited by T Daniel Coggin and Frank J Fabozzi Foundations of Economic Value Added, Second Edition by James L Grant Financial Management and Analysis, Second Edition by Frank J Fabozzi and Pamela P Peterson Measuring and Controlling Interest Rate and Credit Risk, Second Edition by Frank J Fabozzi, Steven V Mann, and Moorad Choudhry Professional Perspectives on Fixed Income Portfolio Management, Volume edited by Frank J Fabozzi The Handbook of European Fixed Income Securities edited by Frank J Fabozzi and Moorad Choudhry The Handbook of European Structured Financial Products edited by Frank J Fabozzi and Moorad Choudhry The Mathematics of Financial Modeling and Investment Management by Sergio M Focardi and Frank J Fabozzi Short Selling: Strategies, Risks, and Rewards edited by Frank J Fabozzi The Real Estate Investment Handbook by G Timothy Haight and Daniel Singer Market Neutral Strategies edited by Bruce I Jacobs and Kenneth N Levy Securities Finance: Securities Lending and Repurchase Agreements edited by Frank J Fabozzi and Steven V Mann Fat-Tailed and Skewed Asset Return Distributions by Svetlozar T Rachev, Christian Menn, and Frank J Fabozzi Financial Modeling of the Equity Market: From CAPM to Cointegration by Frank J Fabozzi, Sergio M Focardi, and Petter N Kolm Advanced Bond Portfolio Management: Best Practices in Modeling and Strategies edited by Frank J Fabozzi, Lionel Martellini, and Philippe Priaulet Analysis of Financial Statements, Second Edition by Pamela P Peterson and Frank J Fabozzi Collateralized Debt Obligations: Structures and Analysis, Second Edition by Douglas J Lucas, Laurie S Goodman, and Frank J Fabozzi Handbook of Alternative Assets, Second Edition by Mark J P Anson Introduction to Structured Finance by Frank J Fabozzi, Henry A Davis, and Moorad Choudhry Financial Econometrics by Svetlozar T Rachev, Stefan Mittnik, Frank J Fabozzi, Sergio M Focardi, and Teo Jasic Developments in Collateralized Debt Obligations: New Products and Insights by Douglas J Lucas, Laurie S Goodman, Frank J Fabozzi, and Rebecca J Manning Robust Portfolio Optimization and Management by Frank J Fabozzi, Petter N Kolm, Dessislava A Pachamanova, and Sergio M Focardi Advanced Stochastic Models, Risk Assessment, and Portfolio Optimizations by Svetlozar T Rachev, Stogan V Stoyanov, and Frank J Fabozzi How to Select Investment Managers and Evaluate Performance by G Timothy Haight, Stephen O Morrell, and Glenn E Ross Bayesian Methods in Finance by Svetlozar T Rachev, John S J Hsu, Biliana S Bagasheva, and Frank J Fabozzi Structured Products and Related Credit Derivatives by Brian P Lancaster, Glenn M Schultz, and Frank J Fabozzi Quantitative Equity Investing: Techniques and Strategies by Frank J Fabozzi, Sergio M Focardi, and Petter N Kolm Introduction to Fixed Income Analytics, Second Edition by Frank J Fabozzi and Steven V Mann The Handbook of Traditional and Alternative Investment Vehicles by Mark J P Anson, Frank J Fabozzi, and Frank J Jones The Theory and Practice of Investment Management Second Edition Asset Allocation, Valuation, Portfolio Construction, and Strategies FRANK J FABOZZI HARRY M MARKOWITZ EDITORS John Wiley & Sons, Inc Copyright © 2011 by John Wiley & Sons, Inc All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada 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, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 646-8600, or on the Web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 748-6008, or online at http://www.wiley.com/go/permissions Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993, or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books For more information about Wiley products, visit our Web site at www.wiley.com Library of Congress Cataloging-in-Publication Data The theory and practice of investment management / Frank J Fabozzi, Harry M Markowitz, editors.—2nd ed p cm.—(Frank J Fabozzi series) Includes index ISBN 978-0-470-92990-2 (hardback); 978-1-118-06741-3 (ebk); 978-1-118-06751-2 (ebk); 978-1-118-06756-7 (ebk) Investments Business enterprises—Finance I Fabozzi, Frank J II Markowitz, H (Harry), 1927HG4521.T455 2011 332.6—dc22 2010054035 Printed in the United States of America 10 Contents About the Editors Contributing Authors Foreword xiii xv xvii PART ONE Instruments, Asset Allocation, Portfolio Selection, and Asset Pricing CHAPTER Overview of Investment Management Frank J Fabozzi and Harry M Markowitz Setting Investment Objectives Establishing an Investment Policy Selecting a Portfolio Strategy Constructing the Portfolio Measuring and Evaluating Performance Key Points CHAPTER Asset Classes, Alternative Investments, Investment Companies, and Exchange-Traded Funds Mark J P Anson, Frank J Fabozzi, and Frank J Jones Asset Classes Overview of Alternative Asset Products Investment Companies Exchange-Traded Funds Mutual Funds vs ETFs: Relative Advantages Key Points Questions 4 6 14 15 15 21 31 36 39 41 44 v vi CONTENTS CHAPTER Portfolio Selection Frank J Fabozzi, Harry M Markowitz, Petter N Kolm, and Francis Gupta Some Basic Concepts Measuring a Portfolio’s Expected Return Measuring Portfolio Risk Portfolio Diversification Choosing a Portfolio of Risky Assets Issues in Portfolio Selection Key Points Questions CHAPTER Capital Asset Pricing Models Frank J Fabozzi and Harry M Markowitz Sharpe-Lintner CAPM Roy CAPM Confusions Regarding the CAPM Two Meanings of Market Efficiency CAPM Investors Do Not Get Paid for Bearing Risk The “Two Beta” Trap Key Points Questions CHAPTER Factor Models Guofu Zhou and Frank J Fabozzi Arbitrage Pricing Theory Types of Factor Models Factor Model Estimation Key Points Appendix: Principal Component Analysis in Finance Questions CHAPTER Modeling Asset Price Dynamics Dessislava A Pachamanova and Frank J Fabozzi Financial Time Series Binomial Trees Arithmetic Random Walks 45 47 49 52 56 60 68 76 78 79 79 81 82 83 94 95 100 101 103 104 105 112 118 119 124 125 125 127 128 Contents Geometric Random Walks Mean Reversion Advanced Random Walk Models Stochastic Processes Key Points Questions CHAPTER Asset Allocation and Portfolio Construction Noël Amenc, Felix Goltz, Lionel Martellini, and Vincent Milhau Asset Allocation and Portfolio Construction Decisions in the Optimal Design of the Performance-Seeking Portfolio Asset Allocation and Portfolio Construction Decisions in the Optimal Design of the Liability-Hedging Portfolio Dynamic Allocation Decisions to the Performance-Seeking and Liability-Hedging Portfolios Key Points Appendix Questions vii 134 142 148 152 157 158 159 161 173 179 195 196 202 PART TWO Equity Analysis and Portfolio Management CHAPTER Fundamentals of Common Stock Frank J Fabozzi, Frank J Jones, Robert R Johnson, and Pamela P Drake Earnings Dividends The U.S Equity Markets Trading Mechanics Trading Costs Stock Market Indicators Key Points Questions CHAPTER Common Stock Portfolio Management Strategies Frank J Fabozzi, James L Grant, and Raman Vardharaj Integrating the Equity Portfolio Management Process Capital Market Price Efficiency 205 207 208 210 213 215 220 222 224 226 229 229 230 viii CONTENTS Tracking Error and Related Measures Active vs Passive Portfolio Management Equity Style Management Passive Strategies Active Investing Performance Evaluation Key Points Questions CHAPTER 10 Approaches to Common Stock Valuation Pamela P Drake, Frank J Fabozzi, and Glen A Larsen Jr Discounted Cash Flow Models Relative Valuation Methods Key Points Questions CHAPTER 11 Quantitative Equity Portfolio Management Andrew Alford, Robert Jones, and Terence Lim Traditional and Quantitative Approaches to Equity Portfolio Management Forecasting Stock Returns, Risks, and Transaction Costs Constructing Portfolios Trading Evaluating Results and Updating the Process Key Points Questions CHAPTER 12 Long-Short Equity Portfolios Bruce I Jacobs and Kenneth N Levy Constructing a Market-Neutral Portfolio The Importance of Integrated Optimization Adding Back a Market Return Some Concerns Addressed Evaluating Long-Short Key Points Questions 233 239 240 245 247 264 267 268 271 271 278 284 285 287 289 292 298 300 302 304 305 307 308 312 316 321 323 324 325 Contents CHAPTER 13 Multifactor Equity Risk Models Frank J Fabozzi, Raman Vardharaj, and Frank J Jones Model Description and Estimation Risk Decomposition Applications in Portfolio Construction and Risk Control Key Points Questions CHAPTER 14 Fundamentals of Equity Derivatives Bruce M Collins and Frank J Fabozzi The Role of Derivatives Listed Equity Options Futures Contracts Pricing Stock Index Futures OTC Equity Derivatives Structured Products Key Points Questions CHAPTER 15 Using Equity Derivatives in Portfolio Management Bruce M Collins and Frank J Fabozzi Equity Investment Management Portfolio Applications of Listed Options Portfolio Applications of Stock Index Futures Applications of OTC Equity Derivatives Risk and Expected Return of Option Strategies Key Points Questions ix 327 328 330 336 341 343 345 345 348 366 370 375 380 381 382 383 384 386 390 399 410 413 414 PART THREE Bond Analysis and Portfolio Management CHAPTER 16 Bonds, Asset-Backed Securities, and Mortgage-Backed Securities Frank J Fabozzi General Features of Bonds U.S Treasury Securities 415 417 417 421 Solutions 21 An index fund is a portfolio of securities designed to exactly replicate the return and risk profile of an established index Traditionally, the only approach to establishing an index fund was to purchase a replicating portfolio in the cash market designed to track the S&P 500 With the arrival of equity index derivatives in the early 1980s, synthetic index funds were created The investor purchases stock index futures as a substitute for the cash index and invests the proceeds in a money market instrument a Given BPI and BIF , the minimum risk hedge ratio can be found by Hedge ratio = h = B PI × B IF where BIF = the beta of the stock index relative to the stock index futures contract BPI = the beta of the portfolio relative to the stock index b The hedge ratio h in the above expression is referred to as a minimum hedge ratio (also called an optimal hedge ratio) because the ratio minimizes the variance of returns to the hedged position An equity swap can be used to exchange the returns to equity index for the returns to the bond index The swap would involve exchanging the total returns on the equity index for the bond index based on a notional amount of $5 million The first approach involves changing the composition of the equity portfolio in order to position the portfolio to take advantage of stocks, stock sectors, some different weighting allotments, or other criteria that the manager believes will cause the portfolio to perform better than a passive benchmark In the second approach, index fund managers can use a stock index futures arbitrage to increase or enhance returns The third approach is to use OTC to either modify the composition of the portfolio or to create a structured product CHAPTER 16 a The advantage to the issuer is that it can reduce its interest expense by calling the bond issue when market interest rates have declined below the issue’s coupon rate 22 SOLUTIONS b There are three disadvantages The first is that the cash flow is uncertain because the bond holder does not know when the issue may be called The second is that there is reinvestment risk because when the issue is called, the bond holder must reinvest the proceeds received at a lower interest rate The third reason is explained in Chapter 17 It is that the price appreciation of the bond when interest rates decline is not as great as for an otherwise option-free bond In general the statement is correct There are exceptions in the case of government-owned corporations such as the TVA whose debt is not guaranteed by the full faith and credit of the U.S government Although large institutional investors and many investment banking firms have a group that performs credit analysis to assess the likelihood of a bond issuer defaulting, typically investors rely on nationally recognized statistical rating organizations that perform credit analysis and issue their conclusions in the form of a credit rating Unlike a bullet bond that has a single maturity date, an amortizing bond repays principal over the bond’s life Since principal is returned over time, maturity does not reflect how long the bond’s principal is outstanding Instead, for securities such as asset-backed and mortgagebacked securities, the average life is used a Disagree There are both taxable and tax-exempt municipal bonds b Disagree The treatment of interest income even for a tax-exempt municipal bond varies from state to state Tax-backed bonds are secured by some form of tax revenue of the issuing municipality Revenue bonds are issued for enterprise financings that are secured by the revenues generated by the completed projects themselves, or for general public-purpose financings in which the issuers pledge to the bondholders the tax and revenue resources that were previously part of the general fund a A residential mortgage loan’s payments consists of three parts: (1) interest, (2) regularly scheduled principal payments (i.e., amortization), and (3) prepayments b Because the homeowner has the right to repayment all or part of the outstanding loan balance at any time, a mortgage loan is similar to a callable bond where the corporation can call a bond The cash flow a mortgage passthrough security depends on prepayments To project cash flow it is therefore necessary to project prepayment and that can only be done by assuming some prepayment rate (speed) Solutions 23 a The effect of prepayments is that the amount and timing of the cash flows from a mortgage passthrough security are not known with certainty This risk is referred to as prepayment risk b Contraction risk is the risk that a mortgage passthrough security will shorten in average life due to a decline in interest rates, resulting in an increase in the prepayment rate Extension risk is the risk that a mortgage passthrough security will lengthen in average life due to a rise in interest rates, resulting in a decline in the prepayment rate c Disagree The statement is incorrect because a CMO redistributes the prepayment risk among different bond classes but cannot eliminate prepayment risk in the aggregate 10 a Because there is no government guarantee, it is necessary to have credit support to create investment-grade bonds The credit support is called credit enhancement b The amount of credit enhancement is determined by rating agencies based on the target rating sought for each bond class 11 a In a senior-subordinated structure, there is a senior bond class and at least one subordinated bond class which absorbs first absorb losses from the collateral before the senior bond classes realize any losses b The senior-subordinated structure is form of (internal) credit enhancement because it is the subordinated bond classes that provide credit support for the senior bond classes This happens because the losses must exceed the amount of the subordinated bond classes before the senior bonds realize any losses due to defaults c The limitation of a third-party guarantee is that the downgrading of that third-party will result in a downgrade of bond classes in the structure depending on the performance of the collateral 12 A private label deal is backed by a pool of prime mortgage loans while a subprime deal is backed by a pool of loans by borrowers with either an impaired credit history or a second (or worse) lien on the property 13 Balloon risk is the inability to pay off the balloon balance of a commercial loan when due because of the borrower’s inability to refinance the property Because the loan cannot be repaid at the scheduled payment date, the loan is said to extend and hence there is extension risk CHAPTER 17 Bond 2’s price must be wrong since the coupon rate is greater than the required yield and the price should be greater than 100, not below 24 SOLUTIONS 100 Because Bond is a zero-coupon bond, its price cannot exceed par value (assuming no negative interest rates) Bond 5’s price must be less than 100 since the coupon rate is less than the required yield A bond can have several yield to call values since a bond can have more than one call date a This cannot be determined since the total return is uncertain Bond A matures at the end of the holding period Although Bond B has a higher yield, its four-year total return cannot be determined because the return depends on what a six-year bond is selling for in the market at the end of four years Also, in both cases, the total return cannot be determined because of reinvestment risk b As in (a), this cannot be determined Now Bond A’s yield depends on two-year interest rates in the market at the end of four years because the proceeds received when the bond matures must be reinvested for two years Bond B has the same problem as in (a) because Bond B’s total return depends on interest rates on four-year bonds at the end of six years Moreover, in both cases, the total return cannot be determined because of reinvestment risk a $90.62 b Increasing the yield by one basis point gives a price of $90.53 Therefore, the price value of a basis point (in absolute value) is $0.09 Note that if the yield is decreased by one basis point, the price is $90.71 so the price value of a basis point is the same value c We know that 6y = 0.0010 and V0 = $90.62 The following can be calculated: Price if yield decreased by 10 basis points to 5.9%(V−) = $91.5043 Price if yield increased by 10 basis points to 6.1%(V+) = $89.7425 Using equation (17.5), Duration = $91.5043 − $89.7425 = 9.72 2($90.62)(0.0010) d Since the bond is an option-free bond, the duration is modified duration Actually, modified and effective duration will be the same for this bond e For a 100 basis point change in market yields, this bond’s price will change by approximately 9.72% Solutions 25 f For a 25 basis point change in market yields, this bond’s price will change by approximately 2.43% g For a 50 basis point increase in market yields, this bond’s price will decline by approximately 4.86% Per $100 of par value, the bond’s price will decline by 4.86% of $90.62 or $4.40 Duration is a good approximation of the change in a bond’s price for a small change in interest rates For larger changes in interest rates, the approximation is not as good The approximation can be improved by using the bond’s convexity measure a The portfolio duration is 9.06 as shown below: Bond A Market Value $13,000,000 Percentage of Portfolio 9% Duration Percent × Duration = Contribution to Portfolio Duration 0.28 B $27,000,000 19% 1.35 C $60,000,000 43% 3.43 D $40,000,000 29% 14 4.00 Portfolio $140,000,000 100% 9.06 b If interest rates change by 50 basis points, the portfolio will change by approximately 4.53% c The contribution to portfolio duration for each bond is shown in the last column of the above table d The assumption is that the interest rates for all bonds change by the same number of basis points a Bond A’s coupon rate is considerably higher than prevailing market interest rates so it is a more likely candidate to be called than Bond B (which is not likely to be called since it would have to be replaced with a bond issue that has a higher interest rate) Hence, Bond A would be expected to exhibit negative convexity b Bond B is closer to an option-free bond in its price volatility characteristics than Bond A so it is would be more appropriate to use modified duration A 10-year key rate duration of 0.35 for a portfolio means that holding all spot rates constant and changing the spot rate by 100 basis points, the portfolio’s value will change by roughly 0.35% 26 SOLUTIONS CHAPTER 18 With the arbitrage-free approach, cash flows are discounted using spot rates taken from the Treasury spot rate curve that correspond to the maturity date of the cash flow The key to the arbitrage-free valuation approach is the existence of the Treasury strips market Since Treasuries can be stripped and reconstituted, a coupon Treasury should be thought of a portfolio of zero-coupon bonds If this is not true, traders will take advantage of any mispricing The process of stripping and reconstitution assures that the price of a Treasury issue will not depart materially (depending on transaction costs) from its arbitrage-free value The credit spread increases with maturity The lower the credit rating, the steeper the term structure of credit spreads The nominal spread for a non-Treasury security involves calculating the difference between the risky bond’s yield and the yield on comparable maturity benchmark Treasury security It is the yield spread at one point on the curve The Z-spread is the spread that will make the present value of the cash flows from the risky bond, when discounted at the Treasury spot rate plus the spread, equal to the risky bond’s full price It is a measure of the spread that the investor would realize over the entire Treasury spot curve if the bond were held to maturity a An increase in volatility makes the embedded call option more valuable In a tree, we will see this as more nodes that have bigger payoffs to the issuer who owns the call option If the call option is more valuable, the bondholder will pay a lower price for the callable bond relative to an otherwise the same option-free bond b The option-adjusted spread is the constant spread that, when added to the forward rates on the tree, will make the arbitrage-free value equal to the market price The OAS is that part of the Z-spread that compensates investors for the risks of the security in question after adjusting for the embedded option c An increase in volatility will make the embedded call option more valuable As a result, the option cost is greater Holding the Z-spread constant, the OAS must shrink a The valuation process starts at maturity which barring default are known and works backwards from right to left (maturity to today) b The benchmark option-free bonds are valued at the market prices which are taken as given The model is calibrated to these market prices Consequently, no arbitrage opportunities are possible Solutions 27 a 5.19% b The statement that forward rates reflect the market’s consensus of future spot interest rates is strictly true only if investors not demand an additional risk premiums for holding bonds with longer maturities and if investors’ preference for positive convexity does not influence the yield curve’s shape Forward rates should be interpreted as break-even levels for future spot rates OAS is the part of the Z-spread after adjusting for the embedded option It is compensation for the risks of the security after accounting for the option The risks depend on what benchmark yield curve is used The cash flow received in a given period is determined not only by the current level of the interest rate but also by the path interest rates took to get to that current level CHAPTER 19 There are several problems with the selection of ABCD Capital as the benchmark provider for ABCD Asset Management as they relate to the principles of a good index: Relevance to the investor or representative of the market The first potential problem with the index is that it does not seem to include investment grade corporate debt, a large part of the investment grade debt market Clearly, this benchmark index is not representative of the market, but it may also be irrelevant to the investors Leaving out corporate debt would make the index irrelevant for those investors seeking to earn returns from credit spreads in addition to the other components of the index This may be the intention of ABCD Asset Management and not be a problem, but it is something they should be aware of Q High-quality data This is most likely not an issue, but it could become one if the instruments being marked are illiquid or are mismarked by ABCD Capital’s trader Since this index is provided by the investment bank, investors are likely to be at the mercy of the bank’s trader A better index may include prices from multiple sources to minimize the probability of a pricing error Q Independence If ABCD Asset Management uses this index, it could be perceived as a lack of independence due to the common parent company, even if the entities are completely separately operated This problem arises in practice quite frequently and as a result, the asset Q 28 SOLUTIONS management arm of many banks will not use the indexes provided by their sister companies in the investment banking arm a In particular, the results using mean–variance optimization for custom index creation are going to depend on the risk level chosen by the index creator This can create several problems: At any given risk level, some assets may not be included in an optimal portfolio The asset may be suboptimal at all risk levels or may not be appropriate at the desired risk level The problem becomes that the index may not be representative of the market Q A second problem is that it may be difficult to have transparent rules and consistent constituents When using this methodology, rules and the sources of data would have to be very well defined in order to track the benchmark The mere fact that it will take a great deal of effort to follow may make the index a suboptimal choice b Just because there are some problems, one needs to recognize the need for trade-offs when evaluating the appropriateness of an index In this case, the gains from having a custom index that provides the best performance benchmark may be worth the sacrifices that would have to be made with regard to some of the principles An investor can adopt one of the three approaches to scenario-based portfolio optimization: a Maximize expected return, in which subjective probabilities are assigned to each scenario and the objective is to maximize the average return The investor can express a view about the rank-ordering of scenarios, overweighting those that are deemed more likely with higher probabilities while underweighting others The end result will reflect the bias imposed by the investor, e.g if a higher probability is assigned to bearish scenarios, portfolio duration will be shorter b Maximize return under a specific scenario that captures the investor’s base case Here maximum emphasis is placed on generating profits under that particular outcome, without any explicit consideration for the risk under the other scenarios This is equivalent to maximizing expected return while putting 100% probability on the base case scenario c Maximize worst case return across all scenarios Here the objective is to have a conservative return, with limited downside across various scenarios In a way, the investor is agnostic about the scenario and is looking to benefit from relative value Q Solutions 29 Some of the constraints that ABCD can impose include: a Duration bands The duration of the portfolio cannot deviate by more than some percentage from that of the index This ensures that the portfolio will not have an outsized directional bet b Partial duration Mimic the allocation of the index in various duration buckets This is aimed at mitigating the risk of losses due to market moves that are not captured by the limited set of scenarios under consideration c Asset allocation weights Replicate the fixed income sectors of the benchmark within a certain band In general money managers not want to deviate too much from the asset weighting of their target and will shift their allocation by some amount, rather than making an all-in bet on any one market sector d Loss constraints e Issue weights In order to avoid biasing the results, the scenarios should encompass a broad set of outcomes For example, there should be bearish scenarios as well as bullish ones, flattening scenarios as well as steepening ones, and so on The important thing to note here is that these scenarios should bracket the forwards For example, when the curve is upward sloping, the forward curve will have higher rates and be generally flatter Therefore, it is not sufficient to have some scenarios where rates are simply higher than the spot curve: The “bearish” scenarios in the scenario set should have rates higher than the forward curve—balanced, of course, by “bullish” scenarios where rates are below the forwards The weights and the constraints can be thought of as two different facets of the same thing As constraints become more stringent, this tends to decrease the variability of performance across the scenarios In other words, no one scenario is allowed to far outweigh the others in terms of influencing portfolio composition A similar result can be achieved by adopting a maxmin optimization approach, which balances out returns across scenarios However, one should not assume that the maxmin approach is equivalent to expected return maximization with equal probabilities; it is not There is typically a subset of scenarios that gives rise to inferior performance Maxmin assigns enough “probability” to that set of scenarios, to boost their performance as much as possible In some cases, performance can be enhanced to such an extent that all the scenarios produce the same projected return 30 SOLUTIONS CHAPTER 20 The portfolio manager must develop a multitude of forecasts and utilize these forecasts in a variety of ways throughout the investment process The portfolio manager should have knowledge of: (1) economics, (2) politics, (3) history, (4) psychology, and (5) statistics, in addition to other disciplines in order to develop this forecast The portfolio manager must have an in-depth knowledge of the assumptions inherent to the forecast and understand the subsector economic analysis, such as trade account product distribution, monetary targets, non-economic objectives, cultural norms, tax policies, and the marketplace for which the forecast applies The forecast becomes a baseline set of criteria in which to measure and monitor capital inflows and the effects on a given investment region or country Excesses will reveal themselves through interest rates and asset prices Current levels of interest rates and bond prices are a reflection of or reaction to the collective forecasts and opinion of all bond investors given their research into the polices and relative competitive economic advantages of a given market This is where the potential relative advantage exists for the thoughtful global fixed income portfolio manager to succeed The portfolio manager should take existing prices and compare them to an independently created forecast The major characteristics or features that a portfolio manager will manage to include: duration, cash flow distribution on various yield curves, convexity, credit quality dispersion, country, currency and sector exposure Underlying all these characteristics in a fixed income portfolio is a complex set of considerations and decisions A portfolio manager should have the highest conviction in their proprietary forecast when they identify an underlying secular change in an economy or a changes that are harbingers of long term trend shifts is consistent with cyclical forecasted changes or ones that will support the longer term secular trends as well as consistent with market technicals or attractive supply and demand characteristics A portfolio manager should consider multiple investment opportunities to capture the widest opportunity set However, the investment landscape of less crowded markets may include structural risks that can take the form of increased illiquidity, volatility, political risk and access, among others These risks must be priced into any assessment of value the global fixed income portfolio manager must make Solutions 31 CHAPTER 21 The interest rate risk of each security is given by the product of its interest rate duration (the loading to the interest rate risk) and the volatility of interest rates, mi,rates = Di · m6R Therefore, m1,rates = 120 and m2,rates = 180 The spread risk is captured by the product of its loading (DTS) times the volatility of the spreads factor, mi,spreads = SDi · Si · m6S/S = DTSi · m6S/S Therefore: m1,spreads = 180 and m2,spreads = 65 The systematic risk comes from both risk factors considered in this example: σ i ,sys = σ i2,rates + σ i2,spreads + 2ρσ i ,rates σ i ,spreads Therefore, m1,syst = 184 and m2,sys = 172 The idiosyncratic risk of each bond is given by σ i ,idio = DTSi ⋅ σ idio ΔS / S Therefore,  m1,idio = 252 and m2,idio = 91 The systematic and idiosyncratic risks of a bond are independent Therefore, to find the total volatility of each security, we just have to combine the idiosyncratic risk to the systematic risk calculated before: σ i = σ 2i ,syst + σ i2,idio which gives m1 = 312 and m2 = 195 bps/month respectively Despite the shorter duration, the first bond is significantly more risky because of its higher spread! The interest rate duration of the portfolio is calculated as the weighted sum of the duration of the two securities Since the weights are equal, we have D = 0.5 · D1 + 0.5 · D2 = and the spread duration times the spread of the portfolio is DTS = 0.5 · SD1 · S1 + 0.5 · SD2 · S2 = 1225 Isolated interest rate risk for the portfolio is given by the formula σ isolated = D ⋅ σ ΔR = 150.0 bps/month rates 32 SOLUTIONS Isolated credit spreads risk for the portfolio is given by the formula σ isolated = DTS ⋅ σ ΔS / S = 122.5 bps/month spreads Isolated systematic risk is given by the formula (σ σ isolated = syst isolated rates ) + (σ isolated spreads ) + 2ρσ isolated σ isolated = 162.7 bps/month rates spreads Idiosyncratic risk is calculated assuming it is independent between the two issuers: σ isolated = idio (0.5 ⋅ SD ⋅ S ⋅ σ ) + (0.5 ⋅ SD ⋅ S idio ΔS / S 2 ⋅ σ idio ΔS / S ) = 134.0 bps/month Total risk is calculated assuming independence between systematic and idiosyncratic risk: σ= (σ isolated syst ) + (σ isolated idio ) = 210.8 bp ps/month Using the definition of risk contribution we have (D ⋅ σ ) = ΔR σ contr rates σ contr spreads σ contr idio + ρD ⋅ σ ΔR DTS ⋅ σ ΔS / S ( DTS ⋅ σ ) = (σ = ΔS / S isolated idio σ ) σ = 80.6 bps/month + ρD ⋅ σ ΔR DTS ⋅ σ ΔS / S σ = 45.1 bps/month = 85.1 bps/month By design they sum up to the total risk of the portfolio of 210.8 bps/ month Using the isolated bond volatilities from question and the formula σ= (0.5 ⋅ σ ) + (0.5 ⋅ σ ) 2 + ⋅ 0.5 ⋅ 0.5 ⋅ ρbonds σ1 σ we get lbonds = 0.35 The easiest way to answer this question is use the correlation between the returns of the two bonds calculated in question 7: Solutions 33 σ contr (0.5 ⋅ σ ) = σ contr (0.5 ⋅ σ ) = 2 + ρbonds ⋅ 0.5 ⋅ σ1 ⋅ 0.5 ⋅ σ σ + ρbonds ⋅ 0.5 ⋅ σ1 ⋅ 0.5 ⋅ σ σ = 140.7 bps/month = 70.1 bps/month As expected, they sum up to the total portfolio risk CHAPTER 22 The statement is not correct, so the answer is to disagree Although it is true that futures contracts are marked to market, forward contract may or may not be Typically, they are When the target duration is greater than current portfolio duration, this means dollar duration must be added to the portfolio a This can be done with Treasury bond futures contracts by buying these contracts Actually, it involves buying enough dollar duration so that the sum of the current portfolio’s dollar duration plus the dollar duration for the Treasury bond futures contracts equals the target dollar duration implied by the target duration b This can be done with interest rate swaps in which the portfolio manager pays floating and receives fixed Doing so increases the dollar duration of the portfolio a Given that there many acceptable Treasury bonds that can be delivered by the short to satisfy delivery of the Treasury bond futures contract, the conversion factors make delivery equitable to both parties The conversion factors adjust the price of each Treasury issue so that they are economically equivalent to the hypothetical Treasury bond underlying the contract b There are many Treasury bonds that are acceptable or deliverable to satisfy the contract The one that provides the highest implied repo rate is the cheapest-to-deliver issue c For each Treasury bond issue that is deliverable, an implied repo rate is computed (i.e., rate of return from buying a deliverable bond, shorting the contract, and delivering the bond at the settlement date) The one with the high implied repo rate from among all the deliverable issues is the cheapest-to-deliver issue Two are two reasons First, the cash-and-carry model assumes that there are no interim case flows So adjustments have to be made to the 34 SOLUTIONS theoretical price to allow for futures having interim cash flows as well as the underlying providing cash payments Second, there are delivery options available to the short These delivery options—swap, timing, and wild card—are valuable to the short and therefore they reduce the theoretical price derived from a pure cash-and-carry model For a futures option that is a call option, the buyer has the right to purchase one designated futures contract at the strike price If the buyer exercises the call option, the writer acquires a corresponding short position in the futures contract The futures position of both parties is then marked to market CHAPTER 23 It is difficult to short corporate bonds in the cash market A portfolio manager can the equivalent by buying credit protection via a credit default swap By doing so, the portfolio manager makes swap payments which is the economic equivalent of making interest payments if the portfolio manager took a short position in the corporate bond If there is credit event, the portfolio manager gets par value for the issue, benefitting by buying the corporate bond below par in the market Given the infrequent trading of certain corporate bond issues, it is not always easy to obtain the bonds in the cash market By selling a singlename CDS, the portfolio manager does the equivalent of owning a corporate bond The portfolio manager receives the swap payments just as the manager would be receiving coupon interest payments if the bonds were owned If there is a credit event, the portfolio manager would have to make a payment to the protection buyer, realizing a loss in the same ways as if the bond were purchased If a credit event occurs, the swap premium payment ceases in the case of a single-name CDS (but paid up to the credit event date) and the contract is terminated For an index, however, the swap payment continues to be made by the credit protection buyer but the amount of the quarterly swap premium payment is reduced This is because the notional amount is reduced as a result of a credit event for the reference obligor CDX and LCDX differ in two ways First is the difference in the recovery assumption The difference in the assumption is due to the difference in valuations of secured (in the case of the LCDX) and unsecured debt (in the case of the CDX) should a bankruptcy occur Second is the difference in assumption in the case of a cancellation (i.e., where Solutions 35 the corporation pays off all of its outstanding first lien loans without issuing new first lien debt) LCDS is cancelled after 30 days if no debt substitute is found and the original index notional amount is reduced by 1% If a portfolio manager wants to increase exposure to the corporate bond sector, one way of doing so is to sell protection on a CDX based on investment-grade corporate bonds (e.g CDX.IG) Buying that same CDX reduces exposure [...]... Overview of Investment Management Frank J Fabozzi, Ph.D., CFA, CPA Professor in the Practice of Finance Yale School of Management Harry M Markowitz, Ph.D Consultant he purpose of this book is to describe the activities and investment vehicles associated with investment management Investment management also referred to as portfolio management and money management requires an understanding of: T How investment. .. in the market value of the portfolio at the end of the period The second assumption is that if there are distributions from the portfolio, they either occur at the end of the evaluation period or are held in the form of cash until the end of the evaluation period In our example, $10 million is distributed to the client But when did that distribution actually occur? To understand why the timing of the. .. University Professor Fabozzi is the editor of the Journal of Portfolio Management and an associate editor of the Journal of Fixed Income, Journal of Asset Management, Review of Futures Markets, and Quantitative Finance He is a trustee for the BlackRock family of closed-end funds In 2002, he was inducted into the Fixed Income Analysts Society’s Hall of Fame and is the 2007 recipient of the C Stewart... Questions About the Web Site Index 658 658 661 663 About the Editors Frank J Fabozzi is Professor in the Practice of Finance in the Yale School of Management Prior to joining the Yale faculty, he was a Visiting Professor of Finance in the Sloan School at MIT He is a Fellow of the International Center for Finance at Yale University and on the Advisory Council for the Department of Operations Research and Financial... Portfolio Construction, and Strategies, Second Edition Edited by Frank J Fabozzi and Harry M Markowitz Copyright © 2011 John Wiley & Sons, Inc PART One Instruments, Asset Allocation, Portfolio Selection, and Asset Pricing The Theory and Practice of Investment Management: Asset Allocation, Valuation, Portfolio Construction, and Strategies, Second Edition Edited by Frank J Fabozzi and Harry M Markowitz Copyright... (1) the distribution is made at the end of the evaluation period, as is assumed in the return calculation; and (2) the distribution is made at the beginning of the evaluation period In the first case, the portfolio manager had the use of the $10 million to invest for the entire evaluation period By contrast, in the second case, the portfolio manager loses the opportunity to invest the funds until the. .. distributions from the portfolio to a client or beneficiary of the portfolio be taken into account The rate of return, or simply return, expresses the dollar return in terms of the amount of the market value at the beginning of the evaluation period Thus, the return can be viewed as the amount (expressed as a fraction of the initial portfolio value) that can be withdrawn at the end of the evaluation period... Foreword Then and Now in Investing, and Why Now Is So Much Better Peter L Bernstein This Foreword originally appeared in the first edition of The Theory and Practice of Investment Management Peter Bernstein passed away in June 2009 References to the updated chapters mentioned in the Foreword are provided by the editors s I read this book for the first time, I was constantly reminded of the contrast between the. .. still consisted only of the slide-rules and hand-turned or electric (not electronic) desk-top calculators we used in the 1950s, the theories comprising the subject matter of this book, and that support today’s investment practices, would never have moved beyond their pages in scholarly journals into the real world of investing Q Q Q To give you a flavor of the profound nature of the changes that have... at the end of each subperiod while keeping the portfolio’s initial market value intact In our first example, in which the average monthly return is 5%, the investor must add 10% of the initial portfolio market value at the end of the first month, can withdraw 20% of the initial portfolio market value at the end of the second month, and can withdraw 5% of the initial portfolio market value at the end of
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