PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted BooK - DERIVATIVES AND PORTFOLIO MANAGEMENT Readings and Learning Outcome Statements v Study Session 16 - Derivative Investments: Forwards and Futures Study Session 17 - Derivative Investments: Options, Swaps, and Interest Rate and Credit Derivatives 50 Self-Test - Derivatives 142 Study Session 18 - Portfolio Management: Capital Market Theory and the Portfolio Management Process 145 Self-Test - Portfolio Management 212 Formulas 217 Index 223 PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted SCHWESERNOTES™ 2016 LEVEL II CFAđ BOOK 5: DERIVATIVES AND PORTFOLIO MANAGEMENT â2015 Kaplan, Inc All rights reserved Published in 2015 by Kaplan, Inc Printed in the United States of America ISBN: 978-1-4754-3533-7 PPN: 3200-6845 If this book does not have the hologram with the Kaplan Schweser logo on the back cover, it was distributed without permission of Kaplan Schweser, a Division of Kaplan , Inc., and is in direct violation of global copyright laws Your assistance in pursuing potential violators of chis law is greatly appreciated Required CFA Institute disclaimer: "CFA Institute does not endorse, promote, or warrant the accuracy or quality of the products or services offered by Kaplan Schweser CFA ® and Chartered Financial Analyst® are trademarks owned by CFA Institute." Certain materials contained within this text are the copyrighted property of CFA Institute The following is the copyright disclosure for these materials: "Copyright, 2015, CFA Institute Reproduced and republished from 2016 Learning Outcome Statements, Level I, II, and III questions from CFA ® Program Materials, CFA Institute Standards of Professional Conduct, and CFA lnstitute's Global Investment Performance Standards with permission from CFA Institute All Rights Reserved." These materials may not be copied without written permission from the author The unauthorized duplication of these notes is a violation of global copyright laws and the CFA Institute Code of Ethics Your assistance in pursuing potential violators of this law is greatly appreciated Disclaimer: The Schweser Notes should be used in conjunction with the original readings as set forth by CFA Institute in their 2016 Level II CFA Study Guide The information contained in these Notes covers topics contained in the readings referenced by CFA Institute and is believed to be accurate However, their accuracy cannot be guaranteed nor is any warranty conveyed as to your ultimate exam success The authors of the referenced readings have not endorsed or sponsored these Notes Page iv ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted READINGS AND LEARNING OUTCOME STATEMENTS READINGS The following material is a review of the Derivatives and Portfolio Management principles designed to address the learning outcome statements set forth by CFA Institute STUDY SESSION 16 Reading Assignments Derivatives and Portfolio Management, CFA Program Curriculum, Volume 6, Level II (CFA Institute, 2015) 47 Forward Markets and Contracts 48 Futures Markets and Contracts page page 29 STUDY SESSION 17 Reading Assignments Derivatives and Portfolio Management, CFA Program Curriculum, Volume 6, Level II (CFA Institute, 2015) 49 50 51 52 Option Markets and Contracts Swap Markets and Contracts Interest Rate Derivative Instruments Credit Default Swaps page 50 page 92 page 120 page 128 STUDY SESSION 18 Reading Assignments Derivatives and Portfolio Management, CFA Program Curriculum, Volume 6, Level II (CFA Institute, 2015) 53 54 55 56 An Introduction to Multifactor Models Analysis of Active Portfolio Management Economics and Investment Markets The Portfolio Management Process and the Investment Policy Statement ©2015 Kaplan, Inc page 145 page 167 page 184 page 198 Page v PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Readings and Learning Outcome Statements LEARNING OUTCOME STATEMENTS (LOS) The CFA Institute Learning Outcome Statements are listed below These are repeated in each topic review; however, the order may have been changed in order to get a better fit with the flow of the review STUDY SESSION 16 The topical coverage corresponds with the following CFA Institute assigned reading: 47 Forward Markets and Contracts The candidate should be able to: a explain how the value of a forward contract is determined at initiation, during the life of the contract, and at expiration (page 6) b calculate and interpret the price and value of an equity forward contract, assuming dividends are paid either discretely or continuously (page 8) c calculate and interpret the price and value of 1) a forward contract on a fixedincome security, 2) a forward rate agreement (FRA), and 3) a forward contract on a currency (page 12) d evaluate credit risk in a forward contract, and explain how market value is a measure of exposure to a party in a forward contract (page 21) The topical coverage corresponds with the following CFA Institute assigned reading: 48 Futures Markets and Contracts The candidate should be able to: a explain why the futures price must converge to the spot price at expiration (page 29) b determine the value of a futures contract (page 30) c explain why forward and futures prices differ (page 31) d describe monetary and nonmonetary benefits and costs associated with holding the underlying asset, and explain how they affect the futures price (page 35) e describe backwardation and contango (page 36) f explain the relation between futures prices and expected spot prices (page 36) g describe the difficulties in pricing Eurodollar futures and creating a pure arbitrage opportunity (page 39) h calculate and interpret the prices of Treasury bond futures, stock index futures, and currency futures (page 40) STUDY SESSION 17 The topical coverage corresponds with the following CFA Institute assigned reading: 49 Option Markets and Contracts The candidate should be able to: a calculate and interpret the prices of a synthetic call option, synthetic put option, synthetic bond, and synthetic underlying stock and explain why an investor would want to create such instruments (page 51) b calculate and interpret prices of interest rate options and options on assets using one- and two-period binomial models (page 54) Page vi ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Readings and Learning Outcome Statements c d e f g h j explain and evaluate the assumptions underlying the Black-Scholes-Merton model (page 68) explain how an option price, as represented by the Black-Scholes-Merton model, is affected by a change in the value of each of the inputs (page 70) explain the delta of an option and demonstrate how it is used in dynamic hedging (page 73) explain the gamma effect on an option's delta and how gamma can affect a delta hedge (page 78) explain the effect of the underlying asset's cash flows on the price of an option (page 78) determine the historical and implied volatilities of an underlying asset (page 79) demonstrate how put-call parity for options on forwards (or futures) is established (page 80) compare American and European options on forwards and futures, and identify the appropriate pricing model for European options (page 82) The topical coverage corresponds with the following CFA Institute assigned reading: 50 Swap Markets and Contracts The candidate should be able to: a distinguish between the pricing and valuation of swaps (page 92) b explain the equivalence of 1) interest rate swaps to a series of off-market forward rate agreements (FRAs) and 2) a plain vanilla swap to a combination of an interest rate call and an interest rate put (page 93) c calculate and interpret the fixed rate on a plain vanilla interest rate swap and the market value of the swap during its life (page 94) d calculate and interpret the fixed rate, if applicable, and the foreign notional principal for a given domestic notional principal on a currency swap and estimate the market values of each of the different types of currency swaps during their lives (page 101) e calculate and interpret the fixed rate, if applicable, on an equity swap and the market values of the different types of equity swaps during their lives (page 105) f explain and interpret the characteristics and uses of swaptions, including the difference between payer and receiver swaptions (page 107) g calculate the payoffs and cash flows of an interest rate swaption (page 107) h calculate and interpret the value of an interest rate swaption at expiration (page 108) evaluate swap credit risk for each party and during the life of the swap, distinguish between current credit risk and potential credit risk, and explain how swap credit risk is reduced by both netting and marking to market (page 109) j define swap spread and explain its relation to credit risk (page 11 O) The topical coverage corresponds with the following CFA Institute assigned reading: 51 Interest Rate Derivative Instruments The candidate should be able to: a demonstrate how both a cap and a floor are packages of 1) options on interest rates and 2) options on fixed-income instruments (page 120) b calculate the payoff for a cap and a floor and explain how a collar is created (page 122) ©2015 Kaplan, Inc Page vii PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Readings and Learning Outcome Statements The topical coverage corresponds with the following CFA Institute assigned reading: 52 Credit Default Swaps The candidate should be able to: a describe credit default swaps (CDS), single-name and index CDS, and the parameters that define a given CDS product (page 129) b describe credit events and settlement protocols with respect to CDS (page 130) c explain the principles underlying, and factors that influence, the market's pricing of CDS (page 131) d describe the use of CDS to manage credit exposures and to express views regarding changes in shape and/or level of the credit curve (page 134) e describe the use of CDS to take advantage of valuation disparities among separate markets, such as bonds, loans, equities, and equity-linked instruments (page 135) STUDY SESSION 18 The topical coverage corresponds with the following CFA Institute assigned reading: 53 An Introduction to Multifactor Models The candidate should be able to: a describe arbitrage pricing theory (APT), including its underlying assumptions and its relation to multifactor models (page 145) b define arbitrage opportunity and determine whether an arbitrage opportunity exists (page 146) c calculate the expected return on an asset given an asset's factor sensitivities and the factor risk premiums (page 147) d describe and compare macroeconomic factor models, fundamental factor models, and statistical factor models (page 149) e explain sources of active risk and interpret tracking risk and the information ratio (page 154) f describe uses of multifactor models and interpret the output of analyses based on multifactor models (page 156) g describe the potential benefits for investors in considering multiple risk dimensions when modeling asset returns (page 161) The topical coverage corresponds with the following CFA Institute assigned reading: 54 Analysis of Active Portfolio Management The candidate should be able to: a describe how value added by active management is measured (page 167) b calculate and interpret the information ratio (ex post and ex ante) and contrast it to the Sharpe ratio (page 171) c state and interpret the fundamental law of active portfolio management including its component terms-transfer coefficient, information coefficient, breadth, and active risk (aggressiveness) (page 17 4) d explain how the information ratio may be useful in investment manager selection and choosing the level of active portfolio risk (page 176) e compare active management strategies (including market timing and security selection) and evaluate strategy changes in terms of the fundamental law of active management (page 176) f describe the practical strengths and limitations of the fundamental law of active management (page 178) Page viii ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Readings and Learning Outcome Statements The topical coverage corresponds with the following CFA Institute assigned reading: 55 Economics and Investment Markets The candidate should be able to: a explain the notion that to affect market values, economic factors must affect one or more of the following: (1) default-free interest rates across maturities, (2) the timing and/or magnitude of expected cash flows, and (3) risk premiums (page 184) b explain the role of expectations and changes in expectations in market valuation (page 184) c explain the relationship between the long-term growth rate of the economy, the volatility of the growth rate, and the average level of real short-term interest rates (page 185) d explain how the phase of the business cycle affects policy and short-term interest rates, the slope of the term structure of interest rates, and the relative performance of bonds of differing maturities (page 187) e describe the factors that affect yield spreads between non-inflation-adjusted and inflation-indexed bonds (page 188) f explain how the phase of the business cycle affects credit spreads and the performance of credit-sensitive fixed-income instruments (page 189) g explain how the characteristics of the markets for a company's products affect the company's credit quality (page 189) h explain how the phase of the business cycle affects short-term and long-term earnings growth expectations (page 190) explain the relationship between the consumption-hedging properties of equity and the equity risk premium (page 190) j describe cyclical effects on valuation multiples (page 190) k describe the implications of the business cycle for a given style strategy (value, growth, small capitalization, large capitalization) (page 191) describe how economic analysis is used in sector rotation strategies (page 191) m describe the economic factors affecting investment in commercial real estate (page 192) The topical coverage corresponds with the following CFA Institute assigned reading: 56 The Portfolio Management Process and the Investment Policy Statement The candidate should be able to: a explain the importance of the portfolio perspective (page 199) b describe the steps of the portfolio management process and the components of those steps (page 199) c explain the role of the investment policy statement in the portfolio management process and describe the elements of an investment policy statement (page 200) d explain how capital market expectations and the investment policy statement help influence the strategic asset allocation decision and how an investor's investment time horizon may influence the investor's strategic asset allocation (page 200) e define investment objectives and constraints and explain and distinguish among the types of investment objectives and constraints (page 201) f contrast the types of investment time horizons, determine the time horizon for a particular investor, and evaluate the effects of this time horizon on portfolio choice (page 205) g justify ethical conduct as a requirement for managing investment portfolios (page 205) ©2015 Kaplan, Inc Page ix PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted The following is a review of the Derivative Investments: Forwards and Futures principles designed to address the learning outcome statements set forth by CFA Institute Cross-Reference to CFA Institute Assigned Reading #47 FORWARD MARKETS AND CONTRACTS Study Session 16 EXAM Focus This topic review covers the calculation of price and value for forward contracts, specifically equity forward contracts, T-bond forward contracts, currency forwards, and forward (interest) rate agreements You need to have a good understanding of the no-arbitrage principle that underlies these calculations because it is used in the topic reviews of futures and swaps pricing as well There are several important price and value formulas in this review A clear understanding of the sources and timing of forward contract settlement payments will enable you to be successful on this portion of the exam without depending on pure memorization of these complex formulas In the past, candidates have been tested on their understanding of the relationship of the payments at settlement to interest rate changes, asset price changes, and index level changes The pricing conventions for the underlying assets have been tested separately The basic contract mechanics are certainly "fair game," so don't overlook the easy stuff by spending too much time trying to memorize the formulas WARM-UP: FORWARD CONTRACTS The party to the forward contract that agrees to buy the financial or physical asset has a long forward position and is called the long The party to the forward contract that agrees to sell/ deliver the asset has a short forward position and is called the short We will illustrate the basic forward contract mechanics through an example based on the purchase and sale of a Treasury bill Note that while forward contracts on T-bills are usually quoted in terms of a discount percentage from face value, we use dollar prices here to make the example easy to follow Consider a contract under which Party A agrees to buy a $1,000 face value 90-day Treasury bill from Party B 30 days from now at a price of $990 Party A is the long and Party B is the short Both parties have removed uncertainty about the price they will pay or receive for the T-bill at the future date If 30 days from now T-bills are trading at $992, the short must deliver the T-bill to the long in exchange for a $990 payment If T-bills are trading at $988 on the future date, the long must purchase the T-bill from the short for $990, the contract price Each party to a forward contract is exposed to default risk, the probability that the other party (the counterparty) will not perform as promised Typically, no money changes hands at the inception of the contract, unlike futures contracts in which each party posts an initial deposit called the margin as a guarantee of performance ©2015 Kaplan, Inc Page PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Study Session 16 Cross-Reference to CFA Institute Assigned Reading #47 - Forward Markets and Contracts At any point in time, including the settlement date, the party to the forward contract with the negative value will owe money to the other side The other side of the contract will have a positive value of equal amount Following this example, if the T-bill price is $992 at the (future) settlement date, and the short does not deliver the T-bill for $990 as promised, the short has defaulted Professor's Note: A video explaining the basics offorward contracts can be found in the online Schweser Candidate Resource Library WARM-UP: FORWARD CONTRACT PRICE DETERMINATION The No-Arbitrage Principle The price of a forward contract is not the price to purchase the contract because the parties to a forward contract typically pay nothing to enter into the contract at its inception Here, price refers to the contract price of the underlying asset under the terms of the forward contract This price may be a U.S dollar or euro price but it is often expressed as an interest rate or currency exchange rate For T-bills, the price will be expressed as an annualized percentage discount from face value; for coupon bonds, it will usually be expressed as a yield to maturity; for the implicit loan in a forward rate agreement (FRA), it will be expressed as annualized London Interbank Offered Rate (LIBOR); and for a currency forward, it is expressed as an exchange rate between the two currencies involved However it is expressed, this rate, yield, discount, or dollar amount is the forward price in the contract The price that we wish to determine is the forward price that makes the values of both the long and the short positions zero at contract initiation We will use the noarbitrage principle: there should not be a riskless profit to be gained by a combination of a forward contract position with positions in other assets This principle assumes that (1) transactions costs are zero, (2) there are no restrictions on short sales or on the use of short sale proceeds, and (3) both borrowing and lending can be done in unlimited amounts at the risk-free rate of interest This concept is so important, we'll express it in a formula: forward price = price that prevents profitable riskless arbitrage in frictionless markets A Simple Version of the Cost-of-Carry Model In order to explain the no-arbitrage condition as it applies to the determination of forward prices, we will first consider a forward contract on an asset that costs nothing to store and makes no payments to its owner over the life of the forward contract A zero-coupon (pure discount) bond meets these criteria Unlike gold or wheat, it has no storage costs; unlike stocks, there are no dividend payments to consider; and unlike coupon bonds, it makes no periodic interest payments Page ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Study Session 18 Cross-Reference to CFA Institute Assigned Reading #56- The Portfolio Management Process and the Investment Policy Statement B The Elams' time horizon is long term and at least two-fold: the time until retirement and their retirement years It is possible that a third time horizon could develop should the Elams decide to support their children through post-secondary education Should they decide to retire at age 60 , their pre-retirement time horizon would be 30 years C The main liquidity constraint presented in the case is immediate and significant (the $60,000 in credit card debt) Schneider should recommend that the Elams eliminate this liability with the inheritance funds immediately No special legal or regulatory problems are apparent Prudent investor rules apply if William is interested in creating a trust fund ©2015 Kaplan, Inc Page 211 PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted SELF-TEST: PORTFOLIO MANAGEMENT Use the following information to answer Questions through Faster Analytics Capital Management makes portfolio recommendations using various factor models Bill Adams, chief economist at Faster Analytics, is responsible for providing macroeconomic and capital market forecasts Mauricio Rodriguez, a Faster Analytics research analyst, is examining the prospects of several portfolios: the FACM Century Fund (CF), the FACM Esquire Fund (EF), the FACM Zeta Fund (ZF), and the FACM Delta Benchmark (DB) Exhibit 1: Selected Data for CF, ZF and Their Benchmark Information ratio (CF) 0.12 Information ration (ZF) 0.25 Benchmark Sharpe ratio 0.30 Benchmark total risk(s) 20% Rodriguez's supervisor Barbara Woodson asks Rodriguez to use the Capital Asset Pricing Model (CAPM) and a multifactor model (APT) to make a decision about whether to continue or terminate the EF fund The two factors in the multifactor model are not identified To help with the decision, Adams provides Rodriguez with the capital market forecasts shown in Exhibit Exhibit 2: Capital Market Forecasts Risk-free rate 4% Market portfolio risk premium 8% APT factor risk premium 5% APT factor risk premium 2% Inflation rate 3% After examining the prospects for the EF portfolio, Rodriguez derives the forecasts in Exhibit Exhibit 3: EF Data Expected Return 12% CAPM beta 0.80 APT factor risk sensitivity 1.50 APT factor risk sensitivity 2.00 Rodriguez also develops a 2-factor macroeconomic factor model for the EF portfolio The two factors used in the model are the surprise in GDP growth and the surprise in investor sentiment The equation for the macro factor model is: Page 212 ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Self-Test: Portfolio Management During an investment committee meeting, Woodson makes the following statements related to the 2-factor macroeconomic factor model: Statement 1: An investment allocated between CF and EF that provides a GDP growth factor beta equal to one and an investor sentiment factor beta equal to zero will have lower active factor risk than a tracking portfolio consisting of CF and EF Statement 2: When markets are in equilibrium, no combination of CF and EF will produce an arbitrage opportunity Rodriguez says to Woodson that for a long-term default-risk-free bond, if the covariance between the bond's price and investors' inter-temporal rate of substitution is positive, the bond will trade at a lower price than it otherwise would, and that covariance will capture the risk premium on the bond In their final meeting, Rodriguez informs Woodson that the DB portfolio consistently outperformed its benchmark over the past five years "The consistency with which DB outperformed its benchmark is amazing The difference between the DB monthly return and its benchmark's return was nearly always positive and varied little over time," says Rodriguez The highest possible Sharpe ratio for a portfolio consisting of a combination of the CF fund and the benchmark is closest to: A 0.32 B 0.35 C 0.38 For an investor in the ZF Fund, the optimal level of active risk, and the corresponding total excess return (over risk-free rate), are respectively closest to: Optimal active risk A 12.0% 9.2% B 16.7% 10.2% C 18.6% 11.9% Considering the data provided in Exhibits and 3, should Rodriguez recommend that Faster Analytics continue to invest in the EF fund using an analysis based on the: CAPM? Total excess return 2-factor APT? A Yes Yes B Yes No C No Yes Rodriguez's statement regarding default risk-free bond is most likely: A correct B incorrect about the existence of a risk premium on a default-risk-free bond C incorrect about the covariance being positive ©2015 Kaplan, Inc Page 213 PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Self-Test: Portfolio Management Are Woodson's statements and regarding the macro factor model correct? A Both statements are correct B Only statement is correct C Only statement is correct The historical performance of the DB portfolio is best summarized as: A high active risk B high tracking risk C high information ratio Page 214 ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Self-Test: Portfolio Management SELF-TEST ANSWERS: PORTFOLIO MANAGEMENT A The optimal combination of the CF fund and the benchmark portfolio will result in highest possible Sharpe ratio The Sharpe ratio for the optimal portfolio consisting of the benchmark and the CF fund can be calculated using the following equality: SR?= SRl + IR 2 SRp = ~SR + 1Rc = ~0.30 + 0.12 = 0.3231 B 25 Optimal active risk = crzF* = [IRzF)crs = ( · )0.20 = 0.1667 = 16.67% SR 0.30 Expected excess return for ZF (active return): E(RA) = IR x O'A = (0.25) x (0 1667) = 4.17% Benchmark excess return = (0.30) x (0 20) = 6% Total excess return= 4.17% + 6% = 10.17% B The equations for required rate of return using the CAPM and a 2-factor APT are respectively: CAPM: REF = RF + ~EF[E(RM) - RF] 2-factor APT: REF= RF+ ~EF,/;\ 1) + ~EF,i(A) Using the data provided in Exhibits and 3: CAPM required rate of return= 0.04 + 0.80(0.08) = 0.104 = 10.4% 2-factor APT required rate of return = 0.04 + 1.5(0.05) + 2(0.02) = 0.155 = 15.5% The expected return for the EF fund is 12%, which exceeds the CAPM required return Therefore, Rodriguez predicts that the EF portfolio return will exceed its CAPM required return; a signal to continue investing in EF However, the forecasted EF return of 12% is less than the 2-factor APT model required return of 15.5%; this is a signal to not invest in EF C The covariance between the uncertain future price of a default-risk-free bond and the investor's intertemporal rate of substitution is negative - resulting in a positive risk premium for a longer-term default-risk-free bond C A portfolio that has a factor beta equal to one for one factor and factor betas equal to zero for all other factors is called a "factor portfolio." In contrast, a portfolio that has factor betas equal to the benchmark factor betas is called a "tracking portfolio." Unlike the tracking portfolio, the factor portfolio betas are not identical to the benchmark betas As a result, factor portfolios have higher active factor risk (which refers to the deviations of a portfolio's factor betas from those of the benchmark) Therefore, Woodson's first statement is not correct Her second statement is correct When markets are in equilibrium, all expected (i.e., forecast) asset returns are equal to their required returns An arbitrage opportunity refers to an investment that requires no cost and no risk yet still provides a profit If markets are in equilibrium, no profits can be earned from a costless, riskless investment ©2015 Kaplan, Inc Page 215 PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Self-Test: Portfolio Management C The information ratio equals active return divided by active risk Active return equals the average difference between the CF portfolio return and the benchmark return Active risk equals the standard deviation of the CF return minus benchmark return From the comments made by Rodriquez about the historical performance of the CF portfolio, we know that the numerator of the information ratio is positive and that the denominator is very close to zero Therefore, the information ratio will be high The fund standard deviation is very close to that of its benchmark (since its returns were nearly always a constant percentage above the benchmark) The CF fund rose and fell with the benchmark (same risk as the benchmark) but always beat the benchmark (outperformed the benchmark) Therefore, tracking risk (which is also referred to as active risk) is low Page 216 ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted FORMULAS STUDY SESSIONS 16 & 17: DERIVATIVE INVESTMENTS definition of the futures price: futures price = spot price x (1 + r iT - r) forward contract price: FP = S0 x (1 +Rf) T forward contract value of long position: at initiation: zero, because priced to prevent arbitrage FP during life of contract: st at expiration: equity forward contract price: FP( on an equity security) = (S - PVD) x (1 + Rf )T FP( on an equity security) = [so x (1 + Rf?] - FVD FP equity forward contract value: Vt (long position)= [Sr -PVDr] -1 - - - ~ ~ - (l + RfiT- r) equity index forward contract price: ( 8c xT) RcxT (Rc-oc) xT FP(onanequ1tymdex)=S x e f = S0 x eXe f equity index forward contract value: Vt ( of the long position) = [ e Sr ]- [ FP ] 8cx(T-r) Rcfx(T-r) e ©2015 Kaplan, Inc Page 217 PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Formulas fixed income forward contract price: FP ( on a fixed income security) = ( S0 - PVC) x (1 +Rf) T = [so x (l +Rf ?]-FVC fixed income forward contract value: Ve ( long position) = [Sc - PVCc] - currency forward contract price: Fr (currency forward contract) = S0 x FP 1- - - - - - (1 + Rr)(T-c) (1+Roc? T (l+Rpc) currency forward contract value: Ve ( currency forward contract) = Fr Sc (l+RpclT- c) continuous time price and value formulas for currency forward contracts: Fr (currency forward contract)= S0 Ve ( currency forward contract) = [ xe (R c oc - Rc ) x T Fe Sc ]-[ Fr eRkx(T-c) eRocx(T-c) I generalized no-arbitrage futures price: Treasury bond futures contract price: FP = [bond price x (1 +Rf) T - FVC] x ~F put-call parity for European options: C + x (l+Rf? Page 218 ©2015 Kaplan, Inc = P0 + S0 PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Formulas put-call parity for European options with cash flows: binomial model: D u l+Rr-D U-D al f l max {O, [(one-year rate - cap rate) x notional principal]} expiration v ue o cap et = + one-year rate al expiration v ue o f fl l max {O, [(floor rate - one-year rate) x notional principal]} oor et = + one-year rate delta and dynamic hedging: L1C~N(d )xL15 L1P ~ [N( di)-1] x L15 forward put-call parity: C + X - FT (1 + Rf f P0 = l-Z4 Z1 +Z2 +Z3 +Z4 fixed swap rate (with four payments): C = - - - - - - - ' - - - - payoff to cap buyer: al pnnc1pa l) X c·m d ex rate - cap stn"k) d"1c payment= max [0, (notion peno e X (actual days)] 360 ©2015 Kaplan, Inc Page 219 PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Formulas payoff to floor buyer: · 1pnnc1pa · · l) x (fl oor stn'ke - m d ex rate) x (actual days)] · d'JC payment= max [0, (notJona peno 360 upfront premium % (paid by protection buyer) ""' (CDS spread - CDS coupon) x duration price of CDS (per $100 notional)"'=' $100 - upfront premium(%) profit for protection buyer ""' change in spread x duration x notional principal STUDY SESSION 18: PORTFOLIO MANAGEMENT APT equation expected return active return = risk free rate + I::(factor sensitivity) x (factor risk premium) = factor return + security selection return mutifactor model return attribution: k factor return = L ((3pk - f3bk) X (),k) i=l active risk squared active factor risk = active factor risk + active specific risk = active risk squared - active specific risk n spec1.fi c ns k active = 6~(Wpt -W,b.)2a I Et i= l active return = portfolio return - benchmark return n portfolio return = Rp = L wp,;R; i=l n benchmark return = Rs = L wB,iRi i=l information ratio RA active return active risk Page 220 ©2015 Kaplan, Inc PRINTED BY: Xiangzhi taidong@pdx.edu Printing is for personal, private use only No part of this book may be reproduced or transmitted without publisher's prior permission Violators will be prosecuted Book - Derivatives and Portfolio Management Formulas portfolio Sharpe ratio SR P = Rp -RF STD(Rp) information ratio= IR= TC x IC x vlBR expected active return= E(RA) = IR x a A "full" fundamental law of active management: E(RA) = (TC)(IC)viBR