Teaching Note on Factor Model with a View --- A tutorial. This version: May 15, Prepared by Zhi Da *
|
|
- Kristian Gardner
- 6 years ago
- Views:
Transcription
1 Copyrght by Zh Da and Rav Jagannathan Teachng Note on For Model th a Ve --- A tutoral Ths verson: May 5, 2005 Prepared by Zh Da * Ths tutoral demonstrates ho to ncorporate economc ves n optmal asset allocaton n the frameork of for model. The tutoral s structured n a queston-and-anser format. Please try to solve each queston before lookng at ts anser. All orgnal data and detaled calculaton are contaned n an excel spreadsheet --- forve.xls. In addton, MarkotzII s requred for the optmal portfolo calculaton. Basc problem: You are nterested n nvestng n sx portfolos, formed by sortng all stocks accordng to ther market captalzaton and book-to-market rato. Book-to-market Market Cap Lo Medum Hgh Small Portfolo : Small groth Portfolo 2: Small neutral Portfolo 3: Small value Bg Portfolo 4: Bg groth Portfolo 5: Bg neutral Portfolo : Bg value You beleve that the returns are affected by macro economc varables and the dynamcs can be captured by a four-for model, here the excess return of portfolo (or asset) can be rtten as: R = a + b F + b F + b F + b F + e. () t t The frst for s the excess return on the stock market ndex portfolo. The second for s the change n the slope of the term structure. The thrd for s the change n the yeld spread beteen Baa and Aaa bonds. The fourth for s Ol nflaton (percentage change n Ol prce). The quarterly tme seres of the four fors and excess returns of the sx portfolos 2 from 994 to 2003 are also provded n forve.xls. Today s Dec 3, 2003 and you are currently holdng a passve portfolo of the sx assets. Hoever one energy expert recently told you that the ol prce next year s gong to be a lot hgher than you mght expect. Specfcally, hs forecast of ol nflaton for year 2004 s 25% hgher than the consensus forecast. You are very confdent n hs forecast and therefore ant to ncorporate ths ve n your asset allocaton decson. * Ths tutoral s prepared under the supervson of Prof Rav Jagannathan for the teachng of FINC40 nvestment. Detaled descrpton on the sx portfolos and ther returns can be found n Prof Ken French s ebste: 2 The excess return s defned as portfolo return mnus rsk free rate.
2 Queston : What are the for loadngs for each portfolo? Equaton () can be estmated usng regresson n Excel. To do that, go to Tools --- Data Analyss --- Regresson. In ths case, Y corresponds to excess returns of one of the sx portfolos and X corresponds to the four fors. The regresson coeffcents are the for loadngs. Repeat the regresson sx tmes to obtan the for loadngs for all sx portfolos as reported n Table. In general, the market for s sgnfcant for all portfolos. In addton, the term spread for s sgnfcant for the small groth portfolo and the ol for s sgnfcant for the bg value portfolo. In another ords, the bg value portfolo ll be affected the most by the ol prce shock. Queston 2: What s the varance of each of the sx portfolo returns? What s the varance due to for exposure,.e., systematc varance? What s the resdual or specfc varance? What s the varance of the value-eghted market portfolo? What s the specfc and systematc varance of the market portfolo? Usng the for loadngs, e can decompose the total varance of any asset nto systematc varance and resdual varance. Let b denote a vector contanng for loadngs for asset,.e., b = [ b b2 b3 b4 ]. Let Σ denote the covarance matrx of the four fors. Then, e have: Var = SysVar + Re svar, SysVar = b Σb '. We can also do the same varance decomposton for the market portfolo. Let denote a vector contanng the market portfolo s current eghts n the sx assets and Ω denote the covarance matrx of the sx assets. Usng the market values of the sx portfolos at the end of year 2003, e can compute the eghts to be: Mkt port eght Portfolo : Small groth Portfolo 2: Small neutral Portfolo 3: Small value Portfolo 4: Bg groth Portfolo 5: Bg neutral Portfolo : Bg value 2.95% 3.89% 2.23% 58.07% 24.0% 8.7% Then e can compute the total varance of the market as: Var = Ω'. To compute the systematc varance of the market, e need to fnd out the for loadngs of the market, hch are smply eghted averages of for loadngs of ndvdual asset: b, j = SysVar = b j = b, j Σb, and '. 2
3 To compute the covarance matrx Σ and Ω, go to Tools --- Data Analyss --- Covarance. To carry out matrx operaton, use excel functon MMULT() for matrx multplcaton and TRANSPOSE() for matrx transpose. 3 Notce, the market portfolo have a postve resdual. In ths example, all fors are macro varables (rather than rsk fors) hch are convenent for convertng ves on economy to changes n expected returns. Queston 3: Assume the expected returns of the sx portfolos for year 2004 are: Expected return Portfolo : Small groth Portfolo 2: Small neutral Portfolo 3: Small value Portfolo 4: Bg groth Portfolo 5: Bg neutral Portfolo : Bg value In addton, e assume every nvestor (ncludng yourself) has a rsk averson of and the rsk free rate s 3%. What ll be the optmal portfolo eghts? We solve ths problem usng the MarkotzII spreadsheet. Compute standard devatons and correlatons of the sx portfolos usng the hstorcal returns. Input expected returns, standard devatons, correlatons, rsk averson and rsk free rate nto the MarkotzII and use solver to fnd the optmal portfolo eghts that maxmze the slope of the CAL. Number of securtes: Fll n Names No Name Fron Expected Standard Correlatons Return Devaton port port 3 port 5 port port 2 port 4 port 2 port port port port port port port port port port port.00 Corr OK? YES Results: Portfolo's Expected Return Portfolo's Standard Devaton Rsk Free Rate Slope of CAL Rsk Averson Coeffcent: A= Weght on optmal rsky portfolo: x*=.00 All nvestor ll hold only the optmal rsky portfolo (x*=) and the eghts of the optmal rsky portfolo concde th those of the current market portfolo. In another ords, under the expected returns n ths questons, all nvestor chooses to hold the same market portfolo. We call these expected returns --- the consensus expected returns. Queston 4: You expect the ol nflaton to be 25% hgher than the consensus forecast. Ho ll your ve on the ol for affect your expectaton (measured as devaton from the consensus) on other three fors? 3 Remember to press CRTL+SHIFT+ENTER at the same tme for matrx operaton n Excel. 3
4 Snce all fors are correlated. If you expect ol nflaton to devate from consensus, you ould also expect other fors to devate. To determne the mp of for surprse on ol nflaton on other fors, e compute the ol beta as: ol β = cov( F, F ) / var( F ). The ol beta of for s just the slope coeffcent hen e regress for on ol nflaton for. Intutvely, t captures the senstvty of other for to changes n ol nflaton. Therefore e have: expected change n F = The for surprses are computed as: ol β ol ol * expected change n ol nflaton. Mkt excess return change n term spread change n credt spread Ol nflaton ol beta for surprse -3.7% -0.2% -0.08% 25.00% Queston 5: What are the ne expected returns of the sx portfolos and the market portfolo under your ve? The ne expected returns are just consensus expected returns plus changes due to for surprses. E 4 b, j F j. = ( R ve) = Consensus ER + The market expected return s agan s eghted-average of expected returns of the sx portfolos. Queston : Suppose you can only nvest n the market portfolo and the rsk free asset. Gven the ve on the ol nflaton, hat ll be the fron nvested n the market, and ho much ll be nvested n the rsk free asset? Compute the expected return on your portfolo and ts standard devaton. What ould be the expected return and the standard devaton f you are forced to hold the market portfolo nstead? What s the certanty equvalent return on the to portfolos -- the combnaton of the market and the rsk free you chose to hold gven the ve, and f you are forced to hold the market? Input the ne expected returns under the ve nto MarkotzII and read off the eght on the optmal rsky portfolo (x*) to be Ths s the fron you should nvest n the market portfolo gven your ve. 4
5 Number of securtes: Fll n Names No Name Fron Expected Standard Correlatons Return Devaton port port 3 port 5 port port 2 port 4 port 2 port port port port port port port port port port port.00 Corr OK? YES Results: Expected return Portfolo's Expected Return Std dev Portfolo's Standard Devaton Certanty Equvalent return Rsk Free Rate Slope of CAL Rsk Averson Coeffcent: A= Weght on optmal rsky portfolo: x*= 0.45 Table 2 summarzes the man results for varous cases. Frst thng to note s that the Sharpe rato comes don sgnfcantly under your ve on ol nflaton snce the ol shock has a substantal negatve mp on expected returns. Consequently, the rsky asset becomes less favorably aganst the rsk free asset. That s hy you choose to nvest more than half of your ealth n rsk free asset hen the rsk free asset s alloed. The certanty equvalent return s 3.80%. Hoever f you are forced to hold the market portfolo only (x=), the certanty equvalent return drops to 2.4%. Ths means that smply by the rsk free asset, there s an mprovement of.% (3.80%-2.4%) n terms of certanty equvalent return. For a total nvestment of $500,000, ths s the same as an ncrease n value at the end of the year of $500,000*.% = $5,782, hch s not a small amount. Queston 7: Suppose you can no n addton choose a dfferent combnaton of the sx portfolos to construct the optmal rsky asset: hat ould be the eghts assgned to each portfolo? What are the expected return and the standard devaton of ths portfolo gven the ve? What fron ll you hold n the rsk free and ths rsky asset? What are the expected return and the standard devaton of your portfolo? What s the certanty equvalent? Ho much do you gan by beng able to use a dfferent rsky asset than beng forced to choose a combnaton of the market and the rsk free? In ths case, nvestor ll form a ne optmal rsky portfolo by optmally nvestng n the sx assets to maxmze the slope of CAL under the ne expected returns. 5
6 Number of securtes: Fll n Names No Name Fron Expected Standard Correlatons Return Devaton port port 3 port 5 port port 2 port 4 port 2 port port port port port port port port port port port.00 Corr OK? YES Results: Expected return Portfolo's Expected Return Std dev Portfolo's Standard Devaton.02 Certanty Equvalent return Rsk Free Rate Slope of CAL Rsk Averson Coeffcent: A= Weght on optmal rsky portfolo: x*= 0.3 Both Sharpe rato and certanty equvalent return ncrease as a result of re-optmzaton after changes n expected returns (Table 2). Compare to the case hen you can only hold the market and rsk free asset (n queston ), the certanty equvalent return ncreases by.35% (5.4%-3.80%). Hoever, you observe extreme postons n some assets hch may not be desrable. 4 Queston 8: Sho that t s possble to thnk of the ne optmal rsky portfolo as a portfolo of the current market portfolo and an ACTIVE portfolo that s managed usng the ve. What s the composton of the ACTIVE portfolo; ts expected return; standard devaton and Sharpe Rato? Snce the market portfolo eght n asset and the ACTIVE portfolo eght n asset should add up to be the optmal rsky portfolo s eght n asset, or, +, = opt,, e can solve for the ACTIVE portfolo eght as:, = opt,,. In addton, e kno: hch mples: =, = = =, =, In another ords, the ACTIVE portfolo s a zero-nvestment strategy here the long and short poston net out and the net nvestment s zero. Once e have the eghts of the ACTIVE portfolo, e can compute the expected return and standard devaton and Sharpe rato n the usual ay: opt, = 0. 4 In f, no the optmal eghts solver calculates are more senstve to the precson level settng n solver. You mght ant to choose a hgh precson level. To do that, go to solver --- optons and choose a very small number n the precson feld.
7 E ( R ve) = =, E( R ve), std. dev = Ω ' and SR = E( R ve) Rf. std. dev Queston 9: What s the alpha th respect to the CAPM of the ACTIVE portfolo from the perspectve of the consensus ve? What s the alpha (gven the expected return on the market gven your ve)? What s the beta? The CAPM alpha s defned as: α = ER Rf β α ve = E ( ER Rf ), [ Rf ]. ( R ve) Rf β E ( R ve) All the expected returns can be computed as usual. To determne the CAPM beta, make use of ts defnton: β cov( R, R = var( R ) ) = Ω Ω ' '. Under the consensus ve, CAPM holds th respect to the current market portfolo. Therefore all asset should have zero alpha ncludng the ACTIVE portfolo. Hoever, the current marker portfolo s no longer the market portfolo under the ol ve (as seen n Q7, you ould rather hold a dfferent optmal rsky portfolo), therefore CAPM does not hold th the current market portfolo and the ACTIVE portfolo has a huge postve alpha of more than 20%. Queston 0: Suppose you can not short sell any asset. What ould be the ne optmal rsky portfolo? Agan sho that ths can be decomposed nto the current market portfolo plus an ve portfolo. What s the expected return, standard devaton, Sharpe Rato of ths ve portfolo? What s the alpha? What s the beta? What s the composton of the nvestor's portfolo? What s the certanty equvalent return? By ho much has the certanty equvalent of the nvestor's portfolo come don by the no short sale constrant gven the ve? Ths queston s smlar to Q7 th addtonal constrants that all eghts must be greater or equal to 0. Usng solver, e obtan the eghts of the constraned optmal rsky portfolo hch nvests only n to assets. Alpha, beta and Sharpe rato of the ACTIVE portfolo n ths case can be computed n a smlar fashon as n Q8 and Q9. 7
8 Number of securtes: Fll n Names No Name Fron Expected Standard Correlatons Return Devaton port port 3 port 5 port port 2 port 4 port 2 port port port port port port port port port port port.00 Corr OK? YES Results: Expected return Portfolo's Expected Return Std dev Portfolo's Standard Devaton Certanty Equvalent return Rsk Free Rate Slope of CAL Rsk Averson Coeffcent: A= Weght on optmal rsky portfolo: x*= 0.3 The no-short-sale constrant reduces the certanty equvalent return from 5.4% n Q7 to 4.05%. Hoever, t s stll slghtly hgher than that n Q here nvestor s restrcted to only the current market portfolo and the rsk free asset. 8
9 Table : For Loadngs and T-values for the sx portfolos For Loadngs port term spread credt spread ol T-values port term spread credt spread ol
10 Table 2: Optmal eghts, expected returns, standard devatons, certanty equvalent returns and Sharpe ratos under varous cases hold market under consensus ve (Q3) hold market + rf under the ol ve (Q) hold market only under the ol ve (Q) hold optmal rsky port + rf under the ol ve (Q7) hold optmal rsky port (th no short sale constrant + rf under the ol ve (Q0) eght on rsky port 00.00% 45.37% 00.00% 3.0% 3.37% eght on rskfree 0.00% 54.3% 0.00% 8.99% 3.3% Expected return 0.75% 4.59%.52% 7.29% 5.09% std-dev 7.94% 8.4% 7.94% 3.34% 9.33% certanty equ ret.88% 3.80% 2.4% 5.4% 4.05% Sharpe rato
Mutual Funds and Management Styles. Active Portfolio Management
utual Funds and anagement Styles ctve Portfolo anagement ctve Portfolo anagement What s actve portfolo management? How can we measure the contrbuton of actve portfolo management? We start out wth the CP
More informationChapter 11: Optimal Portfolio Choice and the Capital Asset Pricing Model
Chapter 11: Optmal Portolo Choce and the CAPM-1 Chapter 11: Optmal Portolo Choce and the Captal Asset Prcng Model Goal: determne the relatonshp between rsk and return key to ths process: examne how nvestors
More informationRisk and Return: The Security Markets Line
FIN 614 Rsk and Return 3: Markets Professor Robert B.H. Hauswald Kogod School of Busness, AU 1/25/2011 Rsk and Return: Markets Robert B.H. Hauswald 1 Rsk and Return: The Securty Markets Lne From securtes
More informationProblem Set 6 Finance 1,
Carnege Mellon Unversty Graduate School of Industral Admnstraton Chrs Telmer Wnter 2006 Problem Set 6 Fnance, 47-720. (representatve agent constructon) Consder the followng two-perod, two-agent economy.
More informationFinal Exam. 7. (10 points) Please state whether each of the following statements is true or false. No explanation needed.
Fnal Exam Fall 4 Econ 8-67 Closed Book. Formula Sheet Provded. Calculators OK. Tme Allowed: hours Please wrte your answers on the page below each queston. (5 ponts) Assume that the rsk-free nterest rate
More informationPrinciples of Finance
Prncples of Fnance Grzegorz Trojanowsk Lecture 6: Captal Asset Prcng Model Prncples of Fnance - Lecture 6 1 Lecture 6 materal Requred readng: Elton et al., Chapters 13, 14, and 15 Supplementary readng:
More informationChapter 11: Optimal Portfolio Choice and the Capital Asset Pricing Model
Chapter 11: Optmal Portolo Choce and the CAPM-1 Chapter 11: Optmal Portolo Choce and the Captal Asset Prcng Model Goal: determne the relatonshp between rsk and return => key to ths process: examne how
More informationElton, Gruber, Brown, and Goetzmann. Modern Portfolio Theory and Investment Analysis, 7th Edition. Solutions to Text Problems: Chapter 9
Elton, Gruber, Brown, and Goetzmann Modern Portfolo Theory and Investment Analyss, 7th Edton Solutons to Text Problems: Chapter 9 Chapter 9: Problem In the table below, gven that the rskless rate equals
More informationElton, Gruber, Brown and Goetzmann. Modern Portfolio Theory and Investment Analysis, 7th Edition. Solutions to Text Problems: Chapter 4
Elton, Gruber, Brown and Goetzmann Modern ortfolo Theory and Investment Analyss, 7th Edton Solutons to Text roblems: Chapter 4 Chapter 4: roblem 1 A. Expected return s the sum of each outcome tmes ts assocated
More informationConsumption Based Asset Pricing
Consumpton Based Asset Prcng Mchael Bar Aprl 25, 208 Contents Introducton 2 Model 2. Prcng rsk-free asset............................... 3 2.2 Prcng rsky assets................................ 4 2.3 Bubbles......................................
More informationTests for Two Correlations
PASS Sample Sze Software Chapter 805 Tests for Two Correlatons Introducton The correlaton coeffcent (or correlaton), ρ, s a popular parameter for descrbng the strength of the assocaton between two varables.
More informationInvestment Management Active Portfolio Management
Investment Management Actve Portfolo Management Road Map The Effcent Markets Hypothess (EMH) and beatng the market Actve portfolo management Market tmng Securty selecton Securty selecton: Treynor&Black
More informationTo Rebalance or Not to Rebalance? Edward Qian, PhD, CFA PanAgora Asset Management
To Rebalance or Not to Rebalance? Edward Qan, PhD, CFA PanAgora Asset anagement To Rebalance or Not to Rebalance It s not THE QUESTION but a very mportant one»to rebalance fxed-weght (FW); Not to Buy and
More informationProblems to be discussed at the 5 th seminar Suggested solutions
ECON4260 Behavoral Economcs Problems to be dscussed at the 5 th semnar Suggested solutons Problem 1 a) Consder an ultmatum game n whch the proposer gets, ntally, 100 NOK. Assume that both the proposer
More informationFORD MOTOR CREDIT COMPANY SUGGESTED ANSWERS. Richard M. Levich. New York University Stern School of Business. Revised, February 1999
FORD MOTOR CREDIT COMPANY SUGGESTED ANSWERS by Rchard M. Levch New York Unversty Stern School of Busness Revsed, February 1999 1 SETTING UP THE PROBLEM The bond s beng sold to Swss nvestors for a prce
More informationINTRODUCTION TO MACROECONOMICS FOR THE SHORT RUN (CHAPTER 1) WHY STUDY BUSINESS CYCLES? The intellectual challenge: Why is economic growth irregular?
INTRODUCTION TO MACROECONOMICS FOR THE SHORT RUN (CHATER 1) WHY STUDY BUSINESS CYCLES? The ntellectual challenge: Why s economc groth rregular? The socal challenge: Recessons and depressons cause elfare
More informationEvaluating Performance
5 Chapter Evaluatng Performance In Ths Chapter Dollar-Weghted Rate of Return Tme-Weghted Rate of Return Income Rate of Return Prncpal Rate of Return Daly Returns MPT Statstcs 5- Measurng Rates of Return
More informationIntroduction. Chapter 7 - An Introduction to Portfolio Management
Introducton In the next three chapters, we wll examne dfferent aspects of captal market theory, ncludng: Brngng rsk and return nto the pcture of nvestment management Markowtz optmzaton Modelng rsk and
More information4. Greek Letters, Value-at-Risk
4 Greek Letters, Value-at-Rsk 4 Value-at-Rsk (Hull s, Chapter 8) Math443 W08, HM Zhu Outlne (Hull, Chap 8) What s Value at Rsk (VaR)? Hstorcal smulatons Monte Carlo smulatons Model based approach Varance-covarance
More informationMultifactor Term Structure Models
1 Multfactor Term Structure Models A. Lmtatons of One-Factor Models 1. Returns on bonds of all maturtes are perfectly correlated. 2. Term structure (and prces of every other dervatves) are unquely determned
More informationMgtOp 215 Chapter 13 Dr. Ahn
MgtOp 5 Chapter 3 Dr Ahn Consder two random varables X and Y wth,,, In order to study the relatonshp between the two random varables, we need a numercal measure that descrbes the relatonshp The covarance
More informationII. Random Variables. Variable Types. Variables Map Outcomes to Numbers
II. Random Varables Random varables operate n much the same way as the outcomes or events n some arbtrary sample space the dstncton s that random varables are smply outcomes that are represented numercally.
More informationECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE)
ECONOMETRICS - FINAL EXAM, 3rd YEAR (GECO & GADE) May 17, 2016 15:30 Frst famly name: Name: DNI/ID: Moble: Second famly Name: GECO/GADE: Instructor: E-mal: Queston 1 A B C Blank Queston 2 A B C Blank Queston
More informationProspect Theory and Asset Prices
Fnance 400 A. Penat - G. Pennacch Prospect Theory and Asset Prces These notes consder the asset prcng mplcatons of nvestor behavor that ncorporates Prospect Theory. It summarzes an artcle by N. Barbers,
More informationAsset Management. Country Allocation and Mutual Fund Returns
Country Allocaton and Mutual Fund Returns By Dr. Lela Heckman, Senor Managng Drector and Dr. John Mulln, Managng Drector Bear Stearns Asset Management Bear Stearns Actve Country Equty Executve Summary
More informationMidterm Exam. Use the end of month price data for the S&P 500 index in the table below to answer the following questions.
Unversty of Washngton Summer 2001 Department of Economcs Erc Zvot Economcs 483 Mdterm Exam Ths s a closed book and closed note exam. However, you are allowed one page of handwrtten notes. Answer all questons
More informationOptimal Portfolio Construction (A Case Study of LQ45 Index in Indonesia Stock Exchange)
Internatonal Journal of Scence and Research (IJSR) ISS (Onlne): 319-7064 Index Coperncus Value (013): 6.14 Impact Factor (013): 4.438 Optmal Portfolo Constructon (A Case Study of LQ45 Index n Indonesa
More informationc slope = -(1+i)/(1+π 2 ) MRS (between consumption in consecutive time periods) price ratio (across consecutive time periods)
CONSUMPTION-SAVINGS FRAMEWORK (CONTINUED) SEPTEMBER 24, 2013 The Graphcs of the Consumpton-Savngs Model CONSUMER OPTIMIZATION Consumer s decson problem: maxmze lfetme utlty subject to lfetme budget constrant
More informationTopic 6 Introduction to Portfolio Theory
Topc 6 Introducton to ortfolo Theory 1. racttoners fundamental ssues. ortfolo optmzaton usng Markowtz effcent fronter 3. ortfolo dversfcaton & beta coeffcent 4. Captal asset prcng model 04/03/015 r. Dder
More informationTests for Two Ordered Categorical Variables
Chapter 253 Tests for Two Ordered Categorcal Varables Introducton Ths module computes power and sample sze for tests of ordered categorcal data such as Lkert scale data. Assumng proportonal odds, such
More informationQuiz on Deterministic part of course October 22, 2002
Engneerng ystems Analyss for Desgn Quz on Determnstc part of course October 22, 2002 Ths s a closed book exercse. You may use calculators Grade Tables There are 90 ponts possble for the regular test, or
More informationChapter 5 Student Lecture Notes 5-1
Chapter 5 Student Lecture Notes 5-1 Basc Busness Statstcs (9 th Edton) Chapter 5 Some Important Dscrete Probablty Dstrbutons 004 Prentce-Hall, Inc. Chap 5-1 Chapter Topcs The Probablty Dstrbuton of a Dscrete
More informationCh Rival Pure private goods (most retail goods) Non-Rival Impure public goods (internet service)
h 7 1 Publc Goods o Rval goods: a good s rval f ts consumpton by one person precludes ts consumpton by another o Excludable goods: a good s excludable f you can reasonably prevent a person from consumng
More informationChapter 5 Bonds, Bond Prices and the Determination of Interest Rates
Chapter 5 Bonds, Bond Prces and the Determnaton of Interest Rates Problems and Solutons 1. Consder a U.S. Treasury Bll wth 270 days to maturty. If the annual yeld s 3.8 percent, what s the prce? $100 P
More informationLecture 6 Foundations of Finance. Lecture 6: The Intertemporal CAPM (ICAPM): A Multifactor Model and Empirical Evidence
Lecture 6 Foundatons of Fnance Lecture 6: The Intertemporal CAPM (ICAPM): A Multfactor Model and Emprcal Evdence I. Readng. II. ICAPM Assumptons. III. When do ndvduals care about more than expected return
More informationInstitute of Actuaries of India
Insttute of ctuares of Inda Subject CT8-Fnancal Economcs ay 008 Examnaton INDICTIVE SOLUTION II CT8 0508 Q.1 a F0,5,6 1/6-5*ln0,5/0,6 Where, F0,5,6 s forard rate at tme 0 for delvery beteen tme 5 and 6
More informationLecture Note 2 Time Value of Money
Seg250 Management Prncples for Engneerng Managers Lecture ote 2 Tme Value of Money Department of Systems Engneerng and Engneerng Management The Chnese Unversty of Hong Kong Interest: The Cost of Money
More informationEvaluating SEB Investment Strategy`s recommended Mutual Fund Portfolios
MÄLARDALEN UNIVERSITY Stockholm, 010-06-03 Department of Mathematcs Master Thess n Mathematcs Tutor: Lars Pettersson Evaluatng SEB Investment Strategy`s recommended Mutual Fund Portfolos Alexander Rostam
More informationRisk, return and stock performance measures
Rsk, return and stock performance measures MIRELA MOMCILOVIC Hgher School of Professonal Busness Studes Vladmra Perca-Valtera 4, Nov Sad bznscentar@gmal.com http://www.vps.ns.ac.rs/sr/nastavnk.1.30.html?sn=237
More informationHeterogeneity in Expectations, Risk Tolerance, and Household Stock Shares
Heterogenety n Expectatons, Rsk Tolerance, and Household Stock Shares John Amerks Vanguard Group Gábor Kézd Central European Unversty Mnjoon Lee Unversty of Mchgan Matthew D. Shapro Unversty of Mchgan
More informationWhich of the following provides the most reasonable approximation to the least squares regression line? (a) y=50+10x (b) Y=50+x (d) Y=1+50x
Whch of the followng provdes the most reasonable approxmaton to the least squares regresson lne? (a) y=50+10x (b) Y=50+x (c) Y=10+50x (d) Y=1+50x (e) Y=10+x In smple lnear regresson the model that s begn
More informationClearing Notice SIX x-clear Ltd
Clearng Notce SIX x-clear Ltd 1.0 Overvew Changes to margn and default fund model arrangements SIX x-clear ( x-clear ) s closely montorng the CCP envronment n Europe as well as the needs of ts Members.
More informationForecasts in Times of Crises
Forecasts n Tmes of Crses Aprl 2017 Chars Chrstofdes IMF Davd J. Kuenzel Wesleyan Unversty Theo S. Echer Unversty of Washngton Chrs Papageorgou IMF 1 Macroeconomc forecasts suffer from three sources of
More informationChapter 6 Risk, Return, and the Capital Asset Pricing Model
Whch s better? (1) 6% return wth no rsk, or (2) 20% return wth rsk. Chapter 6 Rsk, Return, and the Captal Asset Prcng Model Cannot say - need to know how much rsk comes wth the 20% return. What do we know
More informationModule Contact: Dr P Moffatt, ECO Copyright of the University of East Anglia Version 2
UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton 2012-13 FINANCIAL ECONOMETRICS ECO-M017 Tme allowed: 2 hours Answer ALL FOUR questons. Queston 1 carres a weght of 25%; Queston 2 carres
More informationMoney, Banking, and Financial Markets (Econ 353) Midterm Examination I June 27, Name Univ. Id #
Money, Bankng, and Fnancal Markets (Econ 353) Mdterm Examnaton I June 27, 2005 Name Unv. Id # Note: Each multple-choce queston s worth 4 ponts. Problems 20, 21, and 22 carry 10, 8, and 10 ponts, respectvely.
More information2) In the medium-run/long-run, a decrease in the budget deficit will produce:
4.02 Quz 2 Solutons Fall 2004 Multple-Choce Questons ) Consder the wage-settng and prce-settng equatons we studed n class. Suppose the markup, µ, equals 0.25, and F(u,z) = -u. What s the natural rate of
More informationSurvey of Math: Chapter 22: Consumer Finance Borrowing Page 1
Survey of Math: Chapter 22: Consumer Fnance Borrowng Page 1 APR and EAR Borrowng s savng looked at from a dfferent perspectve. The dea of smple nterest and compound nterest stll apply. A new term s the
More informationMeasuring Bond Portfolio Value At Risk: Us And Taiwan Government Bond Markets Empirical Research
Measurng Bond Portfolo Value At Rsk: Us And Tawan Government Bond Markets Emprcal Research Thomas W. Knowles Stuart Graduate School of Busness Illnos Insttute of Technology, USA knowles@stuart.t.edu Ender
More informationSYSTEMATIC LIQUIDITY, CHARACTERISTIC LIQUIDITY AND ASSET PRICING. Duong Nguyen* Tribhuvan N. Puri*
SYSTEMATIC LIQUIDITY, CHARACTERISTIC LIQUIDITY AND ASSET PRICING Duong Nguyen* Trbhuvan N. Pur* Address for correspondence: Trbhuvan N. Pur, Professor of Fnance Char, Department of Accountng and Fnance
More informationDomestic Savings and International Capital Flows
Domestc Savngs and Internatonal Captal Flows Martn Feldsten and Charles Horoka The Economc Journal, June 1980 Presented by Mchael Mbate and Chrstoph Schnke Introducton The 2 Vews of Internatonal Captal
More informationNotes are not permitted in this examination. Do not turn over until you are told to do so by the Invigilator.
UNIVERSITY OF EAST ANGLIA School of Economcs Man Seres PG Examnaton 2016-17 BANKING ECONOMETRICS ECO-7014A Tme allowed: 2 HOURS Answer ALL FOUR questons. Queston 1 carres a weght of 30%; queston 2 carres
More informationQuantitative Portfolio Theory & Performance Analysis
550.447 Quanttatve ortfolo Theory & erformance Analyss Wee of March 4 & 11 (snow), 013 ast Algorthms, the Effcent ronter & the Sngle-Index Model Where we are Chapters 1-3 of AL: erformance, Rs and MT Chapters
More informationInternational Trade Theory (1/2008) Chulalongkorn University Lecture 5 the Heckscher-Ohlin Model (part II) Kornkarun Cheewatrakoolpong, Ph.D.
Internatonal rade heory (1/2008) Chulalongkorn Unversty ecture 5 the Heckscher-Ohln Model (part II) ornkarun Cheeatrakoolpong, Ph.D. he logc - ake { a1, a1, a2, a2} as constant and manpulate the full employment
More informationUnderstanding Annuities. Some Algebraic Terminology.
Understandng Annutes Ma 162 Sprng 2010 Ma 162 Sprng 2010 March 22, 2010 Some Algebrac Termnology We recall some terms and calculatons from elementary algebra A fnte sequence of numbers s a functon of natural
More information3: Central Limit Theorem, Systematic Errors
3: Central Lmt Theorem, Systematc Errors 1 Errors 1.1 Central Lmt Theorem Ths theorem s of prme mportance when measurng physcal quanttes because usually the mperfectons n the measurements are due to several
More informationElton, Gruber, Brown, and Goetzmann. Modern Portfolio Theory and Investment Analysis, 7th Edition. Solutions to Text Problems: Chapter 16
lton, Gruer, rown, and Goetzmann Modern Portfolo Theory and Investment nalyss, 7th dton Solutons to Text Prolems: hapter 6 hapter 6: Prolem From the text we know that three ponts determne a plane. The
More informationAppendix - Normally Distributed Admissible Choices are Optimal
Appendx - Normally Dstrbuted Admssble Choces are Optmal James N. Bodurtha, Jr. McDonough School of Busness Georgetown Unversty and Q Shen Stafford Partners Aprl 994 latest revson September 00 Abstract
More informationValue of L = V L = VL = VU =$48,000,000 (ii) Owning 1% of firm U provides a dollar return of.01 [EBIT(1-T C )] =.01 x 6,000,000 = $60,000.
OLUTION 1. A company wll call a bond when the market prce of the bond s at or above the call prce. For a zero-coupon bond, ths wll never happen because the market prce wll always be below the face value.
More informationThe Integration of the Israel Labour Force Survey with the National Insurance File
The Integraton of the Israel Labour Force Survey wth the Natonal Insurance Fle Natale SHLOMO Central Bureau of Statstcs Kanfey Nesharm St. 66, corner of Bach Street, Jerusalem Natales@cbs.gov.l Abstact:
More informationDoes Stock Return Predictability Imply Improved Asset Allocation and Performance? Evidence from the U.S. Stock Market ( )
Does Stock Return Predctablty Imply Improved Asset Allocaton and Performance? Evdence from the U.S. Stock Market (1954-00) Puneet Handa * Ashsh war ** Current Draft: November, 004 Key words: Predctablty,
More informationScribe: Chris Berlind Date: Feb 1, 2010
CS/CNS/EE 253: Advanced Topcs n Machne Learnng Topc: Dealng wth Partal Feedback #2 Lecturer: Danel Golovn Scrbe: Chrs Berlnd Date: Feb 1, 2010 8.1 Revew In the prevous lecture we began lookng at algorthms
More informationSpatial Variations in Covariates on Marriage and Marital Fertility: Geographically Weighted Regression Analyses in Japan
Spatal Varatons n Covarates on Marrage and Martal Fertlty: Geographcally Weghted Regresson Analyses n Japan Kenj Kamata (Natonal Insttute of Populaton and Socal Securty Research) Abstract (134) To understand
More informationQuiz 2 Answers PART I
Quz 2 nswers PRT I 1) False, captal ccumulaton alone wll not sustan growth n output per worker n the long run due to dmnshng margnal returns to captal as more and more captal s added to a gven number of
More informationElements of Economic Analysis II Lecture VI: Industry Supply
Elements of Economc Analyss II Lecture VI: Industry Supply Ka Hao Yang 10/12/2017 In the prevous lecture, we analyzed the frm s supply decson usng a set of smple graphcal analyses. In fact, the dscusson
More informationTHE VOLATILITY OF EQUITY MUTUAL FUND RETURNS
North Amercan Journal of Fnance and Bankng Research Vol. 4. No. 4. 010. THE VOLATILITY OF EQUITY MUTUAL FUND RETURNS Central Connectcut State Unversty, USA. E-mal: BelloZ@mal.ccsu.edu ABSTRACT I nvestgated
More information15-451/651: Design & Analysis of Algorithms January 22, 2019 Lecture #3: Amortized Analysis last changed: January 18, 2019
5-45/65: Desgn & Analyss of Algorthms January, 09 Lecture #3: Amortzed Analyss last changed: January 8, 09 Introducton In ths lecture we dscuss a useful form of analyss, called amortzed analyss, for problems
More informationChapter 5 Risk and return
Chapter 5 Rsk and return Instructor s resources Overvew Ths chapter focuses on the fundamentals of the rsk and return relatonshp of assets and ther valuaton. For the sngle asset held n solaton, rsk s measured
More informationWhat is the Impact of Stock Market Contagion on an Investor s Portfolio Choice?
What s the Impact of Stock Market Contagon on an Investor s Portfolo Choce? Ncole ranger Holger Kraft Chrstoph Menerdng Ths verson: prl 29, 2008 Fnance Center Münster, Westfälsche Wlhelms-Unverstät Münster,
More informationLinear Combinations of Random Variables and Sampling (100 points)
Economcs 30330: Statstcs for Economcs Problem Set 6 Unversty of Notre Dame Instructor: Julo Garín Sprng 2012 Lnear Combnatons of Random Varables and Samplng 100 ponts 1. Four-part problem. Go get some
More informationFinance 402: Problem Set 1 Solutions
Fnance 402: Problem Set 1 Solutons Note: Where approprate, the fnal answer for each problem s gven n bold talcs for those not nterested n the dscusson of the soluton. 1. The annual coupon rate s 6%. A
More informationRisk and Returns of Commercial Real Estate: A Property Level Analysis
Rsk and Returns of Commercal Real Estate: A Property Level Analyss Lang Peng Leeds School of Busness Unversty of Colorado at Boulder 419 UCB, Boulder, CO 80309-0419 Emal: lang.peng@colorado.edu Phone:
More informationRisk Reduction and Real Estate Portfolio Size
Rsk Reducton and Real Estate Portfolo Sze Stephen L. Lee and Peter J. Byrne Department of Land Management and Development, The Unversty of Readng, Whteknghts, Readng, RG6 6AW, UK. A Paper Presented at
More informationISE High Income Index Methodology
ISE Hgh Income Index Methodology Index Descrpton The ISE Hgh Income Index s desgned to track the returns and ncome of the top 30 U.S lsted Closed-End Funds. Index Calculaton The ISE Hgh Income Index s
More informationSavings, Wealth and Ricardian Equivalence
Savngs, Wealth and Rcardan Equvalence I. Introducton In the prevous chapter e studed the decson of households to supply hours to the labor market. Ths decson as a statc decson, beng done thn the same perod.
More informationCalibration Methods: Regression & Correlation. Calibration Methods: Regression & Correlation
Calbraton Methods: Regresson & Correlaton Calbraton A seres of standards run (n replcate fashon) over a gven concentraton range. Standards Comprsed of analte(s) of nterest n a gven matr composton. Matr
More informationA MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME
A MODEL OF COMPETITION AMONG TELECOMMUNICATION SERVICE PROVIDERS BASED ON REPEATED GAME Vesna Radonć Đogatovć, Valentna Radočć Unversty of Belgrade Faculty of Transport and Traffc Engneerng Belgrade, Serba
More informationAnswers to exercises in Macroeconomics by Nils Gottfries 2013
. a) C C b C C s the ntercept o the consumpton uncton, how much consumpton wll be at zero ncome. We can thnk that, at zero ncome, the typcal consumer would consume out o hs assets. The slope b s the margnal
More informationMULTIPLE CURVE CONSTRUCTION
MULTIPLE CURVE CONSTRUCTION RICHARD WHITE 1. Introducton In the post-credt-crunch world, swaps are generally collateralzed under a ISDA Master Agreement Andersen and Pterbarg p266, wth collateral rates
More informationRisk based equity cost calculation in banking *
Rsk based equty cost calculaton n bankng * Mark Wahrenburg Unversty of Cologne, 50923 Cologne, Germany Rajeev De Mello McKnsey and Company, 8703 Erlenbach/Zürch, Swtzerland August 1993 The objectve of
More informationLikelihood Fits. Craig Blocker Brandeis August 23, 2004
Lkelhood Fts Crag Blocker Brandes August 23, 2004 Outlne I. What s the queston? II. Lkelhood Bascs III. Mathematcal Propertes IV. Uncertantes on Parameters V. Mscellaneous VI. Goodness of Ft VII. Comparson
More informationTHE RELATIONSHIP BETWEEN AVERAGE ASSET CORRELATION AND DEFAULT PROBABILITY
JULY 22, 2009 THE RELATIONSHIP BETWEEN AVERAGE ASSET CORRELATION AND DEFAULT PROBABILITY AUTHORS Joseph Lee Joy Wang Jng Zhang ABSTRACT Asset correlaton and default probablty are crtcal drvers n modelng
More informationARE BENCHMARK ASSET ALLOCATIONS FOR AUSTRALIAN PRIVATE INVESTORS OPTIMAL?
ARE BENCHMARK ASSET ALLOCATIONS FOR AUSTRALIAN PRIVATE INVESTORS OPTIMAL? Publshed n the Journal of Wealth Management, 2009, vol. 12, no. 3, pp. 60-70. Lujer Santacruz and Dr Peter J. Phllps Lecturer and
More informationStochastic ALM models - General Methodology
Stochastc ALM models - General Methodology Stochastc ALM models are generally mplemented wthn separate modules: A stochastc scenaros generator (ESG) A cash-flow projecton tool (or ALM projecton) For projectng
More informationSampling Distributions of OLS Estimators of β 0 and β 1. Monte Carlo Simulations
Addendum to NOTE 4 Samplng Dstrbutons of OLS Estmators of β and β Monte Carlo Smulatons The True Model: s gven by the populaton regresson equaton (PRE) Y = β + β X + u = 7. +.9X + u () where β = 7. and
More informationLow-risk anomaly everywhere: Evidence from equity sectors
Low-rsk anomaly everywhere: Evdence from equty sectors Forthcomng: Rsk-Based and Factor Investng, Elsever Scentfc Publcatons, September 2015 Raul Leote de Carvalho s deputy-head of fnancal engneerng at
More informationEconomics 1410 Fall Section 7 Notes 1. Define the tax in a flexible way using T (z), where z is the income reported by the agent.
Economcs 1410 Fall 2017 Harvard Unversty Yaan Al-Karableh Secton 7 Notes 1 I. The ncome taxaton problem Defne the tax n a flexble way usng T (), where s the ncome reported by the agent. Retenton functon:
More informationReal Exchange Rate Fluctuations, Wage Stickiness and Markup Adjustments
Real Exchange Rate Fluctuatons, Wage Stckness and Markup Adjustments Yothn Jnjarak and Kanda Nakno Nanyang Technologcal Unversty and Purdue Unversty January 2009 Abstract Motvated by emprcal evdence on
More informationChapter 10 Making Choices: The Method, MARR, and Multiple Attributes
Chapter 0 Makng Choces: The Method, MARR, and Multple Attrbutes INEN 303 Sergy Butenko Industral & Systems Engneerng Texas A&M Unversty Comparng Mutually Exclusve Alternatves by Dfferent Evaluaton Methods
More informationOn the Style Switching Behavior of Mutual Fund Managers
On the Style Swtchng Behavor of Mutual Fund Managers Bart Frjns Auckland Unversty of Technology, Auckland, New Zealand Auckland Centre for Fnancal Research Aaron Glbert Auckland Unversty of Technology,
More informationTime Diversification in Pension Savings
WORKING PAPER - 26 August 2005 Tme Dversfcaton n Penson Savngs Anders Karlsson 1 Department of Fnance, School of Busness, Stockholm Unversty S-106 91 Stockholm, Sweden 1 PhD. Canddate, Fnance. E-mal aka@fek.su.se,
More informationHarry M. Markowitz. Investors Do Not Get Paid for Bearing Risk 1
Investors Do Not Get Pad for Bearng Rsk Harry M. Markowtz The relatonshp between the excess return of each securty and ts beta, where beta s defned as ts regresson aganst the return on the market portfolo,
More informationCHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS
CHAPTER 9 FUNCTIONAL FORMS OF REGRESSION MODELS QUESTIONS 9.1. (a) In a log-log model the dependent and all explanatory varables are n the logarthmc form. (b) In the log-ln model the dependent varable
More informationFinancial Risk Management in Portfolio Optimization with Lower Partial Moment
Amercan Journal of Busness and Socety Vol., o., 26, pp. 2-2 http://www.ascence.org/journal/ajbs Fnancal Rsk Management n Portfolo Optmzaton wth Lower Partal Moment Lam Weng Sew, 2, *, Lam Weng Hoe, 2 Department
More informationIND E 250 Final Exam Solutions June 8, Section A. Multiple choice and simple computation. [5 points each] (Version A)
IND E 20 Fnal Exam Solutons June 8, 2006 Secton A. Multple choce and smple computaton. [ ponts each] (Verson A) (-) Four ndependent projects, each wth rsk free cash flows, have the followng B/C ratos:
More informationEfficient Project Portfolio as a Tool for Enterprise Risk Management
Effcent Proect Portfolo as a Tool for Enterprse Rsk Management Valentn O. Nkonov Ural State Techncal Unversty Growth Traectory Consultng Company Enterprse Rsk Management Symposum Socety of Actuares Chcago,
More informationMathematical Thinking Exam 1 09 October 2017
Mathematcal Thnkng Exam 1 09 October 2017 Name: Instructons: Be sure to read each problem s drectons. Wrte clearly durng the exam and fully erase or mark out anythng you do not want graded. You may use
More informationMulti-Alpha Equity Portfolios: An Integrated Risk Budgeting Approach for Constrained Robust Portfolios WHITE PAPER
WHITE PAPER Mult-Alpha Equty Portfolos: An Integrated Rsk Budgetng Approach for Constraned Robust Portfolos For professonal nvestors - MAY 2013 2 - Mult-Alpha Equty Portfolos: An Integrated Rsk Budgetng
More informationDiscounted Cash Flow (DCF) Analysis: What s Wrong With It And How To Fix It
Dscounted Cash Flow (DCF Analyss: What s Wrong Wth It And How To Fx It Arturo Cfuentes (* CREM Facultad de Economa y Negocos Unversdad de Chle June 2014 (* Jont effort wth Francsco Hawas; Depto. de Ingenera
More informationMeasures of Spread IQR and Deviation. For exam X, calculate the mean, median and mode. For exam Y, calculate the mean, median and mode.
Part 4 Measures of Spread IQR and Devaton In Part we learned how the three measures of center offer dfferent ways of provdng us wth a sngle representatve value for a data set. However, consder the followng
More information