CFA L2 Apostila 01 Exame 2018 - COMPLETA IMPRESSÃO

Curso Preparatório para o Exame CFA – Level 2 CFA L2 PARTE 1 Exame 2018 Provided by A FK Partners tem orgulho de usar Papel Reciclado.

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FK Partners – 2018 CFA Level 2 Course Introduction Darrin Kerr, CFA Managing Partner  FK Partners darrin.kerr@fkpartners.com About FK Partners • Founded in 2004 in Brazil, FK Partners contributes in a personalized  way to the training and qualification of people who seek more  knowledge in finance, financial certifications or who aim to study abroad. We work in partnership with our students to achieve success,  using education as a tool for development and personal growth. FK Partners is the exclusive distributor in South America of Kaplan  Schweser test preparation material for financial certifications, including for the CFA, FRM and CAIA exams. • Kaplan Schweser is the world leader in providing premier CFA exam  prep materials and continues to be the most trusted name in the  industry. 3 ©2018 FK Partne

Introdução CFA L22018 CFA® Program FK Partners Course Offerings 1 • Financial Certification Preparation: CFA, FRM, CFP, CGA, CEA, CNPI, PQO, Ancord, FBB, CPA 10/20, CA‐300/400/600 • Financial Training: Financial Modeling, Financial Statement Analysis, Valuation, Corporate Credit Analysis, Project Finance Modeling, M&A, Private Equity and LBO, Investor Relations, Derivatives • Study Abroad Preparation: GMAT, GRE, SAT, ACT, TOEFL, Undergrad and Masters Orientation, Admisssions Consulting for MBA, Masters, LLM and PhD candidates 4ers - Exame CFA

First…Congratulations!• Congratulations on passing CFA L1• Passing means that you have demonstrated  the ability and skill to be a successful CFA  candidate• Now…it is time to work harder! 5Candidate Preparation FeedbackAVERAGE HOURS PREPARING FOR  ACTUAL VS. THE EXAM EXPECTED TIME TO  PREPARESource: CFA Institute ©2018 FK Partne

Introdução CFA L2 The CFA Level 2 Exam• Are you ready for Level 2?• MORE difficult and time consuming (No  way!!!)• Requires major commitment• The “get stuck” test!!!! 6 2 2018 CFA Level 2 Exam Format • Morning/Afternoon Sessions – 180 Minutes each – 10 Item Sets each – 6 Question Item Sets – 3.0 minutes each • Each Item set is 5% of the Exam! • Multiple choice – 3 choices • Integrated questions 8ers - Exame CFA

Topic Area Weights by LevelEthical and Professional Standards Level I Level II Level III 15 10‐15 10‐15 0Quantitative Methods 12 5‐10 5‐15 5‐10 0Economics 10 15‐20 0 5‐15 5‐15Financial Reporting and Analysis 20 15‐25 10‐20 10‐20 5‐15Corporate Finance 7 5‐15 5‐15 5‐10 40‐55Equity Investments 10 5‐10Fixed Income 10Derivatives 5ASlotuercren: CaFtAi  Ivnseti tIuntev:  wewswt.mcfaeinsntittuste.org /cfaprog /courseofstudy/to4picareaweights.htmlPortfolio Management 7 Quant (1‐2 Item Sets)• Correlation and Regression• Multiple Regression and Issues in Regression Analysis• Time‐Series Analysis• Probabilistic Approaches: Scenario Analysis,  Decision Trees, and Simulations 11 ©2018 FK Partne

Introdução CFA L2 Ethics (2‐3 Item Sets)• Code of Ethics and Standards of Professional  Conduct• Guidance for Standards I‐VII• CFA Institute Research Objectivity Standards• Trade Allocation: Fair Dealing and Disclosure• Changing Investment Objectives 10 Economics (1‐2 Item Sets)• Currency Exchange Rates: Understanding Equilibrium Value• Economic Growth and the Investment Decision• Economics of Regulationers - Exame CFA 12 3

Financial Reporting & Analysis (3‐4 Item Sets)• Inter‐Corporate Investment Accounting• Employee Compensation: Post‐Employment and Share‐Based (Pension Accounting)• Multinational Operations• Evaluating Quality of Financial Reports• Integration of Financial Statement Analysis Techniques 13 Equity (3‐5 Item Sets)• Equity Valuation: Applications and Processes• Return Concepts• Industry and Company Analysis• Discounted Dividend Valuation• Free Cash Flow Valuation• Market‐Based Valuation: Price and Enterprise  Value Multiples• Residual Income Valuation• Private Company Valuation 15 ©2018 FK Partne

Corporate Finance Introdução CFA L2 (1‐3 Item Sets) 14• Capital Budgeting• Capital Structure• Dividends and Share Repurchases• Corporate Performance, Governance, and Business Ethics• Corporate Governance• Mergers & Acquisitions Fixed Income (2‐4 Item Sets)• The Term Structure and Interest Rate Dynamics• The Arbitrage Free Valuation Framework• Valuation and Analysis: Bonds with Embedded Options• Credit Analysis Models• Credit Default Swaps 16ers - Exame CFA 4

Derivatives (1‐3 Item Sets)• Pricing and Valuation of Forward Commitments• Valuation of Contingent Claims• Derivative Strategies 17 Portfolio Management (1‐2 Item Sets)• The Portfolio Management Process• An Introduction to Multifactor Models• Measuring and Managing Market Risk• Economics and Investment Markets• Analysis and Active Portfolio Management• Algorithmic Trading and High‐Frequency Trading 19 ©2018 FK Partne

Introdução CFA L2 Alternative Investments (1‐2 Item Sets)• Private Real Estate Investments• Publicly Traded Real Estate Securities• Private Equity Valuation• Commodities and Commodity Derivatives 18 June 2018 Costs for Level 2 Candidates Level 2 CFA Exam enrollment fee  US$ 950*  (includes Level 2 curriculum ebooks) * Costs increase after 14/02/2018.ers - Exame CFA 5

Study Planning• Start your program early (300+ hrs) – 10‐12 hrs/week – 25‐30 weeks (6‐7 months) – 15‐20 hrs/week – 18‐22 weeks (4‐5 months)• Study Ethics more than once• Lots of practice exams• Study regularly• Starting LATE + not devoting time = FAILUREThe FK Advantage• Over 13 years serving the CFA market in Brazil• Helped over 4.000 CFA Candidates in Brazil• Helped over 50% of all CFA Chartherholders in Brazil• Over 50 years of CFA aggregate teaching experience• FK Partners study method works!!!• Part of the CFA Institute Approved Prep Provider Program• Discounted Pricing on Schweser Material• FK Partners Coaching and Support Our goal is for you  to PASS!!! ©2018 FK Partne

Introdução CFA L2 FK Partners Study Plan• Start Studying in November• Read all material until end of March – 10‐15 hrs per week• April – Review and Exercises – 15‐20 hrs per week• May/June – Tests, Tests, Tests – 20+ hrs per week – At LEAST 4 tests (6 is better) The FK Partners CFA Course 6 Live Course – Sao Paulo – Over 100 Hours of Live Classes and Exercise  Resolution Sessions (Power Sessions)  – 2 Mini‐Mock Tests – 1 Full Mock Test – Live Mock Test Exercise Resolution Classes • Kaplan‐Schweser Study Material • Integrated class PPTs and Study materials • FK Coaching and Support for help with test  topic doubts and student study plansers - Exame CFA

Our Partners 25 ©2018 FK Partne

Introdução CFA L2 Thank you!!!  Questions???ers - Exame CFA 7

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Fixed Income Investments Study Session 3Quantitative Methods for Valuation Topic Weight: 5–10% Fixed Income Investments Quantitative MethodsQuantitative Methods9. Correlation and Regression ©2018 FK Pa

SS 03 - Quantitative Methods for Valuation Fixed Income Investments Study Session 3Quantitative Methods for Valuation9. Correlation and Regression10. Multiple Regression and Issues in Regression Analysis11. Time-Series Analysis12. Scenario Analysis and SimulationLOS 9.a Calculate/Interpret Correlation and RegressionSchweser B1 pg 111, CFAI V1 pg 256A Scatter Plot of Monthly Returns Shows the Rstock relationship between two 2% variables across time: 1% –3% –2% –1% 1% 2% 3% Rmarket –1%© Kaplan, Inc. Imperfect positive –2% correlation (r ≈ .9) 3artners - Exame CFA 1

LOS 9.a Calculate/Interpret Correlation and RegressionSchweser B1 pg 111, CFAI V1 pg 256Interpreting Correlation Coefficient (r)© Kaplan, Inc. 4LOS 9.c Formulate/Determine Correlation and RegressionSchweser B1 pg 116, CFAI V1 pg 274 Example: Testing CorrelationTest statistical significance of  = 0.8185 based on asample size of 10 and  = 5%. Comp-t = 0.8185 10  2  4.03 1 0.81852 Critical-t = 2.306 Because computed-t > critical-t, Reject Null© Kaplan, Inc. 6 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 9.c Formulate/Determine Correlation and RegressionSchweser B1 pg 116, CFAI V1 pg 274 Testing H0: Correlation = 0 Test of whether the true correlation between two random variables is zero (i.e., variables are truly unrelated) Two-tailed t-test based on the sample correlation, r. With n (pairs of) observations the test statistic is: t=r n2 Degrees of freedom 1 r2 are (n – 2)© Kaplan, Inc. 5LOS 9.d Distinguish Correlation and RegressionSchweser B1 pg 117, CFAI V1 pg 277 Linear Regression Dependent (“Y”) variable: Explained variable Independent (“X”) variable: Explains the variation in the dependent variable Example: Predict number of mortgage applications (dependent) using level of interest rates (independent)© Kaplan, Inc. 7artners - Exame CFA 2

LOS 9.e Describe/Interpret Correlation and RegressionSchweser B1 pg 119, CFAI V1 pg 281Slope Coefficient and InterceptAlgebraic presentation of the slope coefficient andintercept: Error Term Yi = b0 + b1 Xi + ƐDependent Intercept Independent Variable Variable Note that this is Slope 8just the equation Coefficientfor a straight line© Kaplan, Inc.LOS 9.h Calculate Correlation and RegressionSchweser B1 pg 126, CFAI V1 pg 289Predicted Values for “Y” Variable Example: If market return is 1.1%, what is thepredicted stock return according to regressionmodel? Given on exam! Rˆ stock = 0.5% + 0.9 1.1% = 1.5% Note: If actual stock return was 2.3%, the residual is 2.3% – 1.5% = 0.8% (see scatter plot on earlier slide)© Kaplan, Inc. 10 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 9.e Describe/Interpret Correlation and RegressionSchweser B1 pg 119, CFAI V1 pg 281Linear Regression of Monthly Returns“Residual” = actual Rstockminus predicted = 0.8% 2%Intercept bˆ 0 = 0.5% 1% Estimated –3% –2% –1% 1% 2% Rmarketregression equation: 3%Rˆ stock = 0.5% + 0.9Rˆ market –1% Slopˆe b1 = 0.9 –2%© Kaplan, Inc. 9LOS 9.i Calculate/Interpret Correlation and RegressionSchweser B1 pg 126, CFAI V1 pg 289Confidence Interval for Predicted “Y” When building a confidence interval around Y, we use standard error of forecast (sf) due to joint uncertainty from intercept and slope estimates: Yˆ ±  tc × standard error of forecast s2f = SEE2 1+ 1 + (X – X)2   n (n – 1)s2x   Critical t is two-tailed with n – 2 degrees of freedom sf can be approximated by SEE for large samples© Kaplan, Inc. 11artners - Exame CFA 3

LOS 9.i Calculate/Interpret Correlation and RegressionSchweser B1 pg 126, CFAI V1 pg 289Example: Interval for Predicted “Y”Calculate 95% confidence interval for predicted stockreturn when market return is 1.1%, assuming SE offorecast is 0.78. Predicted stock return (point estimate)  1.5   2.20.78  0.2  Yˆ  3.2 5% 2-tailed critical t-value df = 10 12 (reliability factor)© Kaplan, Inc.LOS 9.k Describe Correlation and RegressionSchweser B1 pg 133, CFAI V1 pg 303 Limitations of Regression Relationships change over time (parameter instability) Public knowledge of relationships eliminate usefulness to traders Assumption violations (see later)© Kaplan, Inc. 14 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 9.j Describe/Interpret/Calculate Correlation and RegressionSchweser B1 pg 128, CFAI V1 pg 297 Analysis of Variance (ANOVA)Y Yˆi=bˆ0+bˆ1Xi Yi SSTY Yˆ i Yˆi  b0  b1Xi RSS  n (Yˆi Y )2 i 1 SSE + RSS = SST bˆ0 n – Y)2© Kaplan, Inc. SST  (Yi i 1 X 13 Fixed IncomeQInuavnetsitatmtiveenMtesthods Quantitative Methods 10. Multiple Regression and Issues in Regression Analysisartners - Exame CFA 4

LOS 10.a Formulate/Determine Multiple RegressionSchweser B1 pg 147, CFAI V1 pg 320 Multiple Regression Basic idea: Linear relationship with more than one independent variableDependent variable Independent variables Yi = b0 + b1X1i + b2X2i + …+ bk Xki + εi Intercept Slope coefficients© Kaplan, Inc. Error term 16LOS 10.a Formulate/Determine Multiple RegressionSchweser B1 pg 147, CFAI V1 pg 320Formulate Regression EquationHFR = b0 + b1×WSC + b2×HYB + b3×IFC + εwhere:HFR = hedge fund composite index returnsWSC = Wilshire 1750 small-cap index returnsHYB = CSFB high-yield bond index returnsIFC = IFC emerging markets equity index composite returns© Kaplan, Inc. 18 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.a Formulate/Determine Multiple RegressionSchweser B1 pg 147, CFAI V1 pg 320Formulate Regression Equation Suppose we think hedge fund returns (HFR) are explained by returns on*:  Small cap stocks (WSC)  High-yield bonds (HYB)  Emerging markets (IFC) Example: Formulate a multiple regression equation to describe this relationship. *Adapted from Fung and Hsieh, FAJ Sept/Oct 2002 17© Kaplan, Inc.LOS 10.a Formulate/Determine Multiple RegressionSchweser B1 pg 147, CFAI V1 pg 320Formulate Regression Equation Regress HFR on independent variables for January 1994 through September 2001  93 monthly observations (n = 93)  Three independent “X” variables (k = 3) © Kaplan, Inc. 19artners - Exame CFA 5

LOS 10.b Interpret Multiple RegressionSchweser B1 pg 148, CFAI V1 pg 325 Regression Output: ExampleVariable bi Sbi t tstat  bib0 0.008 0.001 8.0 SbiWSC 0.278 0.022 ???HYB 0.112 0.081 1.4IFC 0.101 0.017 5.9Regression sum of squares = 2,277.6Total sum of squares = 2,600.0© Kaplan, Inc. 20LOS 10.i Evaluate/Analyze Multiple RegressionSchweser B1 pg 159, CFAI V1 pg 333 Mean ANOVA Table SquareSource of Df Sum of (MSR)Variation Squares (MSE) 1Regression n–k–1 (RSS)(explained) n–1 (SSE)Error (SST)(unexplained)Total© Kaplan, Inc. These columns vertically sum 22 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.e Calculate/Interpret Multiple RegressionSchweser B1 pg 153, CFAI V1 pg 331Predicting the Dependent Variable: Example Assume: WSC = 10%, HYB = 3%, IFC = –2% Calculate the predicted HFR value  Plug values into the estimated equation HFR = 0.008 +  0.278  0.10 +  0.112  0.03 +  0.101  –0.02 = 0.037© Kaplan, Inc. 21LOS 10.i Evaluate/Analyze Multiple RegressionSchweser B1 pg 159, CFAI V1 pg 333 Solution: ANOVA TableSource of Df Sum of Squares Mean SquareVariation 3 89 (RSS) 2,277.6 (MSR) 759.2=Regression (MSE) 2,277.6/3(explained) (SSE) 322.4 3.6 =Error 322.4/89(unexplained) Total 92 (SST) 2,600© Kaplan, Inc. R2 = 2, 277.6  87.6% SEE = 3.6  1.9 23 2, 600artners - Exame CFA 6

LOS 10.h Distinguish/Interpret Multiple RegressionSchweser B1 pg 157, CFAI V1 pg 335 Coefficient of Determination R2 in multiple regression indicates that all independent variables (WSC, HYB, and IFC) together explain 87.6% of the variation in HFR.© Kaplan, Inc. 24LOS 10.h Distinguish/Interpret Multiple RegressionSchweser B1 pg 157, CFAI V1 pg 335 Interpreting Adjusted R2 Suppose we add 15 more independent variables:  The R2 increases to 89.0% (from 87.6%).  Adjusted R2 decreases to 86.3% (from 87.2%). Which model should we choose? Point: Choose the model with the highest adjusted R2 (i.e., the model that delivers more with less).© Kaplan, Inc. 26 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.h Distinguish/Interpret Multiple RegressionSchweser B1 pg 157, CFAI V1 pg 335 Adjusted R2 Unadjusted R2 increases when new variables are added. Adjusted R2 applies a penalty factor to reflect R2 quality of added variables. %  n – 1    n – k – 1  Ra2dj  = 1–  1– R2  93 – 1    93 – 3 – 1  Ra2dj  = 1–  1 – 0.876= 0.872 adj R2© Kaplan, Inc. 25 kLOS 10.g Calculate/Interpret Multiple RegressionSchweser B1 pg 155, CFAI V1 pg 333 The F-Statistic Tests whether any of the independent variables explain variation in dependent variable (i.e., test of overall model significance) H0: All slope coefficients = 0 HA: At least one slope coefficient ≠ 0 One-tailed test Reject H0 if F-statistic exceeds critical value Critical F determined by two sets of degrees of freedom (numerator and denominator)© Kaplan, Inc. 27artners - Exame CFA 7

LOS 10.g Calculate/Interpret Multiple RegressionSchweser B1 pg 155, CFAI V1 pg 333 The F-StatisticF = RSS = MSR k MSE – 1) SSE (n – kwith k and (n – k – 1) degrees of freedom Numerator df Denominator df© Kaplan, Inc. 28LOS 10.g Calculate/Interpret Multiple RegressionSchweser B1 pg 155, CFAI V1 pg 333F-Statistic: Hedge Fund: Example F-statistic from the hedge fund return example is:Fstat = 2277.6 = 759.2 = 210.9 3 3.6 322.4 89 Fcritical 3,89 ≈ 2.70 (from F-table) Decision: Reject H0, conclude at least one slope coefficient is not equal to zero© Kaplan, Inc. 30 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.g Calculate/Interpret Correlation and RegressionSchweser B1 pg 155, CFAI V1 pg 333 The F-Statistic DoF 1 Numerator 2345Denominator 1 2 3 > 2.70 . . . 89 100© Kaplan, Inc. 29LOS 10.b Interpret Multiple RegressionSchweser B1 pg 148, CFAI V1 pg 325 Interpreting Coefficients HFR will equal 0.008 if the three independent variables are all zero. All else constant:  1% increase in WSC = 0.278% increase in HFR.  1% increase in IFC = 0.101% increase in HFR. HFR returns are not influenced by HYB. Why? p-value for HYB = 0.137 or t-stat < 2 (see later)© Kaplan, Inc. 31artners - Exame CFA 8

LOS 10.c/d Formulate/Calculate/Interpret Multiple RegressionSchweser B1 pg 149, CFAI V1 pg 322 Regression Coefficient t-Test Typically, a test of statistical significance (i.e., is slope ≠ 0?) H0: bi  0 vs. Ha: bi  0 Use t-test with (n – k – 1) degrees of freedom: tbi = bˆi – bi  estimate  hypothesized  bˆi – 0  slope sbˆi standard error sbˆi standard error© Kaplan, Inc. 32LOS 10.c/d Formulate/Calculate/Interpret Multiple RegressionSchweser B1 pg 149, CFAI V1 pg 322 Example: Test IFC Coefficient Test whether IFC coefficient (b3) is greater than 0.08 at 5% significance level H0: b3 ≤ 0.08 Ha: b3 > 0.08 t-stat = 0.101– 0.08  1.24 0.017 Critical t-value = 1.65 (5%, one-tailed, df = 89) Decision: Fail to reject H0© Kaplan, Inc. 34 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.c/d Formulate/Calculate/Interpret Multiple RegressionSchweser B1 pg 149, CFAI V1 pg 322 Example: Test WSC Coefficient Test statistical significance of coefficient on WSC at 5% significance level H0: b1 = 0 Given in the Fail to Ha: b1 ≠ 0 regression output reject t-stat = 0.278 / 0.022 = 12.6 -2 0 2 12.6 Critical t-value = 2.0 (5%, two-tailed, df = 89) Decision: dRieffjeercetnHt 0fr,ocmonzcelurode b1 significantly Also conclude reject H0 because p-value < 0.05 (see later)© Kaplan, Inc. 33LOS 10.c/d Formulate/Calculate/Interpret Multiple RegressionSchweser B1 pg 149, CFAI V1 pg 322 Interpreting p-Values Another way to test H0 (always agrees with t-test) If p-value < α, then reject H0. Example: If α = 5% (i.e., a 95% confidence level) and the calculated p-value = 0.07, we fail to reject H0. p-value can be viewed as smallest significance level (α) at which we can reject H0.© Kaplan, Inc. 35artners - Exame CFA 9

LOS 10.c/d Formulate/Calculate/Interpret Multiple RegressionSchweser B1 pg 149, CFAI V1 pg 322Interpreting p-Values: ExampleVariable bi Sbi t pb0 0.008 0.001 8.0 <0.001WSC 0.278 0.022 ??? <0.001HYB 0.112 0.081 1.4IFC 0.101 0.017 5.9 0.137 <0.001© Kaplan, Inc. 36 Multiple RegressionSolution: Multiple Regression12/2.6 = 4.62H0: b1≤ 4.62 and H1: b1> 4.62t = (4.6 – 4.62) / 3.5 = – 0.0057 .Critical t (1-tailed, 5% significance, d.o.f = 180 – 3 – 1 = 176) = 1.65Conclusion: Fail to reject the null at 5% (and hence of course at 1%) level ofsignificance.Analyst wants to test the hypothesis that a 2.6% increase in the CPI willresult in an increase in sales of more than 12.0%. The most appropriateconclusion about the hypothesis test is:A. With a 5% level of significance, it would not be possible to reject the null.B. With a 5% level of significance, null would be rejected.C. With a 1% level of significance, null would be rejected.© Kaplan, Inc. 38 ©2018 FK Pa

SS 03 - Quantitative Methods for Valuation Multiple RegressionExample: Multiple RegressionMonthly data from the previous 180 months were used to model sales ($ change insales in 000s) using CPI (% change in the consumer price index); IP (% change inindustrial production); and GDP (% change in GDP).The model estimates (with coefficient standard errors in parentheses underneath) are:sales = 10.2 + (4.6 × CPI) + (5.2 × IP) + (11.7 × GDP) (5.4) (3.5) (5.9) (6.8)Analyst wants to test the hypothesis that a 2.6% increase in the CPI will result in anincrease in sales of more than 12.0%. The most appropriate conclusion about thehypothesis test is:A. With a 5% level of significance, it would not be possible to reject the null.B. With a 5% level of significance, null would be rejected.C. With a 1% level of significance, null would be rejected.© Kaplan, Inc. 37LOS 10.e Calculate/Interpret Multiple RegressionSchweser B1 pg 153, CFAI V1 pg 331Confidence Interval for Coefficient Recall from simple linear regression:  Slope coefficient ± (critical t-stat × standard error of slope) Critical t-stat depends on:  Significance (a.k.a. ) = 1 – confidence level  Degrees of freedom = n – k – 1  Confidence intervals are always two-tailed© Kaplan, Inc. 39artners - Exame CFA 10

LOS 10.e Calculate/Interpret Multiple RegressionSchweser B1 pg 153, CFAI V1 pg 331Confidence Interval for Coefficient: ExampleCalculate a 95% confidence interval for b1. Coefficient0.278 ± (2.0 × 0.022) = (0.234 < b1 < 0.322)Critical t-value Standard error© Kaplan, Inc. 40LOS 10.j Formulate/Interpret Multiple RegressionSchweser B1 pg 164, CFAI V1 pg 336 Dummy Variables: Example Suppose: EPS is regressed against quarter EPSt = b0 + b1Q1t + b2Q2t + b3Q3t + t fourth quarter is omitted quarterwhere:Q1t = 1 if first quarter, 0 otherwiseQ2t = 1 if second quarter, 0 otherwiseQ3t = 1 if third quarter, 0 otherwise© Kaplan, Inc. 42 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.j Formulate/Interpret Multiple RegressionSchweser B1 pg 164, CFAI V1 pg 336 Dummy Variables Dummy variables (a.k.a. binary variables)  Can only take the values of 0 and 1  Can be used in calendar studies  Example: Regressing EPS against binary variables that account for quarter Dummy variable trap: Always use (n – 1) dummy variables to avoid multicollinearity (i.e., 3 dummies for 4 quarters in a year).© Kaplan, Inc. 41LOS 10.j Formulate/Interpret Multiple RegressionSchweser B1 pg 164, CFAI V1 pg 336 Dummy Variables: Example Result: EPSt = 1.25 + 0.75Q1t – 0.20Q2t + 0.10Q3t Question #1: What is the mean fourth quarter EPS?= predicted fourth quarter EPS (for next year)= 1.25 (omitted quarter shows as intercept) Question #2: What’s the predicted first quarter EPS?= intercept + Q1t coefficient = 1.25 + 0.75 = 2.00 43© Kaplan, Inc.artners - Exame CFA 11

LOS 10.f Explain Correlation and RegressionSchweser B1 pg 155, CFAI V1 pg 327Assumptions of Multiple Regression Linear relationship between Y and X No exact linear relationship among X’s Expected value of error term = 0 Variance of error term is constant Errors not serially correlated Error term normally distributed These are related to violations (see later) 44© Kaplan, Inc.LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340Violations of Regression Assumptions For each of the three conditions (heteroskedasticity, serial correlation, and multicollinearity), you should be able to:  Define it  Explain its effect on statistical inference  Detect it  Correct for it© Kaplan, Inc. 46 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340Violations of Regression Assumptions Regression Assumption Condition if Violated Heteroskedasticity Error term has constant variance Serial correlation (autocorrelation) Error terms are not correlated with each other Multicollinearity No exact linear 45 relationship among “X” variables© Kaplan, Inc.LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Heteroskedasticity Arises when error term variance is non-constant Two types of heteroskedasticity:  Type 1: Unconditional heteroskedasticity  Not related to independent variables  Point: Causes no major problems © Kaplan, Inc. 47artners - Exame CFA 12

LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340Heteroskedasticity (continued) Type 2: Conditional heteroskedasticity  Related to independent variables (next slide)  This IS a problem  Impact: t-stats are unreliabletbi = bˆi  estimate Not affected sbˆi standard error Unreliable© Kaplan, Inc. 48LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Detecting Heteroskedasticity Scatter diagrams: Plot residual against each independent variable and against time (see previous slide) Breusch-Pagan test: Regress squared residuals on “X” variables  Point: Test significance of resulting R2 (do the independent variables explain a significant part of the variation in squared residuals?)  H0: No heteroskedasticity  Chi-square test: BP = Rresid2 × n (with k df) 50© Kaplan, Inc. ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Heteroskedasticity (continued) Y Low residual Yˆi = bˆ0+bˆ1xi variance High residual variance 0 X 49© Kaplan, Inc.LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340Correcting for Heteroskedasticity First Method: Use robust standard errors (a.k.a. White-corrected standard errors) Result: Standard errors higher, t-stats lower, and conclusions more accurate Second Method: Use generalized least squares, modifying original equation to eliminate heteroskedasticity© Kaplan, Inc. 51artners - Exame CFA 13

LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Serial Correlation Positive autocorrelation: Each error term tends in same direction as previous term  Common in financial data  T-stats are too high (Type I errors)tbi = bˆi estimate Not affected sbˆi  standard error Too small© Kaplan, Inc. 52LOS 10.k Explain Multiple RegressionSchweser B1 pg 158, CFAI V1 pg 338The DW Statistic: Interpretation DW ≅ 2(1 – r) Three cases: No correlation, positive correlation, and negative correlation  No autocorrelation (ρ = 0)  DW ≅ 2(1 – 0) = 2  Positive serial correlation (ρ = 1)  DW ≅ 2(1 – 1) = 0  Negative serial correlation (ρ = –1)  DW ≅ 2(1 – (– 1) ) = 4© Kaplan, Inc. 54 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Detecting Serial Correlation Scatter plot  Visual inspection of residual errors Durbin-Watson statistic  Formal test of error term correlation  Next slides© Kaplan, Inc. 53LOS 10.k Explain Multiple RegressionSchweser B1 pg 158, CFAI V1 pg 338 The DW Statistic: Interpretation Question: How close to “2” does DW have to be to conclude “no serial correlation”? Answer: Look at ranges in DW tables  Need: Significance level, number of observations (n), and number of independent variables (k)  Table provides pair of critical values (dl and du)  Interpreted on next slide© Kaplan, Inc. 55artners - Exame CFA 14

LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Interpreting DW Values Conclusion: Depends on where calculated value lies relative to dl and du H0: No positive serial correlationReject H0, conclude Do not Positive Serial reject H0Correlation Inconclusive 0 dI du© Kaplan, Inc. 56LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340Correcting for Serial Correlation Preferred method:  Adjust the standard errors upwards using the Hansen method and recalculate t-statistics  Also corrects for conditional heteroskedasticity Result: t-statistics decline, chance of Type I error declines  Improve the specification of the model 58  Explicitly reflect time series nature of data  Incorporate source of autocorrelation© Kaplan, Inc. ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Interpreting DW Values Example Suppose DW = 1.10 in regression with five independent variables and 40 observations The critical DW values are dl = 1.23 and du= 1.79 (from the DW table) Reject Null of “no serial correlation,” conclude positive correlation since 1.10 < 1.23 DW = 1.10© Kaplan, Inc. 0 dI = 1.23 du = 1.79 57LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Multicollinearity Define: Two or more “X” variables are correlated with each other Effects:  Inflates SEs; reduces t-stats; increases chance of Type II errors  Point: t-stats artificially small so variables falsely look unimportant© Kaplan, Inc. 59artners - Exame CFA 15

LOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Detecting MulticollinearityTell-tale signs from regression data:  Observation 1: Significant F-stat (and high R2), but all t-stats insignificant  Observation 2: High correlation between “X” variables (for k = 2 case only)  Observation 3: Sign of coefficient is unexpected Correction:  Omit one or more of the “X” variables© Kaplan, Inc. 60LOS 10.m Describe Multiple RegressionSchweser B1 pg 177, CFAI V1 pg 355 Model Specification Issues Model specification  Selection of explanatory variables  Transformation of variables Affects reliability of inference/hypothesis tests  Point: If model specified incorrectly, regression coefficients will be biased and inconsistent© Kaplan, Inc. 62 ©2018 FK Pa

SS 03 - Quantitative Methods for ValuationLOS 10.k Explain Multiple RegressionSchweser B1 pg 167, CFAI V1 pg 340 Summing It Up Violation Conditional Serial MulticollinearityWhat is it? Heteroskedasticity Correlation Two or more X’s are Effect? Residual variance Residuals are correlated related to level of X’s correlated Type II errors Unreliable hypothesis Type I errors testing (positive Conflicting t and F correlation) statistics; correlationsDetection? Breusch-Pagan among independent chi-square test Durbin-Watson variables if k = 2 test Correction? Use White-corrected Drop one of the standard errors Use the Hansen correlated variabl6e1s© Kaplan, Inc. method to adjust standard errorsLOS 10.m Describe Multiple RegressionSchweser B1 pg 177, CFAI V1 pg 355 Three Types of Model Misspecification  Functional form misspecification 63  Important variables omitted  Variables not transformed properly  Data pooled improperly  Time-series misspecification  X is lagged Y with serial correlation present  Forecasting the past  Measurement error  Other time series problems (next reading)© Kaplan, Inc.artners - Exame CFA 16