CFA Level 2
Study Notes
,Contents
Quantitative Methods.....................................................................................................................................................6
Multiple Regression.....................................................................................................................................................6
1.1 Basics of Multiple Regression............................................................................................................................6
1.2 Evaluation of Regression Model Fit and Model Results.....................................................................................7
1.3 Model Specification...........................................................................................................................................9
1.4 Extensions of Multiple Regression...................................................................................................................11
Time Series Analysis..................................................................................................................................................13
2.1 Linear and Log-Linear Trend Models...............................................................................................................13
2.2 Autoregressive (AR) Models (Time Series).......................................................................................................13
2.3 Random Walks and Unit Roots........................................................................................................................14
2.4 Seasonality.......................................................................................................................................................15
2.5 ARCH Models and Multiple Time Series...........................................................................................................15
Machine Learning......................................................................................................................................................16
3.1 Types of Learning and Overfitting Problems....................................................................................................16
3.2 Supervised Learning Algorithms......................................................................................................................17
3.3 Unsupervised Learning Algorithms and Other Models....................................................................................19
Big Data Projects.......................................................................................................................................................20
4.1 Data Analysis Steps..........................................................................................................................................21
4.2 Data Exploration..............................................................................................................................................22
4.3 Model Training and Evaluation........................................................................................................................23
Economics..................................................................................................................................................................... 24
Currency Exchange Rates: Understanding Equilibrium Value....................................................................................24
5.1 Forex Quotes, Spreads, and Triangular Arbitrage............................................................................................24
5.2 Mark-to-Market Value and Parity Conditions..................................................................................................26
5.3 Exchange Rate Determinants, Carry Trade, and Central Bank Influence.........................................................27
Economic Growth......................................................................................................................................................29
6.1 Growth Factors and Production Function........................................................................................................29
6.2 Growth Accounting and Influencing Factors....................................................................................................31
6.3 Growth and Convergence Theories.................................................................................................................32
Economics of Regulation...........................................................................................................................................33
7.1 Economics of Regulation..................................................................................................................................33
Financial Statement Analysis.........................................................................................................................................35
Intercorporate Investments.......................................................................................................................................35
8.1 Classifications..................................................................................................................................................36
8.2 Investments in Financial Assets (IFRS 9)..........................................................................................................36
8.3 Investments in Associates Part 1 – Equity Method..........................................................................................37
1
, 8.4 Investment in Associates.................................................................................................................................38
8.5 Business Combinations: Balance Sheet............................................................................................................39
8.6 Business Combinations: Income Statement.....................................................................................................39
8.7 Business Combinations: Goodwill....................................................................................................................39
8.8 Joint Ventures..................................................................................................................................................40
8.9 Special Purpose Entities...................................................................................................................................41
Employee Compensation: Post Employment and Share-Based.................................................................................43
9.1 Types of Plans..................................................................................................................................................43
9.2 Defined Benefit Plans – Balance Sheet............................................................................................................44
9.3 Defined Benefits Plans – Part 1: Periodic Cost.................................................................................................46
9.4 Defined Benefit Plans, Part 2 – Periodic Cost Example....................................................................................47
9.5 Plan Assumptions............................................................................................................................................48
9.6 Analyst Adjustments........................................................................................................................................49
9.7 Share-Based Compensation.............................................................................................................................50
Multinational Operations..........................................................................................................................................51
10.1 Transaction Exposure.....................................................................................................................................51
10.2 Translation.....................................................................................................................................................52
10.3 Temporal Method (Monetary non-monetary)...............................................................................................52
10.4 Current Rate Method.....................................................................................................................................53
10.5 Example and Analysis Implications between Methods..................................................................................53
10.6 Ratios.............................................................................................................................................................54
10.7 Hyperinflation................................................................................................................................................55
10.8 Tax, Sales Growth, Financial Results..............................................................................................................55
Analysis of Financial Institutions................................................................................................................................56
11.1 Financial Institutions......................................................................................................................................56
11.2, 11.3, 11.4 CAMELS........................................................................................................................................56
11.5 Other Factors (to consider in analysing a bank).............................................................................................59
11.6 Insurance Companies.....................................................................................................................................59
Evaluating Quality of Financial Reports.....................................................................................................................61
12.1 Quality of Financial Reports...........................................................................................................................61
12.2, 12.3 Evaluating Earnings Quality...................................................................................................................63
12.4 Evaluating Cash Flow Quality.........................................................................................................................65
12.5 Evaluating Balance Sheet Quality..................................................................................................................65
Integration of Financial Statement Analysis Techniques...........................................................................................66
13.1 Framework for Analysis.................................................................................................................................66
13.2, 13.3, 13.4, 13.5, 13.6 Analysis of Purchasing Decision for LT Equity Investment..........................................66
Financial Statement Modelling..................................................................................................................................69
14.1 Forecasting Financial Statements..................................................................................................................69
2
, 14.2 Competitive Analysis and Growth Rate.........................................................................................................72
Corporate Issuers..........................................................................................................................................................73
Analysis of Dividends and Share Repurchases...........................................................................................................73
15.1 Theories of Dividend Policy............................................................................................................................73
15.2 Stock Buybacks..............................................................................................................................................75
ESG Considerations in Investment Analysis...............................................................................................................76
16.1 Global Variations in Ownership Structure.....................................................................................................76
16.2 Evaluating ESG Exposures..............................................................................................................................77
Cost of Capital: Advanced Topics...............................................................................................................................78
17.1: Factors Affecting Cost of Capital and Cost of Debt.......................................................................................78
17.2 ERP and the Cost of Equity.............................................................................................................................79
Corporate Restructuring............................................................................................................................................82
18.1 Restructuring Types and Motivations............................................................................................................82
18.2 Valuation.......................................................................................................................................................84
18.3 Evaluation......................................................................................................................................................85
Equity Valuation............................................................................................................................................................85
Equity Valuation: Applications and Processes...........................................................................................................85
19.1 Equity Valuation: Applications and Processes................................................................................................85
Discounted Dividend Valuation.................................................................................................................................87
20.1 DDM Basics....................................................................................................................................................87
20.2 Gordon Growth Model..................................................................................................................................89
20.3 Multiperiod growth models...........................................................................................................................90
FCF Valuation.............................................................................................................................................................91
21.1 FCF Computation...........................................................................................................................................91
21.2, 21.3, 21.4 Fixed and Working Capital Computation and FCFE FCFF Calculations..........................................92
21.5 FCF Other Aspects..........................................................................................................................................94
Market Based Valuation: Price and Enterprise Value Multiples................................................................................95
22.1, 22.2, 22.3, 22.4 P/E Multiple, P/B Multiple, P/S and P/CF Multiple..............................................................95
21.5 Other Aspects................................................................................................................................................98
Residual Income Valuation........................................................................................................................................99
23.1 Residual Income Defined...............................................................................................................................99
23.2, 23.3 Single Stage or Constant Growth Model for RI.....................................................................................99
23.4 Multi-Stage Residual Income Models..........................................................................................................100
23.5 Considerations of the Residual Income Model............................................................................................101
Private Company Valuation.....................................................................................................................................101
24.1 Private Company Basics...............................................................................................................................101
24.2 Income-Based Valuation..............................................................................................................................102
24.3a Market-Based Valuation............................................................................................................................103
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, 24.3b Asset-Based Valuation...............................................................................................................................104
24.4 Valuation Discounts.....................................................................................................................................104
Fixed Income...............................................................................................................................................................105
Term Structure and Interest Rate Dynamics............................................................................................................105
25.1 Spot and Forward Rates Part 1....................................................................................................................105
25.2 Spot and Forward Rates – Part 2.................................................................................................................106
25.3 Swap Rate Curve and Spread.......................................................................................................................107
25.4 Spread Measures.........................................................................................................................................108
25.5 Term Structure Theory................................................................................................................................108
25.6 Yield Curve Risks and Economic Factors......................................................................................................109
Arbitrage-Free Valuation Framework......................................................................................................................110
26.1 Binomial Trees Part 1...................................................................................................................................110
26.2 Binomial Trees Part 2...................................................................................................................................111
26.3 Interest Rate Models...................................................................................................................................111
Valuation and Analysis of Bonds with Embedded Options......................................................................................112
27.1 Types of Embedded Options........................................................................................................................112
27.2 Valuing Bonds with Embedded Options Part 1............................................................................................113
27.3 Valuing Bonds with Embedded Options Part 2............................................................................................113
27.4 Option Adjusted Spread...............................................................................................................................114
27.5 Duration.......................................................................................................................................................115
27.6 Key Rate Duration........................................................................................................................................115
27.7 Capped and Floored Floaters.......................................................................................................................116
27.8 Convertible Bonds........................................................................................................................................117
Credit Analysis Models............................................................................................................................................118
28.1 Credit Risk Measures...................................................................................................................................118
28.2 Analysis of Credit Risk..................................................................................................................................119
28.3 Credit Scores and Credit Ratings..................................................................................................................119
28.4 Structural and Reduced Form Models.........................................................................................................119
28.5 Credit Spread Analysis.................................................................................................................................120
28.6 Credit Spread...............................................................................................................................................120
28.7 Credit Analysis of Securitized Debt..............................................................................................................121
Credit Default Swaps...............................................................................................................................................121
29.1 CDS Features and Terms..............................................................................................................................121
29.2 Factors Affecting CDS Pricing.......................................................................................................................122
29.3 CDS Usage....................................................................................................................................................123
Derivatives................................................................................................................................................................... 124
Pricing and Valuation of Forward Commitments.....................................................................................................124
30.1 30.2 Pricing and Valuation of Forwards.......................................................................................................124
4
, 30.3 Pricing and Valuation of Fixed Income Forwards.........................................................................................125
30.4 30.5 Pricing and Valuation of Forward Rate Agreements (FRA’s)................................................................126
30.6 Pricing and Valuation of Interest Rate Swaps..............................................................................................127
30.7 Currency Swaps...........................................................................................................................................129
30.8 Equity Swaps................................................................................................................................................130
Valuation of Contingent Claims...............................................................................................................................131
31.1 31.2 Binomial Model and Put-Call Parity.....................................................................................................131
31.3 American Options........................................................................................................................................132
31.4 Hedge Ratio.................................................................................................................................................132
31.5 Interest Rate Options...................................................................................................................................132
31.6 Black-Scholes-Merton (BSM) and Swaptions...............................................................................................133
31.7 Option Greeks and Dynamic Hedging..........................................................................................................135
Alternative Investments..............................................................................................................................................137
32.1 Overview of Types of Real Estate Investment..............................................................................................137
32.2 Investments in Real Estate Through Private Vehicles..................................................................................140
32.3 Investments in Real Estate Through Publicly Traded Securities...................................................................141
Private Equity Investments......................................................................................................................................144
33.1 Valuation Issues...........................................................................................................................................144
33.2 Exit Routes, Costs, Risks, and Financial Performance Ratios........................................................................146
33.1 Fee and Distribution Calculations................................................................................................................148
Introduction to Commodities and Commodity Derivatives.....................................................................................149
34.1 Introduction and Theories of Return...........................................................................................................149
34.2 Analysing Returns and Index Construction..................................................................................................151
Portfolio Management................................................................................................................................................151
Exchange-Traded Funds: Mechanics and Applications............................................................................................151
35.1 ETF Mechanics and Tracking Error...............................................................................................................151
35.2 Spreads, Pricing Relative to NAV, Costs.......................................................................................................152
35.3 ETF Risks and Portfolio Applications............................................................................................................153
Multifactor Models..................................................................................................................................................154
36.1 Multifactor Models......................................................................................................................................154
36.2 Macroeconomic Factor Models, Fundamental Factor Models, and Statistical Models...............................154
36.3 Multifactor Model Risk and Return..............................................................................................................155
Measuring and Managing Market Risk....................................................................................................................156
37.1 VAR..............................................................................................................................................................156
37.2 Using VAR....................................................................................................................................................157
37.3 Sensitivity and Scenario Risk Measures.......................................................................................................158
37.4 Application of Risk Measures.......................................................................................................................159
37.5 Constraints and Capital Allocation Decisions...............................................................................................160
5
, Backtesting and Simulation.....................................................................................................................................160
38.1 Introduction to Backtesting.........................................................................................................................160
38.2 Steps in Backtesting an Investment Strategy...............................................................................................160
38.3 Metrics, Visuals and Problems in Backtesting..............................................................................................161
38.4 Scenario Analysis and Sensitivity Analysis...................................................................................................162
Economics and Investment Markets.......................................................................................................................163
39.1 Valuation and Interest Rates.......................................................................................................................163
39.2 The Business Cycle.......................................................................................................................................164
Analysis of Active Portfolio Management................................................................................................................165
40.1 Value Added by Active Management...........................................................................................................165
40.2 Information Ratio and Sharpe Ratio............................................................................................................166
40.3 The Fundamental Law..................................................................................................................................167
40.4 Active Management.....................................................................................................................................168
Trading Costs and Electronic Markets.....................................................................................................................169
41.1 Explicit and Implicit Trading Costs...............................................................................................................169
41.2 Electronic Trading Systems..........................................................................................................................170
41.3 Characteristics and Uses of Electronic Trading Systems..............................................................................171
41.4 Risks and Surveillance of Electronic Trading Systems..................................................................................172
Ethical and Professional Standards..............................................................................................................................172
42 and 43 Introduction to the Code and Standards.............................................................................................172
Quantitative Methods
Annualized Return=¿
3 Desirable Estimator Properties:
1. Unbiased – an unbiased estimator is one whose expected value equals the parameter intended to be estimated
(won’t be exact because of sampling error but should be close)
2. Efficient - An unbiased estimator should be from the sampling distribution with the smallest variance.
3. Consistent - the probability of estimates close to the value of the population parameter increases as sample size
n increases. As n goes to infinity, the standard error goes to zero.
Multiple Regression
1.1 Basics of Multiple Regression
Linear relationship with more than one independent variable. Used to:
Identify relationships between variables (e.g. Farma French model)
Forecast variables
Test existing theories
P-values – the smallest significance level at which we can reject the null hypothesis (if p-value<α, reject H0)
defines which explanatory variables should be considered significant
Interpretation of slope coefficients
E.g. Coefficient and Standard Error Estimates for Regression of EG10 on PR and YCS
Coefficient Standard Error
6
, Intercept –11.6% 1.657%
PR 0.25 0.032
YCS 0.14 0.280
If PR and YCS=0, EG10 is -11.6%
If PR increases by 1%, expect EG10 to increase by 0.25% holding all else constant
Assumptions of Multiple Regression
Linear relationship between Y and X
No exact linear relationship between X variables (multicollinearity)
Expected value of error term = 0 (no bias in error estimations – over or under estimation)
Variance of error term is constant (homoskedasticity in residuals)
Errors are not serially constant (one error term relates to another)
Error term is normally distributed
Can test for preliminary violations by using a QQ plot (variable distribution compared to a normal distribution with
residuals plotted in a 2D space)
Red line represents normal distribution
Green dots are data points on distribution
1.2 Evaluation of Regression Model Fit and Model Results
T-Test
T-tests test the significance of estimated coefficient at a given confidence level.
X−μ
tb =1
se X
Statistically significant if >tcrit at a given significance level.
F-Test
ANOVA Tables and Goodness of Fit
Decomposes the total variation (SST) into explained (RSS) and unexplained (SSE)
R2 Coefficient of Determination – percentage of variation in dependent variable explained collectively by all the
independent variables (explained/total) e.g. R-squared of 0.63 is 63% of variation explained
7
, RSS
R 2=
SST
o R2 always increases as more independent variables are added (even if marginal contribution is not statistically significant –
overfitting).
Adjusted R2 – Adjusted R2 accounts for the number of variables. Always less than or equal to R 2.
2
Ra =1−¿ ]
o Does not indicate statistical significance of slope coefficients or quality of model fit
o k independent variables acting as a penalty factor – as these increase for Adjusted R2, BIC and AIC, it penalizes both models for
overfitting (adding non-explanatory x variables). Can be negative if a large number of independent variables have no
explanatory power.
o SSE will always decrease by adding more independent variables
Akaike’s Information Criterion (AIC) & Schwarz’s Bayesian Information Criteria (BIC) - evaluate the quality of
model fit among competing models for the same dependent variable. Lower values indicate a better model
under either criteria.
AIC – Used for better forecast.
AIC=n∗ln ( SSEn )+2(k + 1)
Choose model with lowest AIC (will increase with k unless SSE decrease sufficiently)
BIC – Used for better goodness of fit
BIC=n∗ln ( SSEn )+ln ( n)∗(k +1)
Choose model with lowest BIC
Higher penalty for overfitting (when n>8, ln(n) is higher than 2).
General F-Test
General F-test is used to test if all independent variables have explanatory power over dependent variable. Provides
statement on the overall explanatory power of the variables in a model.
RSS U
MSR k
F= = , withk ∧n−k−1 degrees of freedom
MSE SSEU
n−k −1
H 0 :b 1=b 2=b 3=0 H A : at least one bj ≠ 0
Decision rule: reject H0 if F > FCrit
Joint Hypothesis Test (F-Test)
Joint F test used to jointly test a subset of independent variables in a multiple regression. Compares an unrestricted
model (all x variables) to a restricted model (some x variables removed) to test whether q independent variables
have explanatory power over dependent variable.
SSER −SSEU
q
F= , with q∧n−k −1 degrees of freedom
SSEU
n−k −1
q : number of additional independent variables omitted∈restricted model
k :number of independent variables∈unrestricted model
8
, H 0 :b 2=b 3=0 H A :b 2∨b 3≠ 0
Decision rule: reject H0 if F > FCrit
1.3 Model Specification
Model specification is the selection of explanatory variables and transformation of variables. Affects reliability of
hypothesis tests.
Anything that affects the residuals affects the reliability of standard errors
Functional Form Model Misspecification
Misspecification Description Effect Example
Omission of independent Based on economic May lead to biased and If omitted variable is correlated
variables theory, one or more inconsistent regression with other independent
variables regression
variables that should have parameters, serial coefficients (b0 b1 b2) will be
been included are correlation, or biased and inconsistent
omitted. heteroskedasticity in
residuals. If omitted variable is not
correlated with other
independent variables – error
term will reflect value of missing
contribution b0 will be biased
Inappropriate variable The relationship between May lead to e.g. market cap and portfolio
form (transformation) the dependent and heteroskedasticity in returns is not linear but the
natural log of market cap must
independent variables residuals specify the form correctly and
may be non-linear use ln(M) instead of M
(requires natural log)
Inappropriate variable Variables may need to be May lead to e.g. financial statement data
scaling transformed before heteroskedasticity or should be scaled (common size
FS or taking square roots)
estimating the regression. multicollinearity
Data pooled improperly Sample has periods of May lead to e.g. relationship between the
dissimilar economic heteroskedasticity or dependant and independent
variables during the first 3 years
environments (that should serial correlation in is different from the relationship
not be pooled). residuals in the second 3 years must
use two separate estimators
Violations of Regression Assumptions
Violation Effect on Regression Detection Correction
Heteroskedasticity Standard errors are Detecting conditional White-Corrected
Variance of residuals is not the unreliable - standard errors are heteroskedasticity Standard Errors – robust
same across all observations. linked to residuals. 1. Examine scatter plots standard errors calculated and
Unconditional heteroskedasticity – underestimations resulting in Type used to recalculate t-statistics
of residuals.
no increases or decreases with 1 errors for financial data. using original regression
F-stats are unreliable 2. Breusch Pagan Chi- coefficients (higher than
changes in value of independent
variable no major issues with T-stats are unreliable Square Test – tests the biased errors lower t-
regression. significance of residual R2 statistics less type 1 errors)
(standard error is denominator of
Conditional heteroskedasticity – t stat) BP=n∗R2resid
variance increases with the value of Newey-West Corrected
the independent variable issues k degrees of freedom
in statistical inference. One-tailed test (chi-square test) – Standard Errors
only concerned about large
values in the residuals of the R2.
H 0 : Noheteroskedasticity
Serial Correlation Slope Coefficients are 1. Durbin-Watson (DW) Newey-West Corrected
(autocorrelation) inconsistent - if a lagged value statistic – residual serial Standard Errors – used to
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