CFA Level 2 Complete Set

Studentized residuals

To check for only the outliers in the sample

Leverage

to identify high-leverage observations

Breusch-Pagan test statistic

is used to identify conditional heteroskedasticity in residuals.

Durbin-Watson and Breusch-Godfrey

test statistic are used to detect autocorrelation

normal QQ plot

To see if residuals are normally distributed.

coefficient of determination R²

statistic used to identify explanatory power

R²

Explained Variation / Total Variation

RSS / SST

Adjusted R²

1 - [ (n-1 / n-k-1) × (1 - R²)]

F-statistic Generic

mean square regression / mean square error

mean square error

Sum of Squares Error / Degrees of Freedom Error

mean square regression

Sum of Squares Regression / Degrees of Freedom Regression

Dickey-Fuller test, which uses a modified t-statistic

use to test for nonstationarity

The Dickey-Fuller test equation

(x_t – x_t-1) = b₀ + (b₁ - 1) * x_t-1 + e_t

F-statistic

[( SSE_R − SSE_U ) / q ] ÷ [SSE_U / n-k-1]

q = numerator Degrees of Freedom

n-k-1 = denominator Degrees of Freedom

SSE_R

SST – RSS_R

R² Alternative Formula

(correlation coefficient)²

critical t-values

coefficient / standard error

root mean squared error (RMSE)

smallest RMSE is the preferred model

criterion is used to compare the accuracy of autoregressive models in forecasting out-of-sample values (not in-sample values)

root mean squared error (RMSE)

√ Mean Squared Error

VIF

1 / (1 - R²)

to quantify multicollinearity issues

Influential Observations - Leverage Measure

3 [ (k + 1) / n]

influential observations - Studentized Residuals

the absolute values of their studentized residuals exceed Critical value of t-statistic

Equation for Probability

1 / (1 + e^-y )

standard error of the autocorrelation coefficient

1 / √ T

Where T = No.of Observations

K-Means clustering

is an unsupervised machine learning algorithm which repeatedly partitions observations into a fixed number, of non-overlapping clusters

Principal Components Analysis (PCA)

long-established statistical method for dimension reduction,aims to summarize or reduce highly correlated features of data into a few main, uncorrelated composite variables.

Classification and Regression Trees (CART)

a supervised machine learning technique that is most commonly applied to binary classification or regression.

Hyperparameter(in the K-Means algorithm)

a parameter whose value must be set by the researcher before learning begins.

Reduce overfitting

1. Using the k-fold cross validation method

2. Including an overfitting penalty (i.e., regularization term).

Model Overfitting

A model with low bias error and high variance error for out of sample data

Support vector machine

is a linear classifier that determines the hyperplane that optimally separates the observations into two sets of data points, requires the target variable to be a binary classification variable

least absolute shrinkage and selection operator (LASSO)

consistent with a penalized regression algorithm.

k-fold cross-validation

in which the data (excluding test sample and fresh data) are shuffled randomly and then are divided into k equal sub-samples, with k – 1 samples used as training samples and one sample, the kth, used as a validation sample

Model Underfitting

Occur when erroneous assumptions are used in training a model using the training dataset

Random forest algorithms

are a form of continuous supervised models with a target variable.

Structured data-based ML models

1) conceptualization of the modeling task

2) data collection

3) data preparation and wrangling

4) data exploration

5) model training

Text-based ML models

1) text problem formulation,

2) data (text) curation,

3) text preparation and wrangling,

4) text exploration

5) model training.

𝑋_{i(normalized)} 

( X_i - X_min) / (X_max - X_min)

bag-of-words (BOW)

is a collection of a distinct set of tokens from all the texts in a sample dataset.

Precision (P)

TP / (TP + FP)

Accuracy

(TP + TN ) / (TP + TN + FP + FN)

Recall (R)

TP / (TP + FN)

FI Score

2 * (Precision * Recall) / (Precision + Recall)

Lemmatization

Reduces the repetition of words occurring in various forms while maintaining the semantic structure of the text data

Winsorization

A process used for structured numerical data and replaces extreme values and outliers with the maximum (for large-value outliers) and minimum (for small-value outliers) values of data points that are not outliers.

Portfolio balance approach

focuses on long-term implications of fiscal policy on exchange rate

Monetary approach

focuses on implications of monetary policy

Mundell-Fleming model

focuses on short-term implications of monetary/fiscal policies.

endogenous growth theory

This theory argues that economic growth can continue indefinitely as long as technological advances are made.

Carry Trade

borrowing in a lower-yielding currency to invest in a higher-yielding one and netting any profit after allowing for borrowing costs and exchange rate movements

Mark to Market (Value in Price Currency)

[ (FP_t - FP ) (Contract Size) ] / [1 + R (days/360)]

Triangular Arbitrage Trade Exists

If

D_B > C_A Dealer Bid > Calculated Ask

D_A < C_B Dealer Ask > Calculated Bid

lower interest rates, capital outflows

combination of an expansionary monetary policy and a restrictive fiscal policy should lead to

Conditional convergence

means that convergence is conditional on the countries having the same savings rate, population growth rate, and production function.

neoclassical model

convergence should occur more quickly if economies are open and there is free trade and international borrowing and lending

TFP (total factor productivity)

Labor productivity growth – Growth in capital deepening

GDP percentage growth (ΔY/Y)

ΔA/A + αΔK/K + (1 − α)ΔL/L

ΔA/A = percentage growth from total factor productivity (TFP)

ΔK/K = percentage growth in capital

ΔL/L = percentage growth in labor

α = share of income paid to capital factor

1 – α = share of income paid to labor factor, also the elasticity of output with respect to labor

Inter-Temporal Rate of Substitution m_t

( Marginal Utility of consuming 1 unit in future ) / (Marginal Utility of current consuming of 1 unit )

OR

u_t / u_o (U₀ > U_t )

Real Risk Free Rate (R)

[1 / E(m_t) ] - 1

Nominal Risk Free Rate (r) Short Term

R + π

Nominal Risk Free Rate (r) Long Term

R + π + θ

Taylor Rule

Short Term Policy Rates are Positively related to Inflation gap and GDP gap

Term Spread

Yield on Long Term Bond - Yield on Short Term Bond

Breakeven Inflation Rate (BEI) - V1

Nominal Yield on Default Free Bond (TBond) - Real Yield on Default Free Bond (TIPS)

Breakeven Inflation Rate (BEI) - V2

Expected Inflation + Risk Premium for inflation uncertainty

π + θ

Credit Spread

Yield - BEI - R

Expected Active Return E(R_A)

E(R_P) - E(R_B)

IR × σ_A

Risk Adjusted Active Return α_p

R_P - β_pR_B

Active Return Decomposition E(R_A)

∑ ∆W_j × E(R_B) + ∑ W_p × E(R_Aj)

(Active Return from Asset Allocation) + (Active Return from Stock Selection)

∆W_j → W_P - W_B

E(R_Aj) → E(R_Pi ) - E(R_Bi)

Sharpe Ratio

( R_P - R_B ) / σ_P

R_B or R_f

Information Ratio (IR)

R_P - R_B / σ_{(P - B)}

Active Return / Active Risk

Sharpe Ratio of Active Portfolio SR_p²

SR_B² + IR²

Optimal Active Risk σ_A

( IR / SR_B ) × σ_B

Total Portfolio Return Volatility σ_P²

σ_B² + σ_A²

IVAR (incremental value at risk)

measures how changes in the portfolio’s composition affect the portfolio’s VaR.

CVaR (conditional value at risk)

best derived by using either the Monte Carlo or historical methods, in which returns beyond the VaR cutoff may be averaged.This measure is also referred to as “expected tail loss” and “expected shortfall.”

Relative VaR

is a measure of the degree to which the performance of the portfolio might deviate from its benchmark. Relative VaR is also referred to as “ex ante tracking error.”

Scenario analysis

used for estimating how a portfolio might perform under conditions of market stress.

Scenario risk measures

measures estimate the portfolio returns that would result from a hypothetical change in markets. Stress tests and reverse stress tests are examples of this measure

Sensitivity analysis

used to estimate how gains and losses in the portfolio change with changes in the underlying risk factors.

Future Price

Spot Price + Storage Costs - Convenience Yield

Contango

Future Price > Spot Price

Backwardation

Future Price < Spot Price

Total Yield of Commodity Futures

Collateral Yield + Spot Yield + Roll Yield

Spot Yield

∆ Spot Price ÷ Original Spot Price

Roll Yield / Roll Return

(Price of Expiring Futures - Price of new futures ) / Price of Expiring Futures

Capitalization Rate (CAP Rate)

( r - g ) or ( NOI₁ / Value )

Real Estate Valuation - Discounted Cash Flow V_o

∑ PV (NOI_t)

Real Estate Valuation - Direct Capitalization V_o

NOI₁ / (r-g)

or

NOI₁ / (CAP Rate)

NOI (Net Operating Income)

Full Occupancy Rental Income

+ Other Income

−−−−−−−−−−−−−−−−−

= Gross Potential Rental Income

− Vacancy and Collection losses

−−−−−−−−−−−−−−−−−−−

= Effective Gross Income

− Operating Expense

−−−−−−−−−−−−−−−−−−−−

All Risk Yield (ARY)

Rent_comparable / Price_comparable

Market Value V₀

Rent₁ / All Risk Yield (ARY)

Loan to Value

Loan Amount / Appraised Value

Property Under Renovation V₀

V_stablized − PV (NOI_stablized − NOI₁)

Debt Service Coverage Ratio (DSCR)

NOI₁ / Debt Service

Equity Dividend Rate

Cash Flow _{(1st Year)} / Equity Investment

Tax

Tax Rate × (NOI - Depreciation - Interest)

Debt Service

Principle + Interest

OR

Loan Amount × Interest Rate

After Tax Return

(NOI - Interest - Tax) / Equity Investment

Collateral Yield

Annual rate × Period length as a fraction of the year