Reading 1: Introduction To Linear Regression

LEVEL 2 CFA EDUCATION QUICKSHEET quantitative methods READING 1 : INTRODUCTION TO LINEAR REGRESSION where: Y = dependent variable X = independent variable b_0 = intercept b_1 = slope coefficient = error term n = number of observations LINEAR LEAST SQUARES TEST STATIC FOR SLOPE COEFFICIENT Note : Correlation coefficient is labelled as Multiple R in regression output. TEST STATIC FOR CORRELATION COEFFICIENT TEST STATIC FOR THE INTERCEPT PREDICTION INTERVAL FOR LOG-LIN MODEL If sample is very large, where r = sample correlation between regression residuals from one period and those from the previous period LOGISTIC REGRESSION (LOGIT MODEL) LIN-LOG MODEL LIN-LOG MODEL READING 2 ; MULTIPLE REGRESSION where : Y = dependent variable x = independent variable b_0 = intercept b_1, b_2, ...., b_k = slope efficients = error term n = number of observations k = number of independent variables b_0, b_1, b_2,...., b_k = regression coefficients BREUSCH-PAGAN TEST R^2 = R-squared between squared residuals on independent variables DURBIN WATSON TEST READING 3: TIME-SERIES ANALYSIS LINEAR TREND MODELS t = time (independent variable) LOG-LINEAR TREND MODELS READING 4 : BIG DATA PROJECTS Normalization of variable X Standardization of variable X economics READING 5 : CURRENCY EXCHANGE RATES : UNDERSTANDING EQUILIBRIUM VALUE RELATIVE PP EX ANTE PP COVERED INTEREST RATE PARITY MARKET-TO-MARKET VALUE OF A FORWARD CONTRACT Original position : Long base currency d forward at forward rate INTERNATIONAL FISHER EFFECT = Expected inflation rate = Actual inflation rate READING 6 : ECONOMIC GROWTH AND THE INVESTMENT DECISION Return on aggregate equity market P = aggregate value of equities E = aggregate earnings COBB-DOUGLAS PRODUCTION FUNCTION UNCOVERED INTEREST RATE PARITY Y = Output α = Share of output allocated to capital (K) 1 - α = share of output allocated to labor (L) T = total factor productivity (TFP), represents technological progress of the economy ABSOLUTE PP Growth Accounting equation: Growth rate in potential GDP = Long term growth rate of labor force + Long term growth rate in labour productivity Sustainable growth rate of output per capita Sustainable growth rate of output Equilibrium output to capital ratio ENDOGENEOUS GROWTH MODEL Production function : Growth rate of output per capita : y_e = output per worker k_e = capita c = marginal product of capital in the aggregate economy (constant) financial reporting and analysis READING 7 : INTERCORPORATE INVESTMENTS FINANCIAL ASSETS Amortized Cost Ending debt investment = beginning debt investment + interest income - interest received Realized gain = sales proceeds - carrying value of financial asset FVOCI or FVPL Unrealized gain or loss = change in fair value fo financial asset INVESTMENTS IN ASSOCIATES Ending investment in associates = beginning investment in associates + share of net income - share of dividend received amortization of excess purchase price. Impact on investor’s income statement = share of net income - amortization of excess purchase price - share of unrealized profit from downstream or upstream sale. ACQUISITION METHOD Excess purchase price = Acquisition price %ownership x book value of net identifiable assets Partial Goodwill = Acquisition price (%ownership x fair value of net identifiable assets) = acquisition price - %ownership x book value of identifiable net assets - %ownership x excess purchase price attributable to net identifiable assets. Non controlling interest = %NCI x fair value of identifiable net assets Full Goodwill = fair value of entity - fair value of net identifiable assets Non controlling interest = %NCI x fair value of entity IFRS Impairment loss = carrying value of cash generating unit - recoverable amount of cash generating unit US GAAP implied goodwill = fair value of reporting unit - fair value of reporting unit‘s identifiable net assets. impairment loss = carrying value of goodwill - implied goodwill. READING 8 : EMPLOYEE COMPENSATION POST-EMPLOYEMENT AND SHARE-BASED funded status - fair value of plan assets - PV of defined benefit obligation. net Pension Asset = Min(Positive Funded State, Asset Ceiling). periodic pension cost = employer contributions - ( ending funded status beginning funded status ) = current service costs + interest expense + past service costs - actual return on plan assets + actuarial loss (gain). ending benefit obligation = beginning benefit obligation + service cost. +interest cost benefits paid + actuarial loss/(gain). ending fair value of plan assets = beginning fair value of plan assets + actual return on plan assets + employer‘s contribution benefits paid. IFRS periodic pension cost in income statement = current service costs + past service costs + net interest expense/(income) net interest expense/(income) = discount rate x (beginning PBO - beginning plan assets) US GAAP periodic pension cost in income statement = current service costs + amortized past service costs + interest expense - expected return on plan assets + amortized actuarial loss/(gain) interest expense = discount rate x beginning PBO expected return on plan assets = expected rate of return x beginning plan assets READING 9 : ANALYSIS OF FINANCIAL INSTITUTIONS READING 10 : EVALUATING QUALITY OF FINANCIAL REPORTS READING 11 : INTEGRATION OF FINANCIAL STATEMENT ANALYSIS TECHNIQUES Bank can withstand a stress level volume of cash outflows for (LCR x 30) days. PROPERTY AND CASUALTY COMPANIES CORPORATE FINANCE READING 12: CAPITAL STRUCTURE SHARE REPURCHASE Weighted average cost of capital, rWACC Value of levered firm, ANALYSIS OF DIVIDEND SAFETY Cost of Equity, re READING 14 : MERGERS AND AQUISITIONS If acquirer pays using shares: STATIC TRADE OF THEORY: rd = Cost of debt(pre-tax) r0 = Cost of an all- equity firm READING 13: DIVIDENDS AND SHARE REPURCHASES ANALYSIS TARGET PAYOUT ADJUSTMENT MODEL (LINTNER MODEL) CONSTANT DIVIDEND PAYOUT RATIO POLICY COMPARABLE COMPANY ANALYSIS BID EVALUATION READING 15 : CAPITAL BUDGETING Initial Outlay = Annual after-tax operating cash flows, ATOCF Terminal year after-tax non-operating cash flow, TNOCF FCI_nv = fixed capital investment WCI _nv = working capital investment Sal_0 = sales proceeds of old equipment B_0 = net book value of old equipment T = marginal tax rate EQUIVALENT ANNUAL ANNUITY (EAA) [PV] = -Project NPV [I/Y] = Project’s discount rate [N] = Project life [FV] = 0 [CPT] [PMT] EAA EQUITY VALUATION READING 16 : EQUITY VALUATION APPLICATIONS AND PROCESS where: VE = Estimated intrinsic value P = Market Price V = Intrinsic Value Conglomerate Discount = Sum-of-the-parts value - Market Value READING 17 : RETURN CONCEPTS V0 = true intrinsic value Equity risk premium, ERP = GORDON GROWTH MODEL: FAMA-FRENCH MODEL Required return on stock PASTOR-STAMBAUGH MODEL Required return on stock R_F= 1-month T-bill rate (for Fama-French and PastorStambaugh models only) R_mkt-R_f= return on value-weighted market index minus risk-free rate R_small-R_big= Small-cap return premium (R_small CapR_large Cap) R_HBM - R_LBM= value return premium (R_value-R_growth) R_LowLiq- R_HighLiq= Liquidity premium (R_LowLiquidity stocks - R_High liquidity stocks) BUILD UP METHOD: BOND-YIELD-PLUS-RISK-PREMIUM METHOD: BLUME’S ADJUSTMENT FOR REGRESSION BETA IBBOTSON - CHEN MODEL: CAPM: COUNTRY SPREAD MODEL READING 18 : INDUSTRY AND COMPANY ANALYSIS Return on invested capital (ROIC) = H - half-life in years of the high-growth period Sustainable growth rate, PRAT MODEL NOPLAT = Net operating profit less adjusted taxes Return on capital employed (ROCE) = READING 20 : FREE CASH FLOW VALUATION READING 19 : DISCOUNTED DIVIDEND VALUATION FREE CASH FLOW TO THE FIRM (FCFF) VALUATION APPROACH DISCOUNTED DIVIDEND VALUATION FCFE VALUATION APPROACH GORDON GROWTH MODEL FIXED-RATE PERPETUAL PREFERRED STOCK Value of stock= Value of a company with zerogrowth + Present value of growth opportunities (PVGO) SINGLE-STAGE (CONSTANT GROWTH) FCFF AND FCFE MODEL FCFF VALUATION APPROACH FCFE VALUATION APPROACH FREE CASH FLOW TO THE FIRM, FCFF If dividend and earnings growth rate is constant, TWO-STAGE DIVIDEND DISCOUNT MODEL THE H-MODEL Where: NI=Net Income available to common shareholders NCC= Net Noncash Charges (e.g. depreciation) Int= Interest expense FCInv = Investment in fixed capital = Maintenance Capex + Growth Capex = WCInv= Investment in working Capital FREE CASH FLOW TO THE EQUITY, FCFE FCFE = FCFF-Int(1-Tax Rate)+ Net borrowing = CFO- FCInv+ Net borrowing Where: Net Borrowing=Debt issues-Debt repaid If (FCInv- Dep) and WCInv funded using Debt (based on debt ratio) FCFE= NI+ Dep-FCInv+Net borrowing Where: Net borrowing = DR(FCInv-Dep) + DR(WCInv) If company issues preferred shares: Method 2 : Average ROE Approach Earnings Surprise = Reported EPS - Experted EPS Scaled earnings surprise = Standardised unexpected earnings (SUE) = Portfolio P/E TWO-STAGE FREE CASH FLOW MODELS READING 22 : RESIDUAL INCOME VALUATION ECONOMIC VALUE ADDED (EVA) Value of the Firm = Value of operating assets + Value of non-operating assets READING 21 : MARKET-BASED VALUATION PRICE AND ENTERPRISE VALUE MULTIPLES Enterprise Value, EV= Market value of common stock+ Market value of preferred equity+ market value of debt + minority interest- cash and investments MARKET VALUE ADDED (MVA) RESIDUAL INCOME, RI RESIDUAL INCOME MODEL Single-stage residual income valuation model Tobin‘s Q = Continuing Residual Income If RI declines to Long-run level In mature find industry, with premium over book value Underlying Earnings= EPS- Non recurring gains+ non recurring loss NORMALISED EARNINGS Method 1 : Average EPS Approach Clean surplus relationship: READING 23 : PRIVATE COMPANY VALUATION CAPITALISED CASH FLOW METHOD (CCM) EXCESS EARNINGS METHOD (EEM) Excess Earnings= Normalised Earnings - Earnings required to provide the required rate of return on working capital and fixed assets DISCOUNT FOR LACK OF CONTROL AND MARKETABILITY FIXED INCOME READING 24 : THE TERM STRUCTURE AND INTEREST RATE DYNAMICS FORWARD PRICING MODEL FOR PARALLEL SHIFTS IN YIELD CURVE: NON-PARALLEL SHIFTS (i.e. CHANGE IN SLOPE OR CURVATURE): READING 25 : THE ARBITRAGE-FREE VALUATION FRAMEWORK Arbitrage-free value of bond: FORWARD RATE MODEL BACKWARD INDUCTION VALUATION METHODOLOGY CALCULATING SPOT RATE FROM ONEPERIOD FORWARD RATES FIXED SWAP RATE SWAP SPREAD = COX-INGERSOLL-ROSS (CIR) MODEL TED SPREAD = LIBOR-OIS SPREAD = VASICEK MODEL a = Speed of reversion (>0) b = Long-run interest rate 𝜎 = Interest rate volatility Expected Loss = Probability of Default x Loss Given Default HO-LEE MODEL KALOTAY-WILLIAMS-FABOZZI (KWF) MODEL READING 26 : VALUATION AND ANALYSIS BONDS WITH EMBEDDED OPTIONS Value of callable bond = Value of straight bond Value of issuer call option Value of putable bond = Value of straight bond + Value of investor put option STRUCTURAL MODEL CONVERTIBLE BONDS Present Value of Expected Loss (PVOEL) = PV of risk-free bond - PV of risky bond READING 28 : CREDIT DEFAULT SWAPS CDS payout amount = Payout ratio x Notional = (1-Recovery rate) x Notional Upfront payment = PV of protection leg - PV of premium leg READING 27 : CREDIT ANALYSIS MODELS Derivatives READING 29 : Pricing and Valuation of Forward Commitments Forward Pricing: Valuation for Fixed Income forward contracts: Valuation for fixed income futures contracts: Note: CC and CB are continuously compounded rates Interest Rate Swaps (IRS): Pricing: Forward Valuation (Long Position): Forward Rate Agreement (FRA): Payoff at expiration: Long FRA payoff at expiration of FRA = Pricing : Valuation (prior to FRA Experience): Valuation: Pay-fixed, receive-floating IRS Receive-fixed, pay-floating IRS Currency Swap: Pricing for fixed leg of currency in currency 𝑎 Value of a fixed-for-fixed currency swap Fixed Income Forwards and Futures : Pricing: Equity Swap: Value of equity swap (receive fixed-rate, pay equity return) Black-Scholes Option Pricing Model Cash flow for equity leg= National x Periodic equity return Put-call Parity: READING 30: Valuation of Contingent Claims BSM model with Carry benefits: No-Arbitrage Approach: Expectations Approach: Put-call Parity: Black Option Valuation Model: European Options on Futures One-period binomial model: Put-call parity: Note: For interest rate options, π= 0.5 and discount expected option payoff using the 1-period forward rates. Two -period binomial Model: For 2-period American-styled call option with dividend in t = 1: Interest Rate Options: Payer Swaption Receiver Swaption Optimal Number of Hedging Units Alternative Investments READING 31 : Real Estate Investments Net lease= Gross lease- operating expense Appraisal-based Index: Appraisal with Terminal Value (or Resale/Reversion Value): Highest and Best Use: Implied land value= Value after construction- Cost to construct building N= Investor‘s Holding period Going in Cap Rate= Direct Capitalisation Method Value of property (at the time of purchase)= Private Market Real Estate Debt LTV Ratio= Debt Service coverage ratio, DSCR= Equity dividend rate= Value of property (at the time of purchase)= Cap Rate of comparable= Note: Equity dividend rate also called “cash-on-cash“ return. IRR= Cap rate+ Growth rate of NOI If property under renovation. Value of property= Value if renovated Loss in value due to renovation Net Asset Value Approach: NAV Per Share= Gross income multiplier= Where: Value of operating estate= Discounted Cash Flow Method Constant Growth Rate: Funds from Operation: FFO= Adjusted Funds from Operations: AFFO= READING 32 : Private Equity Investments Venture Capital Method: Post money valuation= VC Fractional Ownership= VC Fractional Ownership= Price paid per share= For two stages of financing (Stage A and Stage B) Return Multiples for Private Equity Funds Paid in Capital, PIC= Distributed to paid in, DPI= Residual value to be paid in, RVPI= Total value to be paid in, TVPI= DPI+ RVPI READING 33: Introduction to Commodities ands Commodity Derivatives Portfolio Management READING 34: Exchange-Traded Funds: Mechanics and Applications End-of-day ETF Premium or discount (%)= WML = winners minus losers, a momentum factor; return on a portfolio of past year’s winners minus return on a portfolio of past year’s losers. Intraday ETF premium or discount(%)= Macroeconomic Factor Model: Holding period cost (%)= Round trip trade cost (%)= Fundamental Factor Model: READING 35 : Using Multifactor Models Arbitrage Pricing Theory(APT): Return Attribution Tracking Error, TE= Information ratio, IR= Carhart Four-Factor Model RMRF= Return on a value-weighted equity index minus one-month T-bill rate SMB = small minus big; average return on three small-cap portfolios minus the average return on three large-cap portfolios HML = high minus low; average return on two high book-to-market portfolios minus average return on two low book-tomarket portfolios Active risk squared= Active factor risk + Active Specific risk READING 36 : Measuring and Managing Models Parametric VaR (Using Normal Distribuition) Two- Asset Portfolio: Scanning from Daily returns to annual returns: Percentage change in bond price: =policy rate at time t =level of real short-term interest rates that balance long term savings and borrowing in the economy =rate of inflation =target rate of inflation = logarithmic level of actual GDP = logarithmic level of potential real GDP = output gap Corporate Bond: READING 37 : Economics and Investment Markets One-Period real-risk free rate: Equity: Internal-temporal rate of substitution Commercial Real Estate: Where: = Risk neutral present value = Covariance between investor’s inter-temporal rate of substitution and the random future price the investment at t + 1, based on the information available to investor today. READING 38 : Analysis of Active Portfolio Management s= time to maturity of investment Default-free nominal coupon-paying bond For Optimal Sharpe ratio: Short-dated nominal zero-coupon government bonds(T-Bills) Taylor Rule: For Optimal Sharpe ratio: Transfer Coefficient, TC= Information Coefficient, IC= For Sell orders: Note: Midquote prices calculated based on bid and ask prices at the time order was entered. Mean-variance optimal weights Effective spread= 2 X Effective spread transaction cost estimate. Full Fundamental Law: VWAP Transaction cost estimate: For Buy orders: For Sell orders: Performance Measurement: = Proportion of variation in realised performance attributed to realised information coefficient. = realised information coefficient Ex-ante measurement of skill: Independence of Investment Decision: READING 39 : Trading Costs and Electronic Markets Optimal Mid-quote price= Effective Spread transaction cost estimate: For Buy orders: