1、CFA公式表-Level II Quantitative Methods 1. Simple Linear Regression Correlation: () () xy xy x y Cov r ss t-test for r (df = n-2): 2 2 1 rn t r Estimated slope coefficient: 2 xy x Cov Estimated intercept: 01 byb x Confidence interval for predicted Y-value: c ytS E of forecast 2. Multiple Regression 011
2、2233 () () () iii YbbX bX bX i i Test statistical significance of b; 0 :0 ,1 b Hb b td f n k s Reject if t or p-value 0 h | t critical Confidence Interval: () j jcb bts SST = RSS+SSE MSR = RSS/k MSE = SSE / (n-k-1) Test statistical significance of regression: F = MSR / MSE with df k and n-k-1 (1-tai
3、l) Standard error of estimate (SEE MSE ), Smaller SEE means better fit. Coefficient of determination ( 2 / R RSS SST ). % of variability of Y explained by Xs; Higher R 2means better fit. 3. Regression Analysis-Problems Heteroskedasticity. Non-constant error variance. Detect with Breusch-Pagan test.
4、Correct with White-corrected standard errors. Autocorrelation. Correlation among error terms. Detect with Durbin-Watson test; positive autocorrelation if DWd 1 . Correct by adjusting standard errors using Hansen method. Multicollinearity. High correlation among Xs. Detect if F-test significant, t-te
5、st insignificant. Correct by dropping X variables. 4. Model Misspecification Omitting a variable. Variable should be transformed. Incorrectly pooling data. Using lagged dependent variable as independent variable. Forecasting the past. Measuring independent variables with error. 5. Effects of Misspec
6、ification Regression coefficients are biased and inconsistent, lack of confidence in hypothesis tests of the coefficients or in the model predictions. 6. Linear Trend Model: 01 tt ybb t 7. Log-Linear Trend Models: 01 ln( ) tt ybb t 8. Covariance Stationary: Mean and var. dont change over time. To de
7、termine if a time series is covariance stationary, (1) plot data, (2) run an AR model and test correlations, and/or (3) perform Dickey Fuller test. 9. Unit Root: Coefficient on lagged dep.vb1=1. series with unit root is not covariance stationary. First differencing will often eliminate the unit root
8、. 10. Autoregressive (AR) Models: Specified correctly if autocorrelation of residuals not significant: 01122tttp t p xbb xb x bx t 11. Mean Reverting Level For AR(1): 0 1 (1 ) b b 12. RMSE: square root of avg squared error. 13. Random Walk Time Series: 1 tt xx t 14. Seasonality: Indicated by statist
9、ically significant lagged err. term. Correct by adding lagged term. 15. ARCH: Detected by estimating: 22 011 tt aa Variance o ARCH series: 22 101 tt aa ECONOMICS 1. One Third Rule: at given technology level, 1% increase in capital/labor hour leads to 1/3 % increase in real GDP per hour. 2. Rule of 7
10、0: approximate to double GDP = 70/growth rate. 3. Classical Growth Theory 4. Neoclassical Growth Theory Economic growth stops when real return = target return. Pop. Growth independent of economic growth. 5. New Growth Theory Economic growth continues indefinitely ad technology advances. real rate =
11、incentive to discover new products and methods. Discovery = real return target return. 6. Nominal observed in EX markets. Real exchange rate = E (P/P * ) 7. Balance of Payment: current account + capital account + official reserve account = 0 8. Foreign Exchange: Direct quotes: if quote is per $ (or
12、USD:GBP), this is a direct quote from the perspective of the pound. Bid-ask spread stated as percent of asking price: % (100) askprice bidprice spread askprice Foreign currency is at forward discount (premium) if F is below (above) S, using direct quotes: 360 (/) (1 ) () daymin fwdrate fwdprem disc
13、spotrate ter s Currency appreciates due to: (1) Lower relative income growth rate. (2) Lower relative inflation rate. (3) Higher domestic real interest rate. (4) Improved investment climate. 9. Unanticipated shift to exp. Monetary Policy: Higher income, accelerated inflation, lower real interest rat
14、es, leads to currency dept, current acct surplus, and financial acct deficit. 10. Unanticipated shift to exp. Fiscal Policy: currency appr, current acct deficit, lowest under equity method; proportionate consolidation in between. 3. Pension Accounting: a) PBO components: current service cost, intere
15、st cost, actuarial gains/losses, benefits paid. b) Funded status = plan assets PBO c) Pension expense components: current service cost, interest cost, expected return on plan assets, prior (past) service cost, net actuarial gains/losses. d) Aggressive assumptions/low earnings quality: high discount
16、rate, low compensation growth rate, high expected return. 4. Economic pension expense: if firm contribution, diff = borrowing (and reclass from CFO to CFF) 5. Balance sheet: GAAP vs. IFRS: GAAP: net assets/liability = funded status = economic reality. IFRS: net assets/liab = funded status adj. for u
17、nrecognized items. 6. Underlying Economic Pension Expense: Sum of all changes in PBO (except benefits paid) less actual ROA. Also = change in funded status exclude firms contributions. Service cost= operating expense. Interest and actual ROA repeated as non operating income. 7. Business Combinations
18、: a) Purchase method required under U.S. GAAP and IFRS b) Goodwill not amortized, subject to annual impairment test. 8. Purchase Method Attributes: a) Acquirer assumes assets/liabilities of acquired company. b) Excess FMV of acquired net assets allocated first to intangible assets, then goodwill. c)
19、 Prior operating results not restated. 9. Pooling Method Attributes a) Company f/s combined at book value. b) Prior operating results restated. 10. Impact of Purchase vs. Pooling a) Asset and equity higher, net income lower under purchase method. b) Profit margin, ROA, ROE lower under purchase metho
20、d. 11. Entity is VIE if any of: 12. Multinational Operations: Choice of Method a) Insufficient at-risk equity investment. b) Shareholder lack decision-making rights. c) Shareholder do not absorb losses d) Shareholder do not receive residual benefits. The primary beneficiary consolidates the VIE. Qua
21、lifying SPE: GAAP allows no consol. (use equity method). Not permitted under IFRS. 13. Multinational Operations: Choice of Method For self-contained sub, functional presentation currency; use all-current method: a) Assets/liabilities at current rate. b) Common stock at historical rate. c) Income sta
22、tement at average rate. d) Exposure = shareholders equity e) Dividend at rate when paid. For integrated sub, functional = presentation currency, use temporal method: f) Monetary assets/liabilities at current rate. g) Nonmonetary assets / liabilities at historical rate. h) Sales, SGA at average rate.
23、 i) COGS, depreciation at historical rate. j) Exposure = monetary assets monetary liabilities Net asset position impaired goodwill d) CF: compare growth of operating leases to asset grow, look for in discretionary spend at year end. 20. Fair value hedge: gain/loss from derivative unexpected changes
24、in inflation affect project profitability; reduces the real tax savings from depreciation; decreases value of fixed payments to bondholders; affects costs and revenues differently. 5. Capital rationing: If +NPV capital, choose combination with highest NPV . 6. Real options: Timing, abandonment, expa
25、nsion, flexibility, fundamental options. 7. Economic and accounting income a) Economic Income = AT CF + in projects MV. b) Economic depr based on in investments MV . c) Economic income calculated before interest expense (cost of capital reflected in discount rate) d) Account income = project revenue
26、 costs e) Account dep based on original investment cost. f) Interest (financing costs) deducted before calculating accounting income. 8. Valuation models: a) Econ profit = NOPAT -$WACC; discounted at WACC. b) Residual income = NI equity charge; discounted at required return on equity. c) Claims valu
27、ation separates CFs based on equity claims (discounted at cost of equity) and debt holders (discounted at cost of debt). 9. Operating leverage: variable/fixed cost tradeoff % DOL % EBIT Sales () () qty sales QPV DOL QPV F SV C DOL SV CF 10. Financial leverage: refers to use of fixed-income securitie
28、s (debt and preferred stock). % %i %() ( %) EPS EBIT DFL EBIT EBIT erest EPS DFL EBIT n t11. Total leverage: measures effect on EPS of given change in sales. DTL=DOL DFL 12. Breakeven: BE F Q PV 13. MM Prop I (No taxes): Capital structure irrelevant (no taxes, transaction cost or bankruptcy costs).
29、14. MM Prop II (No Taxes): increased use of cheaper debt increases cost of equity, no change in WACC. 15. MM Proposition I (With taxes): tax shield adds value, value maximized at 100% debt. 16. MM Proposition II (With taxes): tax shield adds value, WACC minimized at 100% debt. 17. Corporate Governan
30、ce Objectives a) Mitigate conflicts of interest between (1) managers and shareholders, and (2) directors and shareholders. b) Ensure assets used to benefit investors and stakeholders. 18. EPS after a share repurchase tan TotalEarnings AfterTaxCostofFunds EPS SharesOuts dingAfterBurback If after-tax
31、cost of debt is less then earnings yield, a share repurchase will increase EPS. If after-tax cost of debt is greater than earnings yield, a share repurchase will decrease EPS. 19. BV per share after a share repurchase: If the share price is greater than the original BVPS, a share repurchase will dec
32、rease BVPS. If the share price is less the original BVPS, a share repurchase will increase BVPS. 20. Effective tax rate on dividends: a) Double taxation or split rate systems: effective rate = corp rate + (1- corp rate)(indiv rate) b) Imputation system: effective tax rate is the shareholders individ
33、ual tax rate. 21. Signaling Effects of Dividend Changes a) Initiation: ambiguous signa b) Increase: positive signal c) Decrease: negative signal unless management sees many profitable investment opportunities. 22. Share Repurchase a) Share repurchase is equivalent to cash dividend, assuming equal ta
34、x treatment. b) Unexpected share repurchase is good news. c) Rational for: 1) prevent EPS dilution; 2) supplement a regular dividend; 3) good investment for company; 4) positive signal to investor; 5) change capital structure. 23. Dividend Policy Approaches a) Residual dividend: dividends based on e
35、arnings less funds retained to finance capita budget. b) Longer-term residual dividend: forecast capital budge, smooth dividend payout. c) Dividend stability: dividend growth aligned with sustainable growth rate. d) Target payout ratio: long-term payout ratio target. 24. Merger Types: Horizontal, ve
36、rtical, conglomerate. 25. Merger Motivations: Achieve synergies, more rapid growth, increase market power, gain access to unique capabilities, diversify, manager personal benefits, tax benefits unlock hidden value, achieving intl goals, and bootstrapping earning. 26. Pre-offer Defense Mechanisms: po
37、ison pills and puts, reincorp. In a state where restrictive takeover laws, staggered board elections, restrict voting rights, supermajority voting, fair price amendments, and golder parachutes. 27. Post-offer Defense Mechanisms: litigation, greenmail, sare repurch, leveraged recap, th “crown jewel”,
38、 ”Pac man”, and “just say no” defense, and white knight/white squire. 28. The Herfindahl-Hirschman Inex (HHI): market power = sum of squared market shres for all industry firms. High or increase HHI mean regulators more likely to challenge a merger. 29. Methods to determine Target Value a) DCF metho
39、d: target performance FCF discounted at adjusted WACC b) Comparable company analysis: target value from relative valuation metrice on similar firms + takeover premium. c) Comparable transaction analysis: target value from takeover transactionl takeover premium included 30. Merger Valuations a) Combi
40、ned firm: V AT =V A+ V T+S C b) Takeover premium (to target): Gain T= TP = P T-V Tc) Synergies ( to acquirer): Gain A= S- TP = S- (P T -V T ) 31. Merger Risk acquirer prefers cash & target prefers stock. 32. Forms of Divestitures: equity carve outs, spin offs, split offs, and liquidations. EQUITY & ALTERNATIVE INVESTMETNS 1. Alpha: a) Ex ante = expected return required return from CAPM or APT b) Ex post = historical holding period return historical return on similar assets 2. Franchise value and growth process Tangible P/E =1/r Franchise P/E = franchise factor growth factor = FF GF
