CFA 公式表-Level II
Quantitative Methods
1. Simple Linear Regression
Correlation: ()()
xy xy x y Cov r s s =
t-test for r (df = n-2): t =
Estimated slope coefficient:
2
xy
x Cov σ
Estimated intercept: 01
ˆˆb y b =-x  Confidence interval for predicted Y-value: ^
c y t SE ±⨯of forecast 2. Multiple Regression
0112233()()()i i i Y b b X b X b X i i ε=+⨯+⨯+⨯+ ● Test statistical significance of b;
0:0
ˆ,1b
H b b t df n k s ==
=-- Reject  if  t or p-value < 0h ||t critical >α
● Confidence Interval:  ˆ()j j c b b t s ±⨯●
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-tail)
●
Standard error of estimate (SEE =), Smaller SEE means better fit.  ● Coefficient of determination (2/R RSS SST =). % of variability of Y
explained by X’s; Higher R 2 means better fit.  3. Regression Analysis-Problems
● Heteroskedasticity. Non-constant error variance. Detect with Breusch-Pagan
test. Correct with White-corrected standard errors.
● Autocorrelation. Correlation among error terms. Detect with Durbin-Watson
test; positive autocorrelation if DW<d 1. Correct by adjusting standard errors
using Hansen method.
● Multicollinearity. High correlation among X’s. Detect if F-test significant,
t-test 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 Misspecification
Regression coefficients are biased and inconsistent, lack of confidence in hypothesis tests of the coefficients or in the model predictions.  6. Linear Trend Model: 01t t y b b t ε=++ 7. Log-Linear Trend Models: 01ln()t t y b b t ε=++
8. Covariance Stationary: Mean and var. don’t change over time. To determine
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.  10. Autoregressive (AR) Models: Specified correctly if autocorrelation of
residuals not significant: t t p t p x b b x b x b x t ε---=+++++
11. Mean Reverting Level For AR(1):
1(1)
b b - 12. RMSE: square root of avg squared error.  13. Random Walk Time Series: 1t t x x t ε-=+
14. Seasonality: Indicated by statistically significant lagged err. term. Correct by
adding lagged term.  15. ARCH: Detected by estimating: 22011t t a a εεμ-=++ Variance o ARCH series: 22101t t a a σε+=+
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 70: 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 => incentive to discover new products and methods. ● Discovery => real return > target return.  6. Nominal & Real Exchange Rate
● Nominal ex. Rate (E): price of one currency in terms of another; 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:
appreciates● if quote is ₤ per $ (or 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)()day
min fwdrate fwdprem disc 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 rates, leads to currency dept, current acct surplus, and financial acct deficit.
10. Unanticipated shift to exp. Fiscal Policy: currency appr, current acct deficit,
& financial account surplus.  11. Purchasing Power Parity:
●  Law of one price: a single, clearly comparable good should have same real
price in all countries.
● Relative PPP: Countries with high inflation rates should see their currencies
depreciate.
01()1CounterCurrency t BaseCurrency I S E I
⎛⎫
+=
⎪ ⎪+⎝⎭
S  12. International Fisher Relation: Assumes real interest rates are equal across
borders, so interest differential equals expected inflation difference.
11(11(b b a
a r E I r E I ⎛⎫⎛++=
⎪ ++⎝⎭⎝))⎫⎪⎭
()()b a b a r r E I E I -≈-
13. Uncovered Interest Rate Parity: Countries with high nominal interest rates
should see their currencies depreciate. 01360()1360CounterCurrency n BaseCurrency n r S E n r ⎛⎫⎛⎫+ ⎪ ⎪⎝⎭⎝⎭⨯=⎛⎫⎛⎫+ ⎪ ⎪
⎝⎭⎝
⎭S
14. Interest Rate Parity: Countries with high nominal interest rates will have their
currencies sell at forward discount to prevent arbitrage. ()()
11b a r F S r +=
+ 15. Currency Arbitrage: up the bid and down the ask Financial Statement Analysis
1. Accounting for InterCorp Investments
a)  Minority passive: < 20% owned, no significant influence.
i. Held-to-maturity at cost on B/S; interest and realized gain/losses on I/S ii. Available-for-sale at FMV with unrealized gains/loss in equity on B/S;
dividends, interest, realized gains/losses on I/S
iii. Held-for-trading at FMV , dividend, interest, realized and unrealized
gains/losses on I/S.
b)  Minority active: 20-50% owned, significant influence. With equity
method, pro-rata share of the investee’s earnings increase, B/S investment account, also in I/S. Div. received decrease investment account. (div. not in I/S)
c)  Controlling: >50% owned, control. Consolidation, all assets, liability,
revenue, and expense of sub combined with parent, excluding
d)
preferred, similar to regular consolidation, except only include pro-rata share. US GAAP: equity method.
2.
Financial Effect of Choice of Method: equity, consolidation, proportionate
consolidation.
a)
All three methods report same net income.  b)
All three methods report same ROE
c)  Asset, liabilities, sales are highest under consolidation; lowest under
equity method; proportionate consolidation in between.  3. a)  b)
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 rate, low
compensation growth rate, high expected return.
4.Economic pension expense: if < firm contribution, diff = ↓ in overall pension
obligation. 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 unrecognized items.
6.Underlying Economic Pension Expense: Sum of all changes in PBO (except
benefits paid) less actual ROA. Also = change in funded status exclude firm’s contributions. Service cost= operating expense. Interest and actual ROA repeated as non operating income.
7.Business Combinations:
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)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 method.
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.
Qualifying 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 statement at average rate.
d)Exposure = shareholder’s equity