CFA二级公式表

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: 2xy

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

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: 01122......t t t p t p x b b x b x b x t ε---=+++++

11. Mean Reverting Level For AR(1): 01(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

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4. Neoclassical Growth Theory