CFA level II formula sheet PDF

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Formula Sheet

Level II 2020

FinQuiz Formula Sheet CFA Program Level II 𝑆𝑆𝑇

(for single independent variable R2 = r2) Reading 4: Introduction to Regression 1

/) ∑-23(,- ., / )(0- .0

1.

Sample!Cov!(X, Y) =

2.

Correlation Coefficient = r,0 = r=

3.

789(,,0)

4.5

789:;

(?(0)

t-test (for normally distributed variables) =

•

?√4.B

t==

!t!distribution!with!(n − C

5.?

2)deg. of!freedom 4.

• •

5.

Intercept (b0) =

b0 = y - b1 x=

Slope or regression coefficient = !b5 = 789(S,T) or 9>?(S)

=

U )(T.T/) ∑(S.S ∑( S.SU)C

9.

! b - b1 Test statistic = t = 1 sb1 Confidence Interval =

YYW

4.Z.5

=X

∑1 [ )C -23 (T- .T 4.Z.5

Coefficient of Determination (R2) = =

YY\.YYW YY\

b1 ± t cs b1

d

= ` (𝑦c ce5

− 𝑦U)B

Source of Variability

DoF

Sum of Squares

Mean Sum of Squares

Regression (Explained)

1

RSS

MSR = RSS/1

Error (Unexplained)

n-2

SSE

MSE = SSE/n-2

Total

n-1

SST= RSS + SSE

ANOVA (Analysis of variance) = ANOVA

SS 𝑆𝑆𝑅

Regression df = k

d

= ` (𝑦bc ce5 B

− 𝑦U)

Standard Error of Estimate SEE = SW =

X 6.

•

Linear Regression = Yi = b0 + b1Xi + εi,

Total df = n-1

𝑆𝑆𝐸 Error df = n-k-1

d

= ` (𝑦c ce5

− 𝑦b)B

MSS 𝑆𝑆𝑅 𝑘

F 𝑆𝑆𝑅g 𝑘

𝑆𝑆𝐸 g(𝑛 − 𝑘 − 1)

𝑆𝑆𝐸 𝑛−𝑘 −1

10. F-Statistic or F-Test =

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lmo

=!

pqq )! r qqs (turu3)

(

(df numerator = k = 1) (df denominator = n – k – 1 = n – 2) 11. Prediction Intervals = Yv ± t 7 sx 5

(,., / C

) 𝑤ℎ𝑒𝑟𝑒!sxB = sB }1 + + • and (4.5) 0) = 𝜆 ∑’…e5 ‘𝑏U… ‘ 2. 3.

∑dce5 (𝑌c − 𝑌c )B + 𝜆 ∑’…e5 ‘𝑏•’ ‘ When l = 0, LASSO penalized regression = OLS regression

Reading 8: Big Data Projects 1.

yˆt +1 = bˆ0 + bˆ1 (T + 1)

𝑋c(d“”•–—c˜™š) =

›œ .›•œt ›•žŸ.›•œt

where Xi = value of observation

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µt is

ˆ 0 +α1 εˆ 2t t+1 = σˆ 2t +1 = α

Reading 6: Time Series Analysis 1.

where

an error term • Predicting variance of errors in period

xˆ t+2 = bˆ 0 + bˆ1 xt+1 6.

Correcting Seasonality in Time Series Models: •

xˆ t+1 = bˆ0 + bˆ1 xt •

Smoothing Past Values with n-Period Moving Average =

xt + xt -1 + xt -2 + ..... + xt -( n -1)

5. Chain Rule of Forecasting: • One-period ahead forecast =

∑ •Ž2C( •bŽ.•bŽu3 ) C

•

Level II 2020

Formula Sheet

Performance Metrics: 2. Accuracy = (TP + TN)/(TP + FP + TN + FN) F1 score = (2*P*R)/(P + R) 3.

4.

Level II 2020

5

•

(1 + i°) = S∫ ¹1 + i∫ º » g

•

F∫ /° = S∫ ‰( g

•

Using day count convention:

°

' )1+ id (

Receiver Operating Characteristic (ROC): False positive rate (FPR) = FP/(TN + FP) and True positive rate (TPR) = TP/(TP + FN), which is same as recall

° 5¾‡∫

5¾‡¼ )

Š

½

®∫ /¼

7.

Ff / d -S f / d S f/d

! Actual $* &, = #" 360 %+

' ! Actual $*' 1 * , S f /d )1+ i f # &,) " 360 %+)( Ff /d ,+ (

d

(𝑃𝑟𝑒𝑑𝑖𝑐𝑡𝑒𝑑c − 𝐴𝑐𝑡𝑢𝑎𝑙c )B 𝑛

ce5

•

Reading 9: Excerpt from ‘Probabilistic Approaches, Scenario Analysis, Decision Tree & Simulations’

6.

Uncovered Interest Rate Parity : •

Reading 10: Currency Exchange Rates 1. 2.

Bid-offer Spread = Offer price – Bid price Fwd!rate! = Spot!Exchange!rate! +

3.

Forward!premium/discount!(in!%) ! =

!

• • •

4·µ!?>²µ

4.

To convert spot rate into forward quote: • Spot exchange rate × (1 + % premium) • Spot exchange rate × (1 - % discount)

5.

Covered interest rate parity:

% DS

e

f /d

= i f - id

Forward premium or discount: For one year horizon =

"i −i % S f /d $ f d ' ≅ S f /d (i f − id ) # 1+ id &

5ƒ,ƒƒƒ

−1

i f - %DS e f / d = i d

Ff /d − S f /d =

®8?¯>?°!±8‡4²<

4·µ!?>²µ.(x8?¯>?°!±8‡4²...