l 2 formula sheet june 2016

8/17/2019 l 2 Formula Sheet June 2016

1/36

FinQuiz Formula Sheet CFA Level II 2016

Reading 9: Correlation & Regression

1. Sample "#$ %&' ( )*+) ,*+,

-*./

0+1

2.

Correlation Coefficient = 2), ( 34567896:897: or

2 ( 3458)&,:

5;


2/36


Reading 11: Time Series Analysis

1. Linear Trend Models = yt = b0 + b1t+ !t

• Predicted/fitted value of yt in period

(T + 1) = )1(ˆˆˆ 101 ++=+ T bb yt

2. Log-Linear Trend Models = yt = eb0+b

1t

3. Autoregressive Time-Series Models:

• First order autoregressive AR (1) = xt

= b0 + b1 x t-1 + !t

• pth-order autoregressive AR (p) = xt

= b0 + b1 x t-1 + b2 x t-2 + …..+ b p x t-p

+!t

4. Mean reverting level of

1

0

1 b

b x

t

!

=

5. Chain Rule of Forecasting:

• One-period ahead forecast =

ˆ xt +1

= b̂

0 +

b̂1 x

t

• Two-period ahead forecast=

ˆ xt +2

= b̂

0 +

b̂1 x

t +1

6. Random Walks and Unit Roots:

• Random Walk without drift = xt = x t-

1 + !t where, b0 = 0 and b1 = 1.

• Correcting Random Walk = yt = xt - x

t-1

• Random walk with a drift = x t = b0 + x

t-1 + !t where, b0 # 0 and b1 = 1

• By taking first difference yt = xt - x t-1

= b0 + !t

7. Using Dickey-Fuller Test = xt - x t-1 = b0 +

(b1 -1) x t-1 + !t

8.

Smoothing Past Values with n-Period

Moving Average =

n

x x x xnt t t t )1(21 ..... !!!! ++++

9. Correcting Seasonality in Time Series

Models:

• For quarterly data = x t = b0 + b1x t-1 +

b2x t-4 + !t

• For monthly data = xt = b0 + b1x t-1 +

b2x t-12 + !t

10. ARCH model =

t t t µ ! " " ! ++= #1

2

10

2ˆˆ where

t µ is

an error term

• Predicting variance of errors in period

t+1 = !̂ 2

t t +1 = "̂

0 +"

1 #̂

2

t

Reading 12: Excerpt from ‘Probabilistic

Approaches , Scenario Analysis, Decision Tree

& Simulations’

Reading 13: Currency Exchange Rates

1.

Bid-offer Spread = Offer price – Bid price

2. €F@ 2=J ( Q‚#= ƒ„…GEKJ 2=J r

†4


3/36


• For one year horizon =

F f /d ! S f /d =

S f /d i f ! id 1+ i

d

"

#

$%

&

' ( S f /d (i f ! id )

• Using day count convention:

F f /d ! S f /d = S f /d

Actual

360

"

#$%

&'

1+ id Actual

360

"

#$%

&'

(

)

****

+

,

----

(i f ! id )

7. Forward discount or premium as % of spot

rate:

)(/

//

d f d f

d f d f ii

S

S F !"

!

•

If uncovered interest rate parity holds

=

F f /d

! S f /d

S f /d

=%"S e

f /d # (i f ! id )

8. Purchasing Power parity (PPP)

• Pf = S f/d % Pd

• S f/d = Pf / Pd

9.

Relative version of PPP = %'S f/d = (f – (d

10. Ex ante version of PPP = %'Sef/d = (ef –

(ed

11. Real Exchange Rate

qf/d =!!

"

#

$$

%

&=

!!

"

#

$$

%

&

f

d d f

f

d d f

P

P S

P

P S /

/

or!!

"

#

$$

%

&=

f

d d f d f

CPI

CPI S q

//

12. Fisher effect:

•

id = r d + (!

d • if = r f + (

!f

• if – id = (r f – r d) + ((!f - (

!d)

• (r f – r d) = (if – id) - ((!f - (

!d)

13. When both uncovered interest rate parity

and ex-ante PPP hold:

• (r f – r d) = %' S!f/d - %' S

!f/d = 0

• International Fisher Effect: if – id = (!f -

(!d

14. When all the key international parity

conditions are held at all times:

BOP = Current A/C + Capital A/C +

Official Reserve A/C = 0

15.

Real exchange rate = “” = “”

r

q– H q— H ˜– H ˜—

16. Interest Rate Differentials, Carry Trades

and Exchange Rates

q L/ H

= q L/ H

+ (i H

! i L

)! (! " H

!! " L

)! (# H

!# L

)

17. Policy Rate under Taylor rule:

• i = rn +! +" (! ! ! *)+# ( y! y*

• Neutral real policy rate + Current inf

rate + ) (Inf gap) + * (Output gap)

18. Exchange rates using the Taylor Rule =

™šS›‹RšV ( ™šS›‹RšV r 20Rš H 20

šS r

œ Ršž ŸRš H šS H ŸšS r

¡Rš H ¡ ŸRš H ¡šS H ¡ ŸšS H

¢Rš H ¢šS

Reading 14: Economic Growth & The

Investment Decision

1.

Economic growth = Annual % ' in real

GDP or in real per capita GDP

2. P = GDP R£›¤

¤R

3. Expressing in terms of logarithmic rates:

• (1/T) % 'P = (1/T) % 'GDP + (1/T)

%' (E / GDP) + (1/T) % '(P / E)

• % ' in stock MV = % ' in GDP + %

' in share of earnings (profit) in GDP


4/36


+ % ' in the price-to-earnings

multiple

4. A two-factor aggregate production

function: Y = AF (K, L)

5. Cobb-Douglas Production Function = F

(K, L) = K ) L1 - )

6. Under the Cobb-Douglas production

function:

• Marginal product of capital = MPK =

) AK )-1 L 1-) = ) Y/K

• ) Y/K = r!) = r (K) / Y = Capital

income / Output or GDP

7. Output per worker or Average labor

productivity (Y/L or y):

• GDP/Labor input = TFP % capital-to-

labor ratio % share of capital in GDP

• Or y = Y/L = Ak )

8. Contribution of Capital Deepening = Labor

productivity growth rate – TFP

9.

Contribution of Improvement intechnology = Labor productivity growth

rate – Capital Deepening

10. Growth Accounting based on Solow

Approach = 'Y /Y = 'A / A + ) 'K/K +

(1 – )) 'L/ L

11. Labor productivity growth accounting

equation

• Growth rate in potential GDP = LT g

rate of labor force + LT g rate in labor

productivity

12. Balanced or Steady State Rate of Growth

in Neoclassical Growth Theory:

• Growth in physical capital stock = 'K

= sY – +K

13.

In the steady state:

• Growth rate of capital per worker = 'k

/ k = 'y / y = 'A / A + ) 'k / k =¥¦§

1+ ¨! Steady state growth rate of

labor productivity

• Growth rate of Total output = 'Y / Y

= Growth rate of TFP scaled by labor

force share + Growth rate in the labor

force =©

1+ ¨ + n

• Steady state Output-to-capital ratio =ª

«=

1

¬

©

1+ ¨ r r _ ( ®

• Gross investment per worker =©

1+ ¨ r r _ ]

• Slope of straight line = [+ + n + , / (1

– ))]14. During the transition to the steady state

growth path:

• Growth rates of output per capita = 'y

/ y =©

1+ ¨ r ¯°

ª

« H ® (

©

1+¨ + ¯° (y/k – -)

• Capital-to-labor ratio = 'k / k =©

1+ ¨ r °

ª

« H ® (

©

1+¨ + s

(y/k – -)

15.

Proportional impact of the saving ratechange on the capital-to-labor ratio and per

capita income over time:

•

k new

k old

=

Y

K

!

"#

$

%&new

Y

K

!

"#

$

%&old

'

(

))))

*

+

,,,,

1

! -1

•

!

"#

$%&

'=

old

new

old

new

k

k

y

y

16. Production function in the endogenous

growth model = ye = f (k e) = ck e

• Growth rate of output per capita =

'ye/ye = 'k e/k e = sc – + – n

Reading 15: Economics of Regulation

Reading 16: Inventories: Implications for

Financial Statements & Ratios

1. End. Inventory = Beg. inventory +

purchases – COGS

2. ±²" ‚J2 DEA= (U4Š;³ 349Š 4m 44ˆ9 ;5;y³;´³ m4< 9;³

U4Š;³ µ0yŠ9 ;5;y³;´³ m4< 9;³


5/36


3. LIFO Reserve = FIFO Inventory – LIFO

Inventory

4. FIFO COGS = LIFO COGS – ¶_· in LIFOreserve= LIFO COGS – (End LIFO

Reserve – Beg LIFO reserve)

5. N.I (FIFO) = Net Income (LIFO) + [¸ inLIFO reserve % (1 – tax rate)]

6. R.E (FIFO) = R.E (LIFO) + [LIFO reserve

% (1 – tax rate)]

7. Tax liability (FIFO) = Tax liability (LIFO)

+ (LIFO reserve % tax rate)

8. Cumulative amount of Income Tax savings

using the LIFO method e.g. in year 2015=

(LIFO Reserve at end of 2015 % tax rate in

2015)

9. Amount added to R.E e.g. in year 2015, if

FIFO method is used instead of LIFO

method = [LIFO Reserve at end of 2015 %

(1 - tax rate in 2015)]

10. To convert B.S to FIFO:

• Inventory is increased by LIFO

Reserve.

• Cash is decreased by (LIFO Reserve %

Tax rate %).

• Shareholders’ equity (R.E) is

increased by [LIFO Reserve % (1 – tax

rate %)]

11. Inventory Turnover Ratio =¹49Š 4m 44ˆ9 94³ˆ

º5


6/36


6. Adjusted EBITDA=Adj EBIT + dep exp +

amort. Exp. or Adj. EBITDA= EBITDA

(as reported)

7.

Adj. Operating CF =Reported operating

CF – cap int

8. Adj. Investing CF=Reported investing CF

+ cap int

Depreciation:

9.

ÇJ‚ ƒ„‚ ( È


7/36


Reading 18: Interoperate Investments

1. Summary of Accounting Treatment of Investments

Income Statement (I.S) Balance Sheet (B.S) Statement

ofSH’sEq

uity

Held-to-

maturity

" i income = Market rate at purchase % Initial fair value (FV) of a

debt security

Or i income = i pmt – Amort

i pmt = (Coupon rate % Par value)

Amort = i pmt – i income

"

If debt security is sold: Realized g/l reported on I.S = SP – CV or

Amort cost

" Initially, at FV (IFRS) or initial price paid (US

GAAP)

" Subsequently, reported at amort cost at the

subsequent reporting date on B.S.

N/A

Held

for

tradingsecurity

"

i income = Market rate % Initial FV

" Unrealized g/l = FV at the end of Yr t – Amort Cost at end of Yr t

If debt security is sold:" Realized g/l reported on I.S= SP – Recorded FV

" Initially, at FV.

" Subsequently, at FV at subsequent reporting date

on B.S.

Designated

at

fair value

" i income = Market rate at purchase % Initial FV

"

Unrealized g/l = FV at the end of Yr t – Amortized Cost at end of

Yr t

If debt security is sold:

" Realized g/l reported on I.S= SP – Recorded FV

" Reported at FV at the end of Yr t

"

Subsequently, at FV at the subsequent reporting

date on B.S

Available

-for-sale

" i income = Market rate at purchase % Initial Fv

If debt security is sold:

" Cumulative unrealized g/l is removed from OCI and entire g/l

recognized in P&l statement.

Where, Realized g/l in I.S = (SP – Recorded FV) + Unrealized g/l

" Reported at FV at the end of Yr t

" Subsequently, at FV at the subsequent reporting

date on the B.S.

Unrealized g/l (net

of tax) = FV at end

of Yr t – Amort Cost

at end of Yr t

• Unrealized g/l

(net of tax) is

reported as OCI


8/36


9/36


5. Downstream Transactions

Investor’s share of Associate’s

reported NI (% of Ownership Interest

% Reported NI)

xxx

Less: Amort of excess PP (xxx)

Less: Unrealized profit (% of

Ownership Interest % Profit from the

downstream sale in Associate’s NI)

(xxx)

= Equity Income to be reported as a

line item on Investor’s I.S

xxx

Unrealized profit = % of goods unsold % Profit

on the sale to investee

Investor’s share of the unrealized profit =

Unrealized profit % % of goods unsold

Investor’s share of associate’s

reported NI (% of Ownership Interest

% Reported NI)

xxx

Less: Amort of excess PP (xxx)

Add: Realized profit (% of goods

unsold % Unrealized profit)

xxx

= Equity Income to be reported as a

line item on Investor’s I.S

xxx

Business Combinations6. Merger = Company X + Company Y

= Company X

7. Acquisition = Company X + Company Y =

(Company X + Company Y)

8. Consolidation = Company X + Company

Y = Company Z

Goodwill

9. Full Goodwill = Total FV of the

Subsidiary – FV of subsidiary’s

identifiable net assets

10.

Partial Goodwill Method:

• Goodwill = FV of acquisition –

Acquirer’s share of FV of all

identifiable tangible and intangible

assets, liabilities and contingent

liabilities acquired

Or

• Goodwill = Purchase price – parent’s

(acquirer’s) proportionate share of the

FV of subsidiary’s identifiable net

assets.

11. Under Acquisition method, the allocation

of PP:

FV of the stock issued xxx

Add: BV of Investee’s net assets xxx

= Excess PP xxx

FV of the stock issued xxx

Less: FV allocated to identifiable net

assets

(xxx)

= Goodwill xxx

12. Allocation of excess PP: Excess PPP =

Sum of diff b/w FV and BV of identifiable

assets + Goodwill

13. Combined Assets & Liabilities (A&L)

reported on Consolidated B.S under

acquisition method: Consolidated B.S

under acquisition method = BV for A&L

of Investor + FV for A&L acquired from

Acquiree

14.

Combined Paid-in Capital (PIC) = (FV of

the stock issued to effect the transaction –

Par value of the stock issued) + Additional

PIC of investor

15. Minority Interest = % of subsidiary not

owned by the Parent % Subsidiary’s Equity

16. Value of non-controlling interest under full

goodwill method = Non-controlling

interest’s proportionate interest in

subsidiary % FV of subsidiary onacquisition date

17. Value of non-controlling interest under

partial goodwill method = Non-controlling

interest’s proportionate interest in

subsidiary % FVof the subsidiary’s

identifiable net assets on acquisition date

Goodwill Impairment:

18. Goodwill Impairment Test under IFRS:

•

Impaired when CA of the Cash-generating

Unit > RA of the Cash-generating Unit

• Impairment loss = CA of Cash-generating

Unit - RA of Cash-generating Unit where,

RA = Higher of Net SP and its VIU

Net SP = FV – costs to sell

VIU = PV of expected future CF of

cash-generating unit


10/36


19. Goodwill Impairment Test under U.S.

GAAP (Two Step Approach)

• Step 1: Goodwill Impairment Test

• Impaired when CV of Reporting Unit

(including Goodwill) > FV of

Reporting Unit (including Goodwill).

• Step 2: Measurement of Impairment

loss = CV of Reporting unit’s

Goodwill - Implied FV of Reporting

unit’s Goodwill

• Where Implied FV of Reporting unit’s

Goodwill = FV of Reporting Unit –

FV of Reporting unit’s net assets

Reading 19: Employee Compensation: PostEmployment & Share-Based

1. Under DC Plans: Pension exp = Co.’s

annual contribution to plans adjusted for ¸ in yr-end accruals

2. Funded Status = PV of DB obligations –

FV of plan assets

3.

Period pension cost of a Co.’s DB pension

plan = ¸ in Net pension liability or assetadjusted for employer’s contributions

4. Net i exp = Discount rate % Net Pension

liability

where Discount Rate = rate used to

calculate PV of future pension benefits

5. Net i income = Discount rate % Net

Pension asset

6. Net return on plan assets = Actual return

on plan assets – (Plan assets % i rate)

7. Actuarial g/l = Actual return – (Plan assets

% Expected return)

8. Total Periodic Pension Costs =Sum of

components of periodic pension costs

• Total periodic pension cost in a given

period = ¸in Net pension liability or

asset adjusted for employercontributions

• Total Net periodic pension cost (End

Funded Status* – Beg Funded Status*)

– Employer Contribution

where *Pension liability is treated as a

negative

9. Adjusted Total P&L pension exp (income)

• = Current service costs + i costs + (-)

actuarial losses (actuarial gains) + past

service costs (or plan amendments) –

(+) Actual return (loss) on plan assets

Or

• = Reported Total P&L pension exp

(income) + Expected return on plan

assets – Actual return on plan assets

10. Adjusted Pre-tax Income:

• = Reported Pre-tax income + (Actual

return on plan assets – Expected return

on plan assets)

Or

• = Reported Pre-tax income + Total

reported pension and other post-

retirement benefits - Current service

costs - i exp component of pension

cost + Actual return on plan assets

11. Adjusted Net Operating Exp=Reported Net

operating exp – Total reported pension and

other post-retirement benefits + Current

service costs

12. Adjusted i Exp. = Reported i exp. + i exp.

component of pension cost

13. Adjusted i and investment Income

=Reported i and investment income +

Actual return on plan assets

14. Compensation exp. = FV of stock on the

Grant Date

16. "#N‚JEB=A#E J„‚ 2J…#KEAÎJ@ (

š0


11/36


Reading 20: Multinational Operations

1. Cumulative Translation Adjustment = CTA = Assets – Liabilities –

Common Stock – Retained Earnings

2.

Balance Sheet Exposure:Foreign Currency (FC)

B.S Exposure Strengthens Weakens

When assets translated atcurrent X rate > liabilitiestranslated at current X rate

Net Asset B.Sexposure

+vetranslation

adj

-vetranslation

adj

When liabilities translated atcurrent X rate > assetstranslated at current X rate

Net Liability B.Sexposure

-vetranslation

adj

+vetranslation

Adj

(X = exchange)

3. Re-measurement Gain = NI . NI before re-measurement gain

4. Re-measurement Loss = NI . NI before Re-measurement loss

5.

Rules For Translation Of A Foreign Subsidiary’s FC Financial

Statements (F.Ss) Into Parent’s Presentation Currency Under IFRS &

U.S. GAAP

Foreign Subsidiary’s Functional Currency

FC Parent’s PresentationCurrency

Translation Method: Current Ratemethod

Temporal Method

X rate at which F.Ss are

translated from foreignsubsidiary’s bookkeepingcurrency to parent’s

presentation currency.

ASSETS Monetary assets: Cash, a/creceivables

Nonmonetary Assets:i) Measured at current valuei.e. marketable securities &inventories measured at

Current rate

Current rate

Current rate

Current rate

Foreign Subsidiary’s Functional Currency

FC Parent’s PresentationCurrency

market value under the lowerof cost or market rule.ii) Measured at historical

costs e.g. PP&E

Current rate Historical rate

LIABILITIES

Monetary liabilities: a/c payable, LT debt, accruedexp., and deferred incometaxes.

Nonmonetary liabilities:i) measured at current valueii) not measured at currentvalue i.e. deferred revenue

Current rate

Current rate

Current rate

Current rate

Current rate

Historical rate

EQUITYOther than R.E i.e. CommonStock

Retained Earnings (R.E)

Historical rates

Beg R.E +

translated NI – div.translated at

historical rate

Historical rates

Beg R.E + translated NI –

div. translated at historicalrate

Revenues Average rate Average rate

EXPENSES Most Expenses

Expenses related to assetstranslated at historical X rate

e.g. COGS, Dep.,& Amort. etc.

Average rate

Average rate

Average rate

Historical rate

NI Average rate Mixed (a mix of averagerate & historical rate)

Exposure Net Assets or NetLiabilities

Net monetary assets or Netmonetary liabilities

Treatment of translation adj.in parent’s consolidated F.Ss

Accumulated as aseparate component

of equity

Included as g/l in NI


12/36


TEMPORAL METHOD: CURRENTRATE

METHOD Net MonetaryLiability Exposure

Net MonetaryAsset Exposure

FCstrengthens

relative to parent’s presentation

currency

" Rev Ð " Assets Ð

"

Liabilities Ð

" NI Ñ " SH’ equity Ñ " Translation

loss


"

Liabilities Ð

" NI Ð " SH’ equity Ð " Translation

gain


"

Liabilities Ð

" NI Ð " SH’ equity

Ð " +ve

Translationadj.

FC weakensrelative to parent’s

presentationcurrency

" Rev Ñ " Assets Ñ "

Liabilities Ñ

" NI Ð " SH’ equity Ð " Translation

gain


Liabilities Ñ

" NI Ñ " SH’ equity Ñ " Translation

loss


Liabilities Ñ

"

Net Income

Ñ " SH’ equity Ñ

"

-veTranslationadj.

6. Impact of Changing Exchange Rates on Exposure

Foreign Currency

Strengthens Weakens

CURRENT RATE METHOD: Net Assets Net Liabilities

GainLoss

LossGain

TEMPORAL METHOD: Net Monetary Assets Net Monetary Liabilities

GainLoss

LossGain

Hyperinflationary Economy

7. Restatement Factor =¹µ


13/36


Reading 21: Evaluating Quality of Financial

Reports

1. DSR (days sales receivable index) =

(Receivablest/Salest) / (Receivablest–

1/Salest–1)

2. GMI (gross margin index) = Gross

margint–1 / Gross margint

3. AQI (asset quality index) = [1 – (PP&E t+

CAt)/TAt ] / [1 – (PP&Et–1+ CAt-1)/TAt-1]

4. SGI (sales growth index) = Salest/Salest–1

5.

DEPI (depreciation index) = Dep ratet– 1/Dep ratet

where, Dep rate = Dep/(Dep + PP&E)

6.

SGAI (sales, general, and admin exp

index) = (SGAt/Salest) / (SGAt–1/Salest–1)

7. Accruals = (Income before extraordinary

items – Cash from operations)/TA

8. LEVI (leverage index) = Leveraget /

Leveraget–1 where, Leverage = Debt /

Assets

9.

Earnings t+1 = ) + (*1 % Earnings t) + !

10. Account receivable turnover = (365/DSO)

11. Z-score = `LI É¼Š Ò¹

Uº + `LÓ É

VLR

Uº +

ÔLÔ ÉRÁ»U

Uº + ÕLÖ É

×LØ 4m RÀµyŠP

ÁLØ 4m ³y;´y³yŠy9 +

`LÕ ÉS;³9

ULº

Reading 22: Integration of Financial Statement

Analysis

1. DuPont Analysis:

• ROE = Tax Burden % Interest

Burden % EBIT margin % TATO %

Financial Leverage

• ROE = NI/EBT % EBT/EBIT %

EBIT/Sales % Sales/Assets %

Assets/Equity

•

ROE = Net profit margin % asset

turnover % leverage

• Adjusted Asset base = Adjusted Total

Assets = Total Assets of the company

– Investments in Associates

• Adjusted NI = NI of Co – NI from

Associates

• ²@ÂDB=J@ Ù„ ÊD2@JE (¼»+RÀµyŠP y034½

RÁU

•

²@ÂDB=J@ Ù²ÙÚ (ÛÜÝÞÜß àákÞÜß âãLä-Ýåæç-æLèâ-‘ àákâ-‘ âãLä-Ýåæç-æ

>

Accruals and Earnings Quality

2. B.S based aggregate accruals

• Aggregate Accrualst = NOAt – NOAt-1

where, NOAt = Net operating Assets t

= Op Assets t – Op Liab t = [{TA t –

(Cash t + ST invstmnt. t)} – {Total liab

t – (Total LT debt t + Debt in current

liab.)}]

• ÊL Q CBJ@ ²……2DÌB é=A# (¼Èº~+¼Èº~k/

¼Èº~’¼Èº~k/>

3. CF based aggregate accruals:

• Aggregate Accruals = NI t – (CFO t +

CFI t)

• "€ CBJ@ ²……2DÌB é=A# (¼»æ+8¹†Èæ’¹†»æ:

8¼Èºæ’¼Èºæk/:>

• Op. CF before interest and taxes = Op.

CF + cash i paid + cash taxes paid

• Op income adjusted for accounting ¸

= Profit before i& taxes + amort. ofgoodwill

4. "BG éJ=D2E #E ²BBJ=B ( È‰L¹†

º5 ULº

5. Cash Flow to Reinvestment =È‰L¹†

3;‰yŠ;³ O‰0ˆyŠµ


14/36


9. Parent Co. pro-rata share of

subsidiary/affiliates = (Subsidiary’s share

price in FC% Shares held by Parent Co. %

X- rate)/Parent Co. total market

capitalization

10. Implied Value of Parent Co. (excl.

subsidiary/affiliates) = Parent Co.’s Mkt

Cap - Value of subsidiary/affiliate holdings

11. P/E ratio of Parent Co =¤;


15/36


• Total value of Co. = NPV (PV of RI)

+ Original Equity investment +

Original Debt investment

Claims Valuation

17.

Total value of Co. = value of liabilities +

value of equity

Reading 24: Capital Structure

1. ±²"" ( 2Òº¹¹ ( ›

Ø É2ˆÉ ` H = r

R

Ø É2

2. Total value of Co. = V = D + E

3. WACC without taxes = 2Òº¹¹ (›

ØÉ2ˆ r

R

ØÉ2

4. "#B= #M ƒ™DA=¡ ( 2 ( 2u r 82u H 2ˆ:›

R

5.

Ë ( Ç r ƒ ( »0Š


16/36


Payout Policies:

7. Stable Div. Policy

• Expected Ð in Div. = Ð in Earnings % Target payout ratio % Adj. factor

• Adj. factor = 1/no. of yrs. over which

adj. in div. will take place

• Expected Div = Last div. + (Expected

Ð in earnings % Target payout ratio % Adj. factor)

8.

Residual Div. Policy

• Div. = Earnings – (Capital budget %

Equity % in capital structure) or

• Div. = Zero, whichever is greater.

9.

Div. Payout Ratio =›y5L

¼»

10. Div. Coverage Ratio =¼»

›y5L

11. FCFE Coverage Ratio =†¹†R

÷›y5L’SŽ;


17/36


• When takeover premium is given in

%, Estimated takeover price of Target

= (Estimated stock price of Target

based on Comparables) % (1 +

Takeover premium in %)

18. Target Shareholders’ gain = Premium = P T

– V T

where,

P T = price paid for target company

V T = pre-merger value of target

company

19.

Acquirer’s gain = Synergies – Premium =

S – (P T – V T)

20. Post-merger value of the combined

company = V A* = V A + V T + S – C

where,

V A = pre-merger value of the acquirer

C = cash paid to target SH i.e. cash paid =

cash price paid per share of target co. % no.

of shares outstanding of target co.

21. In Stock offer = P T = (N % P AT)

where,

P T = price paid for target co.

N = No. of new shares target receives

P AT = price per share of combined firm

after merger announcement

Reading 29: Equity Valuation: Applications &

Processes

1. Mispricing = VE – P = (V- P) + (VE –

V)

• VE –P: Mispricing

• V–P: True Mispricing

• VE –V: Valuation Error

where,VE = estimated value

P = market price

V = intrinsic value

2. Residual Income Model = NI – (cost of

equity % Beg value Equity)

Reading 30: Return Concepts

1. Dividend yield or investment income =

(DH/P0)

2. Price appreciation R = (PH-P0)/P0

3. HPR = r = {(DH + PH) / P0} – 1 OR r =

{(P1 – P0+CF1) / P0

4.

Expected Alpha = Exp. R – Req. R

5. Realized Alpha (Ex-post alpha) = (Actual

HPR) – (Contemporaneous Req. R)

6.

Expected HPR:

• When an asset’s intrinsic value #

market price, the investor expects to

earn = RR + return from the

convergence of price to value

• When an asset’s intrinsic value =

price, the investor expects to earn RR

only.

• E (R T) & r T + {(V0 – P0) / P0}

where,r T = periodic required RoR,

• {(V0 – P0)/P0} = estimate of return

from convergence over period

7.

IRR:

• Intrinsic value= D1 / (k-g)

• If asset (fairly priced), market price =

intrinsic value: k = (D1 / P0) + g

8. Req ROE = R f + ERP

9. GGM Intrinsic value = D1/ (k-g)

Macroeconomic Model Estimates (Supply side

models):

10.

ERP = [{(1+EINFL) (1+EGREPS)

(1+EGPE)-1} +EINC]-Expected R f R

• where EINFL= expected inf.(

forecasted as) {(1+YTM of 20-yr T-

bonds) / (1+YTM of 20-yr TIPS)} –

1.

• EGREPS = expected growth rate in

real EPS.

•

Real GDP growth rate = labor productivity growth + labor supply

growth rate

Labor supply growth rate = population

growth rate + increase in labor force

participation rate


18/36


• EGPE = expected growth rate in P/E

ratio. (For efficient markets 1+EGPE

= 1+0 = 1.

• EINC = expected income component

(includes dividend yield &

reinvestment R)

11. CAPM: Required Return on share i =

Current expected Rf R + Bi (ERP)

• where ERP = Expected R on mkt

portfolio – R F R

• Beta = Cov of returns with mkt R /mkt

portfolio var.

12. Adjusted Beta = (2/3) (Unadjusted beta) +

(1/3) (1.0)

13.

Beta Estimation for Thinly Traded Stocks

and Nonpublic Companies

• Bu & [1/ {1+ (D/E)}] %Be

• Be’ & [1+ (D’/E’)] %Bu

14. Multifactor Models = r = R f + (RP)1 +

(RP)2 + … + (RP)k

• RPi = (Factor sensitivity)i % (Factor

RP)i.

15. The Fama-French Model (FFM): r i =R f +

Bimarket% RMRF + Bi

size% SMB + Bivalue %

HML

• RMRF = R M –R f

• SMB(small minus big) = Avg. R on 3

small-cap portfolios – avg. R on 3

large-cap portfolios.

• HML (high minus low) = Avg. R on 2

high Book-to-market portfolios – avg.

R on 2 low book-to-market portfolios.

16. Pastor-Stambaugh Model (PSM): r i = R f +

Bimarket

%RMRF + Bisize% SMB + Bi

value %

HML+ BiLiq% LIQ

17. 5-factor BIRR Model: r i = T-bill rate +

(sensitivity to confidence risk % confidence

RP)–(sensitivity to time horizon % time

horizon RP) – (sensitivity to inf. risk % inf.

RP) + (sensitivity to business cycle risk % business cycle RP) + (sensitivity to mkt.

timing risk % mkt. timing RP)

18. Build-Up Approaches for Private Business

Valuation: r i = r f + ERP + Size premi

+Specific Co. premi

19. Bond yield Plus RP (BYPRP) cost of

equity = YTM on the co.’s LT debt + RP

Country Spread Model

20. ERP estimate = ERP for a developed mkt

+ Country prem.

• Country Prem. = yield on emerging

mkt bonds (denominated in currency

of developed market) – yield on

developed mkt. govt. bonds

21. Cost of Capital = WACC = {D/(D+E)}r d

(1-Tax rate) + {E / (D+E)}r E

Reading 31: The five competitive forces that

shape strategy

Reading 32: Your strategy needs a strategy

Reading 33: Industry & company analysis

1. % of sales (specific geographic region) =

Sales of a particular region / Total sales of

a co.

2.

Co.’s projected Rev. growth = Projected

mkt. share % Projected sales of a given

product mkt.

3. Forecasted variable costs = % of rev. Or =

Unit volume % Unit variable costs

4.

COGS =Raw materials + Direct labor +

Overhead (in producing the goods)

5.

Finance costs = (Fixed i rate on debt %

Gross debt at beg. of period) – (i income

rate % cash position at beg of period)

6. Gross debt = LT financial debt + ST

financial debt + Accrued interest

7. Net debt = Gross debt – Cash and cash

equivalents


19/36


8. Effective i rate = i exp / Avg gross debt

9. i rate on avg cash position =i income / Avg

cash position

10.

i rate on avg. net debt = Net i exp / Avg.

net debt

11. Deferred tax asset/liability = Profit and

loss (reported) tax amount – Cash tax

amount

12. Projected A/C receivable = Forecasted

annual sales (assuming all credit sales) %

(Assumed DSO/ 365)

13. Projected inventory = Assumed COGS /

Assumed Inventory TO ratio

14.

ROIC= NOPLAT / Invested Capital = EBI

/ (Operating assets – Operating liab.)

15. ROCE = Op. profit / Capital employed (i.e.

debt and equity capital)

16. Rev. loss for co. due to cannibalization of

demand = Projected no. of units of product

cannibalized by the new substitute product

% Estimated ASP

Where,

• Average selling price (ASP) =¹4½‰;0P¿9 9Šy½;Šˆ ;5L


20/36


Inventories

Add: Trade and other receivables

Add: Cash & cash equivalents

Add: Other current assets

=Total current assets

Total assets = Total non-current +

Total current assets

Share capital

Add: Share premium

Less: Treasury shares

Add: Consolidated reserves+Net profit

to co. owners

Plus: Translation reserve

+/-: Profit or loss recorded in equity

= Equity attributable to

shareholdersPlus: Non-controlling interest

= Equity

LT financial debt

Add: Provision for employee benefits

Add: LT provisions for liabilities and

charges

Add: Deferred tax liabilities

= Total non-current liabilities

ST financial debt and accrued interest

Add: Trade and other payables

Add: Income tax payable

Add: ST provisions for liabilities and

charges

Add: derivative financial instruments

Add: Liabilities held for sale

= Current liabilities

24.

FCFF:

Normalized operating profit

Less: Taxes

= Normalized operating

profit after tax

Add: Dep. & amort.

¸ in WCLess: Capital expenditures

= FCFF

Reading 34: Discounted dividend valuation

1. Asset’s value is PV of its expected future

CFs i.e. Ëu ( ¹†æ

1’< æ0Š\1

2.

RI = NI – (cost of equity % Beg. BV of

common equity)

3. In RI Model: Value of stock = BVPS at t =

0 + PV of expected future residual

earnings

• where, BVPS = common SHs’ equity /

no. of common shares outstanding

• RI model (assumes Clean Surplus

Accounting holds) i.e. BV t = BVt-1 +

NIt – Divt

4.

DDM• With Single HP = Value of Stock =

PV of expected Div. + PV of expected

Selling Price at the end of year one =

Ëu ( ›/81’


21/36


10. Ù2AÌAEK Å‹ƒ 2=A# (¤&R&

(›&81’:

R&8


22/36


• Total value of Equity (common) =

Total Firm value – Market value of

Debt – Preferred stock

9. Finding FCFF and FCFE from EBIT or

EBITDA

• FCFF = EBIT (1 – Tax rate) + Dep –

FCInv – WCInv

• FCFF = EBITDA (1 – Tax rate) + Dep

(Tax rate) – FCInv – WCInv

• FCFE = FCFF – Int (1 – Tax rate) +

Net borrowing + issuance of preferred

stocks – redemption of preferred stock

10. Forecasted FCFF = Forecasted [EBIT %(1

– Tax rate) – FCInv – WCInv]

11. Incremental fixed capital expenditures as a

proportion of sales increases =¹;‰yŠ;³ O‰+›‰ O‰

»03


23/36


8. Yardeni Model CEY = CBY – (b % LTEG)

+ Residual

where,

CEY = current earnings yield on the mkt.

index i.e. E/P.

CBY = current Moody’s Investors Service

A-rated corporate bond yield.

LTEG = consensus 5-year earnings growth

rate forecast for the mkt index.

b = coefficient (measures weight, the mkt

gives to 5-year earnings projections).

• By taking inverse:¤

R (

1

¹Á,+´ É ¾UR£

9. Own Historical P/E: Justified price =

Benchmark value of own historical P/Es % Most recent EPS

10. Terminal Value (T.V) based on

Fundamentals:

• T.V in yr n = (justified trailing P/E) %

(forecasted earnings in year n)

• T.V in year n = (justified leading P/E)

% (forecasted earnings in year n+1)

11.

Terminal Value based on Comparables:• T.V in yr n = (Benchmark trailing

P/E) % (forecasted earnings in year n)

• T.V in yr n = (Benchmark leading

P/E) % (forecasted earnings in year

n+1)

12.

P/B = ¤


24/36


23. Total Invested Capital = TIC = MV of

Common equity + MV of preferred stock +

MV of debt

24.

Earnings surprise UEt = EPS t – E (EPS t)

where,

UEt= unexpected earnings for quarter t

EPSt= reported/actual EPS for quarter

t

E(EPSt) = expected EPS for the

quarter

• Percent Earning Surprise =R;


25/36


26/36


10. All Risks Yield = ²é' (V0Š

V30Š 9;³9 ‰


27/36


"&$ Private market real estate debt

• Loan-to-value = Loan / value of the

property

• Max. loan amount based on LTV ratio

= LTV ratio (in %) % Appraisal value

of property (in $)

• Debt serve coverage ratio = NOI/Debt

service

• Debt service=Interest + Principal

payments on the mortgage.

• Principal payments=Part of the loan

payment that amortizes the loan over

the loan term.

• Max.debt service based on DSCR =

NOI/DSCR

•

When the loan is interest-only,Max.loan amount based on DSCR=

Max. debt service based on DSCR /

Debt interest rate

26. Equity dividend rate or Equity yield rate =

Cash flow / Equity

where, Cash flow = NOI – Debt

Service

Equity = Price – Mortgage

27. Calculating Leveraged IRR:

CF received by the equity investor from

the sale = Sale price – Mortgage balance

PV = – Initial investment

PMT = Cash flow

n = Holding period

FV = Cash flow received from sale

CPT# I/Y! Leveraged IRR.

28. Calculating Unleveraged IRR:

Cash flow received by the equity investor

from the sale = Sale price + NOI in the 1 st

year

PV = – Initial investment

PMT = NOI in the 1st year

n = Holding period

FV = Sale price

CPT# I/Y!Unleveraged IRR.

Reading 40: Publicly traded real estate

securities

1. Rent paid by Tenants = Net rent +

Proportionate share of the common areacosts of the mall (based on space leased)

2. NAVPS = (MV of R.E Co.’s assets – MV

of R.E Co.’s liab.) / # of shares outstanding

3. Appraised value = NOI / Cap rate

4. Estimating NAVPS:

• Pro forma cash NOI = NOI – Non

cash rents* + Adj. for full impact of

acquisitions

• *Non-cash rent = Avg. contractual

rent over the leases’ terms – Cash rent

actually paid.

• Estimated future expected cash NOI =

Pro forma cash NOI + Expected

growth in NOI

• Estimated value of operating real

estate =Estimated future expected cash

NOI / Cap rate

• Estimated gross asset value =

Estimated value of operating real

estate + BV of Cash & equivalents +

BV of Land held for future

development + BV of a/c receivables

+ BV of Prepaid/other assets

• Net asset value = Estimated gross

asset value – Total debt – Other liab.

(but not deferred taxes)

• NAVPS = Net asset value / # of shares

outstanding

5.

P/FFO = Current stock prices / Yr-aheadestimated FFO

• FFO = Net earnings + Dep. Exp. on

R.E + Deferred tax charges – g/l from

sales of property and debt

restructuring + Losses on sales of

property and debt restructuring OR

• FFO = EBITDA – Interest Expense

6. P/AFFO = Current stock prices / Yr-ahead

estimated AFFO

• AFFO = FFO – Non cash rent* –

Recurring Maintenance type Capital

expenditures – Leasing costs (i.e.

leasing agent’s commissions –

Tenants’ improvement allowances)

• *Non-cash rent = Straight-line rent -

Cash rent paid during the period


28/36


7. Estimated Value of a REIT Co. in yr N

= (P/FFO of overall REIT group for

yr N) % REIT co.’s expected FFO in yr

N or

= (P/AFFO of overall REIT group for

yr N) % REIT co.’s expected AFFO inyr N

Reading 41: Private equity valuation

1. PIC:

• PIC = Cumulative capital (CC) called

down

• PIC Multiple = PIC / CC

2.

DPI = Sum of distb. / CC called down (orPIC)

3. RVPI = NAV after distb. / CC called down

(or PIC)

4. TVPI = DPI + RVPI

5.

Mgmt. fees = % fee % PIC

6. Carried interest= % % (NAV before distb.

–CC) in year when NAV before distb. Is

first > CC

'()*)+,-)*. /+**0)1 02-)*)3- 4 5 6 789:

;),


29/36


30/36


Reading 44: The arbitrage free valuation

framework

Reading 45: Valuation & analysis: Bonds with

embedded options

1. Value of callable bond = Value of straight

bond – Value of issuer call option

2.

Value of issuer call option = Value of

straight bond – Value of callable bond

3. Value of putable bond = Value of straight

bond + Value of investor put option

4.

Value of investor put option = Value of

putable bond – Value of straight bond

5. The rate in the up state = R u = R d% e2/ @

where, Rd = Rate in the down state

/ = Interest rate volatility

t = Time in years between “time slices”

6.

Duration (Øk+Øè

>ÉØ&É ¸,

7. Convexity (Øè’Øk+ >ÉØ&

>É Ø&É ¸, ?

8. Effective Duration =¤Øk + ¤Øè

>É ¸¹µÉ §I&

¸Jüû:î ? É §I&

10. Value of capped floater = Value of straight

bond – Value of embedded cap

11. Value of floored floater = Value of straight

bond + Value of embedded floor

Analysis of a Convertible Bond

12.

Conversion Ratio (CR) = No. of shares ofC.stock from exercising call option

13. Conversion Price (or stated conversion

price) = Par value of convertible bond ÷

CR

14. Conversion Value (or Parity) = Market

price of C.stock % CR

15.

Straight Value or Investment Value =Market value of a security without

conversion option

16.

Min. Value of a Convertible Security is

(greater of conversion value or straight

value)

17. Market Conversion Price or Conversion

Parity Price =×;


31/36


4. Black-Scholes Option pricing Formula =

S t = A

t N (d

1)! ke

!r(T !1) N (d

2)

Where,

1

)(2

1

)(ln

2

1!

!+

!+

""#

$

%%&

'

=

T

t T t T r K

A

d

t

(

(

d2 = d1 – / Ù H `

5. Value of debt = D (t, T) = PV of payoff on

co.’s debt if default occurs + PV of payoff

on co.’s debt if default does not occur =

)()( 2)1(

1 d N Ked N A T r

t

!!

+!

•

where, N (d2) = Risk neutral probability of the co.’s debt not

defaulting

6. Credit Risk Measures

• Probability of the debt defaulting =

Prob. (AT< K) = 1 – Prob. (AT 1 K) =

1 – N(e2)

Where,

•

t T

t T t T u

K

A

e

t

!

!+!+""#

$

%%&

'

=

(

( )(2

1)(ln 2

1

• e2 = e1 - / Ù H ` 7. Co.’s asset R in CAPM (a static one-period

model):

Co.’s asset R = R f + ! of co.’s asset

(Expected R per year on Mkt. portfolio –

R f )

= R f + (! of co.’s asset % Mkt.’s ERP)

8.

Price of debt{ @& a (

^ «

1’û/¸ 1’û/è¸ D 1’û•è¸

9. Credit risk measures in reduced form

model:

• Default probability over [0,T] = Prob

@ K a ( ̀ H

^ë L M «

1’N L&¸ ’ 1 ’N L¸ D 1’N L•k¸ ¸

•

Expected loss =

ë̂\u¥+¸ ë L M «

1’N L&¸ ’ 1 ’N L¸ D1’N LM ¸

O vZ ¸

• Present value of the expected loss = K

P (t,T) – D (t,T)

10. Historical Estimation

• Probability of default over [t, t+'] =

Prob (t) =!""=

+

N

i

t i

i X b

e 11

1

#

• Parameters estimation:

!=

+="#

$%&

'

(

N

i

t i

i X b

dt

dt

11ln ) Where

dt = {1 if default, 0 if no default}

• To estimate the loss given default:

t(Xt) = !=

+

N

i

i

i t X cc

1

0

Where {ci for i = 1, …, N} are

constants.

11. Price of the coupon bond (assuming no

arbitrage and frictionless markets)

BG (t) = !"

=

++

1

1

),()(),(T

i

T t P F C it CP

12. Credit spread (t) = Avg. yields on risky

zero-coupon bond – Avg. yields on riskless

zero-coupon bond

Or= [Average yields on the risky zero-coupon

bond – Average yields on riskless zero-

coupon bond] + Liquidity premium

or

= Expected % loss per year on the risky

zero-coupon bond + Liquidity Premium

13. PV of expected loss = PV of CF of riskless

debt – PV of CF of risky debt = [P (t,T) –

D (t,T)] XT

Where, XT = Promised CF at T of a risky

Co.

Reading 47: Forward Rate Markets &

Contracts

1. Forward Price = Spot price % (1 + R f )T

F (0, T) = S0 (1 + r)T Or


32/36


S0 = F (0, T) / (1 + r)T

2. Value of a forward contract (of long

position)at time t during contract life

(where t


33/36


4. R C&C Arbitrage (when the Futures

Contra ct is Underpriced)

5. Pricing Futures Contracts when there are

Storage Costs and/or cash flows on the

Underlying asset and/or convenience

yield

• If holding an underlying asset results

in monetary costs and benefits (net

cost), futures price is:

• If holding an underlying asset results

in non-monetary benefits

(convenience yield), futures price is:

6. Pricing T-Bond futures Contract = F (0, T)

= (S0 – PVC) % (1 + r)T

Or

F (0, T) = [S0 % (1 + r)T] – FVC

7. No-arbitrage price of a Stock index futures

contract = F (0, T) = (S0 – PVD) % (1 + r)T

Or F (0, T) = [S0 % (1 + r)T] – FVD

8.

Futures price as stock index discounted at

dividend yield, compounded at Rf rate:

F (0, T) = [S0 / (1 + +)T] % (1 + r) T

Or F (0, T) = S0 (1 – +*) (1 + r)T

9.

Stock Index Futures Contracts with

Continuous Dividends = F (0,T) =

T r T cc

eeS ! "

0Or

F (0,T) =( )T r cc

eS ! "

0

10. No-arbitrage futures price of a unit of

foreign currency in terms of the home

currency for a currency futures contract of

length T in years = F (0, T) = S0 % [(1+ r)T/ (1 + r f ) T]

11. The continuous time price formulas for

currency futures contracts:

F (0,T) =T r T r c fc

eeS !0

or

( ) T r r fcceS !"!0

Reading 49: Options Markets & Contracts

1.

Put-call parity = c0 +X / (1+R f )T = p0 + S0

• European call (synthetic call) = c0 =

p0 + S0 – X / (1+R f )T

• European put (synthetic put) p0 = c0 -

S0 + X/(1+R f )T

• Synthetic stock position = S0 = c0 – p0

+ X/ (1+R f )T

2.

Delta = hedge ratio = number of shares

purchased per call sold

• No. of stocks per option (D) = (C+ - C-

) / (S+ - S-)

• No. of options per stock = 1/D

• No. of calls to sell = No. of shares

hedged / delta of the call option

• Total shares of stock to purchase =

No. of options short % Delta

The two values of the put at the end of the first

period are

• Åµ ( ‰¤

"" ’ 1+‰ ¤"‘

1’<

• Å̂ ( ‰¤‘"’ 1+‰ ¤‘‘

1’<

0 T

1. Borrow money

2. Buy commodity

3. Sell futures

contract

4. Deliver the commodity

against the futures

contract

5. Recover money &

payoff loan

0 T

1. Sell short the

commodity

2. Lend money received

from short sale

3. Buy futures contract

4. Accept delivery

from futures

contract

5. Use commodity

received to cover

the short sale


34/36


3. ƒ„‚A2=A#E $ÌDJ #M …‚ÌJ= (½;O u& 1žP<


35/36


2. Expected Credit Loss (%) = Payout ratio =

1 – Recovery rate (%)

3. Expected Credit Loss Amount or Payout

amount = Payout ratio % Notional amount

4. Loss Given Default:

• Expected loss = Full amount owed –

Expected recovery

• Expected loss = Loss given default %

Probability of default

• Prob. of default (at some point during

T years) = 1 – Prob. of no default

during T years

5.

Value of protection leg = Expected payoffof bond/loan with credit risk - Expected

payoff of bond/loan with no credit risks

6. Value of premium leg = PV of pmts. made

by the protection buyer to the protection

seller

7. Upfront pmt = PV of protection leg – PV

of premium leg

8.

Credit spread & Prob. of default % Loss

given default (%)

9. Credit spread Pricing Conventions

• Upfront premium = PV of credit

spread – PV of fixed coupon Or =

(Credit spread – Fixed coupon) % D of

the CDS

• PV of credit spread = Upfront prem. +

PV of fixed coupon

• Credit spread & (Upfront prem./D) +

Fixed coupon

• Upfront premium in % = 100 – Price

of CDS in currency per 100 par

• Price of CDS in currency per 100 par

= 100 – Upfront premium %

10. Profit for the buyer of protection & ¸ inspread in bps % D % NP

11. % change in CDS price = ¸ in spread in bps % D

12.

Basis = CDS spread (prem.) – Bond’scredit spread*

*Bond’s Credit spread = Yield on bond -

Investor’s cost of funding

Bond yield = R f rate + Funding spread +

Credit spread

where, R f + Funding spread = LIBOR

13.

Synthetic CDO = Portfolio of default-free

securities + CDS holdings

Reading 53: An Introduction to Multifactor

Models

1. Multifactor Model = R i = ai + b i1I1 + bi2I2+

…..+ biK IK + !i

2. Arbitrage Pricing Theory = E (R p) = R F +

3 1* p,1 + 3 2* p,2 + …..+ 3 k * p,k

3. Carhart Four Factor Model = E (R p) = R F+

* p1RMRF + + * p2SMB + + * p3HML ++

* p4WML…..+ SP

RMRF = Portfolio’s sensitivity to Mkt.

IndexSMB = small minus big

HML = high minus low

WML = winners minus losers

4. Macroeconomic Factor Model = R i =ai + b

i1 F1 + bi2 F2+ …..+ biK FK + !i

5. biK =Iìùüî ú— w —úû ì¬¬îë Z+T:îûîUî :ìùüî ú— w

F 8—úû :ìùüî¬ ú— w:

6.

Actual Inf. = Predicted Inf. + Surprise Inf.

7. Active R = Xý H XV

8. Active R (decomposition)=

WCq@8CAzC °p_°@zXz@Y H1wtp_·oY?q] °p_°@zXz@Y w É

Z?·@Cq X w r °p·[qz@Y °pAp·@zC_

9. Tracking Error TE = s(R P-R B)

10. Information Ratio = =V\+VÞ

9 V\+VÞ

11. Active risk squared = s2(R P-R B)

12. Active risk squared = Active factor risk +

Active specific risk


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l 2 formula sheet june 2016

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