l 1 Formula Sheet June 2016

8/17/2019 l 1 Formula Sheet June 2016

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FinQuiz Formula Sheet CFA Level I 2016

• r MM =

opf (qr

opf/ G (qr (Rule: r MM>

r BD)

10.

Bond Equivalent Yield = BDY =

Semiannual Yield ! 2

Reading 7: Statistical Concepts & Market

Returns

1. Range = Max Value – Min Value

2. Class Interval = i " z/B

{ where

• i = class interval

• H = highest value

•

L = lowest value, k = No. of classes.

3. Absolute Frequency = Actual No of

Observations (obvs) in a given class

interval

4. Relative Frequency =K|7OwSGI !(I}SILa`

*OGHw 1O OP U|~7

5.

Cumulative Absolute Frequency = Add up

the Absolute Frequencies

6.

Cumulative Relative Frequency = Add upthe Relative Frequencies

7. Arithmetic Mean =FS. OP O|~7 ML JHGH|H7I

1O•OP O|~7 ML GxI JHGH|H7I

8. Median = Middle No (when observations

are arranged in ascending/descending

order)

• For Even no of obvs locate

median atL

k

• For Odd no. of obvs locate

median atL'&

k

9.

Mode = obvs that occurs most frequently

in the distribution

10. Weighted Mean = € 8 2M €MLM[& =

(w1X1+ w2X2+….+ wnXn)

11. Geometric Mean = GM = €& €k l €Lm

with Xi"0 for i = 1,2,…n.

12.

Harmonic Mean = H.M = €z 8 L%

‚ƒ

mƒ„%

13.

Population Mean = µ =…ƒ

mƒ

1 with €M † j

for i = 1,2,.,.,n.

14. Sample Mean = € 8…ƒ

mƒ

L where n =

number of observation in the sample

15.

Measures of Location:• Quartiles =

iM7G(M|SGMOL

‡

• Quintiles =

iM7G(M|SGMOL

u

•

Deciles =iM7G(M|SGMOL

&f,

• Percentiles = Ly = = , + `

&ff

16.

Mean Absolute Deviation = MAD =…Z/…m

ƒ„%

L

17.

Population Var = !2 =…ƒ/ˆ ‰#

ƒ„%

1

18. Population S.D = Šk=…ƒ/ˆ ‰#

ƒ„%

1

19.

Sample Var = s2 = …ƒ/… ‰mƒ„%

L/&

20. Sample S.D = s =…ƒ/… ‰m

ƒ„%

L/&

21. Semi-var =…ƒ/… ‰

L/&!O( Hww …ƒ‹…

22. Semi-deviation (Semi S.D) =

94Œ>;5>;=X4 =…ƒ/… ‰

L/&

!O( Hww …ƒ‹…

23. Target Semi-var =…ƒ/y ‰

L/&!O( Hww …ƒ‹y

where B = Target Value

24. Target Semi-Deviation =

:;5Ž4: 94Œ>;5>;=X4 =

…ƒ/y ‰

L/&!O( Hww …ƒ‹y

25.

Coefficient of Variation = CV = F…

where s= sample S.D and € = sample

mean

26. Sharpe Ratio =)IHL $O(GPOwMO N/)IHL NP N

F•i OP $O(GPOwMO N

27. Excess Kurtosis = Kurtosis – 3




• x = success out of n trials

• n-x = failures out of n trials

•

p = probability of success

• 1-p = probability of failure

•

n = no of trials.

2. Probability Density Function (pdf) = f(x)

=&

|/H

j eW5 ; ¡ ¢ ¡ œ =

F(x) =Ÿ/H

|/H eW5 ; £ ¢ £ œ

3. Normal Density Funct = e ¢ 8&

™ k¤4¢’

/cŸ/ˆd‰

k™‰ ¥¦§ ? ¨ £ ¢ £ , ̈

4.

Estimations by using Normal Distribution:

• Approximately 50% of all obsv fall in

the interval © ªk

oŠ

• Approx 68% of all obvs fall in the

interval © ª Š

•

Approx 95% of all obvs fall in the

interval © ª«Š

• Approx 99% of all obvs fall in the

interval © ª¬Š

•

More precise intervals for 95% of the

obvs are © ª +•®Š and for 99% of the

observations are © ª «•¯°Š•

5. Z-Score (how many S.Ds away from the

mean the point x lies) ± 8

9:;=<;5< =W5Œ;² 5;=<WŒ ;5>;œ²4 8

…/ˆ

™ (when X is normally distributed)

6. Roy’s Safety-Frist Criterion = SF Ratio = NE /N³

™E

7.

Sharpe Ratio = = NE /N´

™E

8. Value at Risk = VAR = Minimum $ loss

expected over a specified period at a

specified prob level.

9. Mean (µL) of a lognormal random variable

= exp (µ + 0.50%2)

10.

Variance (%L2) of a lognormal random

variable = exp (2µ+ %2) ! [exp (%2) – 1].

11. Log Normal Price = ST = S0exp (r 0,T)

Where, exp = e and r 0,t = Continuously

compounded return from 0 to T

12. Price relative = End price / Beg price =

St+1/ St=1 + R t, t+1

where,

Rt, t+1 = holding period return on the stock from t to t + 1.

13. Continuously compounded return

associated with a holding period from t to t

+ 1:

r t, t+1= ln(1 + holding period return) or

r t, t+1 = ln(price relative) = ln (S t+1 / St) = ln

(1 + R t,t+1)

14. Continuously compounded return

associated with a holding period from 0 to

T:

R 0,T= ln (ST / S0) or 5f–* 8 5*/&–* ,

5*/k–*/& , µ , 5f–&

Where,

r T-I, T = One-period continuously

compounded returns

15. When one-period continuously

compounded returns (i.e. r 0,1) are IID

random variables.

“ 5f–* 8 “ 5*/&–* , “ 5*/k–*/& ,

µ , “ 5f–& 8 ©] And

A;5>;=X4 8 Šk 5f–* 8 Š k]

S.D. = % (r 0,T) = % ]

16.

Annualized volatility = sample S.D. of

one period continuously compounded

returns ! ]

Reading 10: Sampling and Estimation

1.

Var of the distribution of the sample mean

=™‰

L

2. S.D of the distribution of the sample mean

=™‰

L




3. Standard Error of the sample mean:

• When the population S.D (!) is known

= Š… 8™

L

• When the population S.D (!) is not

known = 9… 87

L where s = sample

S.D estimate of s =

9;Œ’²4 ;5>;=X4 8

9k 23454 9k =…ƒ/… ‰m

ƒ„%

L/&

4. Finite Population Correction Factor = fpc

=1/L

1/& where N= population

5.

New Adjusted Estimate of Standard Error= (Old estimated standard error ! fpc)

6. Construction of Confidence Interval (CI) =

Point estimate ± (Reliability factor !

Standard error)

• CI for normally distributed population

with known variance = ¢ ª ±Hvk™

L

• CI for normally distributed population

with unknown variance = ¢ ª ±Hvk

F

L where S = sample S.D.

7.

Student’s t distribution

µ = € ª :HvkF

L

8. Z-ratio = Z = x !µ

! / n

9. t-ratio = t = x !µ

s / n

Reading 11: Hypothesis Testing

1. Test Statistic =¶·¸¹º» ¶¼·¼½¾¼½¿ ÀÁ¹Â¼Ã»¾½Ä»Å Æ·ºÇ» ÂÈ ¹Â¹ ¹·É·¸»¼»É

¾¼·ÊÅ·ÉÅ »ÉÉÂÉ ÂÈ ¾·¸¹º» ¾¼·¼½¾¼½¿ Ë

*when Pop S.D is unknown, the standard

error of sample statistic is give by Ì… 8

F

L

*when Pop S.D is unknown, the standard

error of sample statistic is give by Š… 8

™

L

2. Power of Test = 1-Prob of Type II Error

3. ± 8…/ˆh

Í

m

(when sample size is large or

small but pop S.D is known)

4. ± 8…/ˆh

-

m

(when sample size is large but

pop S.D is unknown where s is sample

S.D)

5. :L/& 8…/ˆh

-

m

(when sample size is large or

small and pop S.D is unknown and pop

sampled is normally or approximately

normally distributed)

6. Test Statistic for a test of diff b/w two pop

means (normally distributed, pop var

unknown but assumed equal)

t =

…%/…‰ / ˆ%/ˆ‰

ÎÏ‰

m%'

ÎÏ‰

m‰

%v‰ where ÌR

k

= pooled

estimator of common variance =L%/& F%

‰' L‰/& F‰‰

L%' L‰/k where <e 8 =& , =k ?

«.

7. Test Statistic for a test of diff b/wn two

pop means (normally distributed, unequal

and unknown pop var unknown)

t = …%/…‰ / ˆ%/ˆ‰

Î%‰

m%'

Î‰‰

m‰

%v‰ In this df calculated as

<e 8

Î%‰

m% '

Î‰‰

m‰

‰

Î%‰

m%

‰

m%'

Î‰‰

m‰

‰

m‰

8. Test Statistic for a test of mean differences

(normally distributed populations,

unknown population variances)

•

: 8J/ˆÐh

FJ

• sample mean difference = < 8

&

L<M

LM[&

• sample variance = ÌJ

k 8J%/J ‰m

ƒ„h

L/&

• sample S.D = ÌJ

k




• sample error of the sample mean

difference = 9 < 8FÐ

L

8. Chi Square Test Statistic (for test

concerning the value of a normal

population variance) €k 8 L/& F‰

™h‰ where

= ?+ 8 <e ;=< Ìk 8

9;Œ’²4 ;5>;=X4 8…ƒ/… ‰m

ƒ„h

L/&

9. Chi Square Confidence Interval for

variance

Lower limit = L =L/& F‰

…Ñv‰‰ and Upper limit

= U = =

L/& F‰

…%ÒÑv‰‰

10. F-test (test concerning differences between

variances of two normally distributed

populations) F =F%

‰

F‰‰

Ì&k 8 +9: 9;Œ’²4 ;5 2>:3 =& Wœ9 Ì&

k 8

«=< 9;Œ’²4 ;5 2>:3 =k Wœ9

<e& 8 =& ? + =ÓŒ45;:W5 <e

<ek 8 =k ? + <4=WŒ>=;:W5 <e

11. Relation between Chi Square and F-

distribution = Ô 8…%

‰

.

…‰‰

L

where:

•

€&k is one chi square random variable

with one m degrees of freedom

•

€kk is another chi square random

variable with one n degrees of

freedom

12. Spearman Rank Correlation = 57

8 + ?® <&

kLM[&

= =k ? +

•

For small samples rejection points for

the test based on 57are found using

table.

•

For large sample size (e.g. n>30) t-test

can be used to test the hypothesis i.e.

: 8= ? « &vk57

+ ? 57k &vk

Reading 12: Technical Analysis

1.

Relative Strength Analysis =ÕÉ½¿» ÂÈ ·¾¾»¼

ÕÉ½¿» ÂÈ ¼Ã» Ö»Ê¿Ã¸·É× Ø¾¾»¼

2. Price Target for the

• Head and Shoulders = Neckline –

(Head – Neckline)

• Inverse Head and Shoulders =

Neckline + (Neckline– Head)

3. Simple Moving Average =ÕÙ'ÕÚ'ÕÛl•'ÕÊ

Ü

4. Momentum Oscillator (or Rate of Change

Oscillator ROC):

• Momentum Oscillator Value M = (V-

Vx) 0+jj

(where V = most recent closing price

and Vx = closing price x days ago)

• Alternate Method to calculate M ="

"0+jj

5.

Relative Strength Index = RSI = +jj ?

&ff

&'NF where

RS =ÝR axHLTI7

iOL axHLTI7

6. Stochastic Oscillator (composed of two

lines %K and %D):

•

Þß 8 +jjQ/B&‡

z&‡/B&‡ where:

C = latest closing price, L14 = lowest price in last 14 days, H14 is highest

price in last 14 days

•

% D = Average of the last three % K

values calculated daily.

7. Put/Call Ratio (Type of Sentiment

Indicators) =ÆÂºÇ¸» ÂÈ ÕÇ¼ à¹¼½ÂÊ¾ áÉ·Å»Å

ÆÂºÇ¸» ÂÈ â·ºº à¹¼½ÂÊ¾ áÉ·Å»Å

8. Short Interest Ratio (Type of Sentiment

Indicators) = ¶ÃÂÉ¼ ãÊ¼»É»¾¼ Øä»É·å» æ·½ºÁ áÉ·Å½Êå ÆÂºÇ¸»

9. Arms Index TRIN i.e. Trading Index (Type

of Flow of funds Indicator) =

5Œ ›=<4¢ W5 ]Y›š 81O•OP KJ~HL g77SI7 ç1O•OP iIawML g77SI7

"OwS.I OP KJ~HL g77SI7ç"OwS.I OP iIawML g77SI7




Reading 13: Demand & Supply Analysis:

Introduction

1. Slope of the demand curve =è éê ëìéíî

è éê ïðñêòéòó ôîõñêöîö

2. Slope of the supply curve =è éê ëìéíî

è éê ïðñêòéòó ÷ðøøùéîö

3. Consumer Surplus = Value that a

consumer places on units consumed –

Price paid to buy those units

• Area (for calculating Consumer

Surplus) = & (Base ! Height) = & (Q0

! P0)

4. Producer Surplus = Total revenue received

from selling a given amount of a good –

Total variable cost of producing that

amount

• Total revenue = Total quantity sold !

Price per unit

• Area (for calculating Producer

Surplus) = & (Base ! Height) = & {(Q0) ! (P0 – intercept point on y-

axis**)}

**where supply curve intersects y-axis

5. Total Surplus = Consumer surplus +

Producer surplus

6. Total Surplus = Total value – Total

variable cost

7. Society Welfare = Consumer surplus +

Producer surplus

8. Price Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö

Þ è éê ëìéíî

)(

)(

P%

Q%

2121

12

2121

12

P P

P P

QQ

QQ

+

!

+

!

=

"

"

9. Income Elasticity of Demand =Þ è éê ïðñêòéòó ôîõñêöîö

Þ è éê úêíûõî=

)(

)(

I%

Q%

2121

12

2121

12

I I

I I

QQ

QQ

+

!

+

!

=

"

"

10. Cross Elasticity =Þ èéê ïðñêòéòó ôîõñêöîö ûü ýûûö þ

Þ è éê ëìéíî ûü ýûûö ÿ

Reading 14: Demand & Supply Analysis:

Consumer Demand

1.

Marginal Utility =è éê !ûòñù "òéùéòó

è éê ïðñêòéòó #ûê$ðõîö

2. Equation of Budget Constraint Line = (PX

! QX ) + (PY ! QY)

3. Slope of Budget Constraint Line =è éê ï%

è éê ï‚ =

ë‚

ë%

4.

Marginal Rate of Substitution =

è éê ï%

è éê ï‚ =&ñì'éêñù "òéùéòó ûü ýûûö þ

&ñì'éêñù "òéùéòó ûü ýûûö ÿ

Reading 15: Demand & Supply Analysis: The

Firm

1. Profit = Total revenue – Total cost

2. Accounting Profit = Total Revenue –

Explicit Costs (or Accounting costs)

3.

Economic Profit

• = Total Revenue – Explicit Costs –

Implicit Costs or

• = Accounting Profit – Implicit Costs

or

• = Total Revenue – Total Economic

Costs

4. Economic costs = Explicit costs + Implicit

costs5. Normal Profit = Accounting Profit –

Economic Profit

6.

Accounting profit = Economic Profit +

Normal Profit

7. Economic rent = (New “Higher” Price

after ( in Demand – Previous Price before

( in Demand) ! QS before ( in Demand




8. Total Revenue (TR):

• = Price ! Quantity or

•

= Sum of individual units sold !

Respective prices of individual Units

sold = ' (Pi ! Qi)

9.

Average Revenue (AR) =!ûòñù )î*îêðî

ïðñêòéòó

10. Marginal Revenue (MR) =è éê !ûòñù )î*îêðî

è éê ïðñêòéòó

11.

Total Variable Cost = Variable Cost per

unit ! Quantity Produced

12. Total Cost = Total Fixed + Total Variable

13. Average total cost (ATC) =!ûòñù #û$ò

ïðñêòéòó ëìûöðíîö = Avg. Fixed Cost + Avg.

Variable Cost

14. Marginal cost (MC) =è éê !ûòñù #û$ò

è éê ïðñêòéòó ëìûöðíîö

15. Marginal Variable Cost =è éê !ûòñù +ñìéñ,ùî #û$ò

è éê ïðñêòéòó ëìûöðíîö

16. Marginal revenue (in perfect competition)

= Avg. Revenue = Price = Demand

17. Profit can be increased by increasing

output when MR> MC

18. Profit can be increased by decreasing

output when MR< MC

19. Break-even price: P = ATC! Output

level where Price = Average Revenue =

Marginal Revenue = Average Total Cost

! where, Total Revenue = Total Cost.

20.

Firms earn Economic Profits when Price >

Average Total Cost

21. Profits occur when Total Revenue (TR) "

Total Cost (TC) & when Price = Marginal

Cost! firm will continue operating.

22. Losses are incurred when there are

Operating profits (Total Revenue "

Variable Cost) but Total Revenue < Total

Fixed Cost + Total Variable Cost ANDwhen Price = Marginal Cost while losses

are < fixed costs! firm will continue

operating.

23. Losses are incurred when there are

Operating losses (Total Revenue (

Variable Cost) AND when losses " fixed

costs! firm will shut down.

24.

Average Product =

!ûòñù ëìûöðíò

ïðñêòéòó ûü -ñ,ûì

25. Marginal Product =è éê !ûòñù ëìûöðíò

è éê ïðñêéòó ûü -ñ,ûì =

è éê !ûòñù .ðòøðò

è éê /û ûü 0ûì1îì$

26. Least-cost optimization Rule:&ñì'éêñù ëìûöðíò ûü -ñ,ûì

ëìéíî ûü -ñ,ûì8

&ñì'éêñù ëìûöðíò ûü ë2ó$éíñù #ñøéòñù

ëìéíî ûü ë2óéíñù #ñøéòñù

27.

Profit is maximized when: MRP = Price or

cost of the input for each type of resource

that is used in the production process

28. Marginal Revenue product = Marginal

Product of an input unit ! Price of the

Product = Price of the input =è éê !ûòñù )î*îêðî

è éê ïðñêòéòó ûü úêøðò îõøùûóîö

29. Surplus value or contribution of an input to

firm’s profit = MRP – Cost of an input

Reading 16: The firm & Market Structures

1. In perfect competition, Marginal revenue =

Avg. Revenue = Price = Demand

2. Marginal Revenue = 3§456 0 + ?

&

ëìéíî 7ùñ$òéíéòó ûü ôîõñêö

3.

Concentration Ratio =÷ðõ ûü $ñùî$ *ñùðî$ ûü ò2î ùñì'î$ò &f üéìõ$

!ûòñù &ñì1îò ÷ñùî$

4. Herfindahl-Hirshman Index = Sum of the

squares of the market shares of the top N

companies in an industry




Reading 17: Aggregate Output, Prices &

Economic Growth

1. Nominal GDP t = Prices in year t !

Quantity produced in year t

2. Real GDP t = Prices in the base year !

Quantity produced in year t

3. Implicit price deflator for GDP or GDP

deflator =*ñùðî ûü íðììîêò óì ûðòøðò ñò íðììîêò óì øìéíî$

*ñùðî ûü íðììîêò óì ûðòøðò ñò ,ñ$î óì øìéíî$ !

100

4. Real GDP = [(Nominal GDP / GDP

deflator) ÷ 100]

5. GDP deflator =/ûõéêñù ýôë

)îñù ýôë0+jj

6. GDP = Consumer spending on final good

& services + Gross private domestic invst

+ Govt. spending on final goods & services

+ Govt. gross fixed invst + Exp – Imp +

Statistical discrepancy

7.

Net Taxes = Taxes – Transfer payments

8.

GDP = National income + Capital

consumption allowance + Statistical

discrepancy

9. National Income = Compensation of

employees + Corp & Govt enterprise

profits before taxes + Interest income +

unincorporated business net income + rent

+ indirect business taxes less subsidies

10. Total Amount Earned by Capital = Profit +

Capital Consumption Allowance

11. PI = National income – Indirect business

taxes – Corp income taxes – Undistributed

Corp profits + Transfer payments

12. Personal disposable income (PDI) =

Personal income – Personal taxes OR GDP

(Y) + Transfer payments (F) – (R/E +

Depreciation) – direct and indirect taxes

(R)

13. Business Saving = R/E + Depreciation

14. Household saving = PDI - Consumption

expenditures - Interest paid by consumers

to business - Personal transfer payments to

foreigners

15.

Business sector saving = Undistributed

corporate profits + Capital consumption

allowance

16. Total Expenditure = Household

consumption (C) + Investments (I) +

Government spending (G) + Net exports

(X-M)

17. Private Sector Saving = Household Saving

+ Undistributed Corporate Profits +

Capital Consumption Allowance

18. GDP = Household consumption + Private

Sector Saving + Net Taxes

19. Domestic saving = Investment + Fiscal

balance + Trade balance

20. Trade Balance = Exports – Imports

21. Fiscal balance = Government Expenditure

– Taxes = (Savings – Inves tment) – Trade

Balance

22. Average propensity to consume (APC) =8''ìî'ñòî #ûê$ðõøòéûê

)îñù úêíûõî

23. Quantity theory of money equation:

Nominal Money Supply ! Velocity of

Money = Price Level ! Real Income or

Expenditure

24. % è in unit labor cost = % è in nominal

wages - % è in productivity

25. Economic growth = Annual % è in real

GDP

26.

Total Factor Productivity growth = Growthin potential GDP – [Relative share of labor

in National Income ! (Growth in labor) +

[Relative share of capital in National

Income ! (Growth in capital)]

27. Growth in potential GDP = Growth in

technology + (Relative share of labor in

National Income ! Growth in Labor) +




(Relative share of capital in National

Income ! Growth in capital]

28. Capital share =Corporate profits + net

interest income + net rental income +

(depreciation/ GDP)

29.

Labor share =7õøùûóîî #ûõøîê$ñòéûê

ýôë

Reading 18: Understanding Business Cycles

1. Price index at time t2 ="HwSI OP GxI QO.7S.RGMOL yH7{IG HG G ‰

"HwSI OP GxI QOL7S.RGMOL yH7{IG HG G %0+jj

Inflation Rate =ëìéíî úêöî9 ñò òéõî òk

&ff? +

2. Fisher Index = ›’ 0›: (where, IL =

Laspeyres index and I p = Paasche Index)

3.

;=>: ²;œW5 XW9: c;:d >=<>X;:W5 8!ûòñù ùñ,ûì íûõøîê$ñòéûê øîì 2ûðì øîì <ûì1îì

.ðòøðò øîì 2ûðì øîì <ûì1îì

4. =6>¦54?@ ¦¥ A¦B6@ 8/ûõéêñù ýôë

&ûêîó ÷ðøøùó

Reading 19: Monetary & Fiscal Policy

1. Total Money created = New deposit/

Reserve Req

2. Money Multiplier =&

)î$îì*î )îC ûì ìî$îì*î ìñòéû

3. Narrow money = M1= currency held

outside banks + checking accounts +

traveller’s check

4.

Broad money = M2 = M1 + time deposits

+ saving deposits

5. M3 = M2 + deposits with non-bank

financial institution

6. Quantity Theory of Money = M ! V = P !

Y where,

M = Quantity of money

V = Velocity of circulation of money

P = Average price level

Y = Real output

7. Neutral Rate = Trend Growth + Inflation

Target

8. Impact of Taxes and Government

Spending: The Fiscal Multiplier

The net impact of the government sector

on AD:

• G – T + B = Budget surplus or Budget

deficit

where, G = government spending , T

=taxes, B =transfer benefits

•

Disposable income = Income – Net

taxes = (1 – t) Income

where, Net taxes = taxes – transfer

payments, t = net tax rate

9. Fiscal Multiplier (in the absence of taxes)

= 1/(1 - MPC)

• MPS = 1 – MPC.

• Total increase in income and spending

= Fiscal multiplier ! G

10. Fiscal Multiplier (in the presence of taxes)

• MPC (with taxes) = MPC ! (1 - t)

• Fiscal multiplier =

&

&/)$Q &/G

• Total ( in income and spending =

Fiscal multiplier ! G

• Initial ( in consumption due to

reduction in taxes = MPC ! tax cut

amount

• Total or cumulative effect of tax cut =

multiplier ! initial change inconsumption

11. Cumulative multiplier =íðõðùñòé*î îüüîíò ûê ìîñù ýôë û*îì ò2î ò<û óîñì$

Þ OP Di$

Reading 20: International Trade & Capital

Flows

1. Terms of trade =ëìéíî ûü î9øûìò$

ëìéíî ûü éõøûìò$

2. Terms of Trade (as an index number) =8*' øìéíî ûü î9øûìò$

8*' øìéíî ûü éõøûìò$

3. Net exports = Value of a country's (exports

–imports)




4. Net welfare effect = consumer’s surplus

loss + producer’s surplus gain + Govt.

revenue

5.

Closed Economy’s output = Y = C+I+G

6. Open Economy’s output = Y =

C+I+G+(X-M)

• Current Account Balance = X-M = Y-

C+I+G

7. Consumption = Income + transfers – taxes

– saving

C = Yd- S p =Y+R-T-S p And,

CA = S p- I+ Govt surplus (or Govt saving)= S p- I+ (T- G- R)S p + Sg = I + CA

where, Sg = Govt savings

S p = I + CA – Sg

• Current Account Imbalance CA = Sp

+ Sg – I

Reading 21: Currency Exchange Rates

1. E¦§64FB G§456 >6H6> 4B I¦A6J?45 5K§§6B5@ 8

Lövü 03ü

2.

M6N> 6O5PNBF6 §N?6côvüd 8 cLö ü 03ü dv3ö 8

Lö ü 0c3ü v3öd

3. M6N> QO5PNBF6 MN?6 öûõî$òéívüûìîé'ê 8

Lövü 0 #ëúR

#ëúS

4. TPNBF6 4B M6N> QO5PNBF6 §N?6 8

+ ,è÷SvR

÷SvR 0

&'èUR UR

&'èUSUS

? +

5.

Direct Quote = &úêöéìîíò ïðûòî

6. Points on a forward rate quote = Fwd X-

rate quote –Spot X-rate quote

7. Forward rate = Spot X-rate +Vûì<ñìö øûéêò$

&f–fff

8. E¦§WN§I G§6A4KAvI4J5¦KB? c4B Þd 8

$øûò þ/ìñòî'cüûì<ñìö øûéêò$v&f–fffd

$øûò þ/ìñòî? +

9.

To convert spot rate into a forward quote(when points are represented as %) = Spot

exchange rate ! (1 + % premium or

discount)

10. Arbitrage relationship is stated as follows:

•

+ , >J 8 Ì ´

Ð

+ , >P&

!´Ð

• In case of indirect quote, Arbitrage

relationship is: + , >J 8

+vÌPvJ + , >P ÔPvJ

•

Ô´

Ð

8 Ì ´

Ð

&'M´

&'MÐ

•

Forward rate as a % of spot rate =!´vÐ

F´vÐ8

&'M´

&'MÐ

11. Return on hedged foreign investment

(with a quoted forward rate) = ÌPvJ + ,

>P&

!´vÐ

12.

Expected % change in the spot rate =FZ^%

FZ? + 8 ÞèÌG'& 8

M´/MÐ

&'MÐ

• Forward points: ÔPvJ ? ÌPvJ 8

ÌPvJ

M´/MÐ

&'MÐX Y (where Y is quoted

interest rate period)

13. Relationship between the trade balance and

expenditure/ saving decisions:

= Ex – Im = (Sav – Inv) + (T – G)

where T= taxes net of transfers

G= government expenditures)

14. Price elasticity of demand = ) =Þ í2ñê'î éê Cðñêòéòó

Þ í2ñê'î éê øìéíî = –

Þ è ï

Þ è ë

15. Expenditure (R) = Price ! Quantity = P !

Q

•

% * in expenditure = % * R = % * P

+ % * Q = (1- )) % * P

16. Basic idea of Marshall-Lerner condition =

ZŸ[Ÿ , Z) [) ? + † j where,

+x=share of exports

)X=price elasticity of foreign demand for

domestic country exports




+M=share of imports

)M =price elasticity of domestic country

demand for imports

17.

Trade balance = Income (GDP) –

Domestic expenditure = Absorption

Reading 22: Financial Statement Analysis: An

Introduction

1. Gross Profit = Revenue – Cost of sales

2. Operating Profit or EBIT = Gross profit –

Operating costs + Other operating income

3.

Profit before tax = EBIT – Interest expense

4. Profit after tax = Profit before tax –

Income tax expense

Reading 23: Financial Reporting Mechanics

1. Owner’s Equity = Contributed Capital +

R.E

2. End R.E = Beg R.E + Net income –

Dividends

3. Assets = Liabilities + Contributed Capital

+ Beg R.E + Revenue – Expenses –

Dividends

Reading 24: Financial Reporting Standards

Reading 25: Understanding Income Statements

1. Revenue recognized on Prorated basis =!ûòñù 8õûðêò ûü #û$ò

!éõî ûü ò2î íûêòìñíò

2. Revenue recognized under Percentage-of-

Completion Method = % of Total cost

spent by the firm ! Total Contract

Revenue

3. Revenue recognized when outcome cannot

be reliably measured = Contract costs

incurred

4. Revenue recognized under installment

method =ëìûüéò

÷ñùî$ 0 Cash receipt

5. Wgtd Avg cost per unit =!ûòñù #û$ò ûü ýûûö$ ñ*ñéùñ,ùî üûì ÷ñùî

!ûòñù ðêéò$ ñ*ñéùñ,ùî üûì ÷ñùî

6. COGS using Wghtd Avg Cost = No of

units sold ! Wghtd Avg cost per unit

7.

COGS using LIFO = Total cost – Value of

ending inventory

8. Annual Depreciation Expense (using

Straight-Line Method) =#û$ò/)î$éöðñù +ñùðî

7$òéõñòîö "$îüðù -éüî

9. Annual Depreciation Expense (Declining

balance method) =&ffÞ

"$îüðù ùéüî ! Acceleration

factor (say 200% or 2) ! Net Book Value

10. Basic EPS =/îò úêíûõî/ëìîüîììîö ôé*éöîêö$

0'2ò 8*' /û ûü $2ñìî$ ûðò$òñêöéê'

11.

Diluted EPS for preferred stock =/îò úêíûõî

0'2ò 8*' /û ûü $2ñìî$ ûv$'/î< íûõõûê $2ñìî$ ò2ñò

<ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê

12. Diluted EPS for convertible debt =/îò éêíûõî '8! M ûê

íûê*îìòé,ùî öî,ò/ëìîüîììîö ôé*0'2ò 8*' ûü $2ñìî$ ûv$'8ööéòéûêñù íûõõûê $2ñìî$

ò2ñò <ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê

13. Diluted EPS using Treasury Stock Method

=c/îò úêíûõî/ëìîüîììîö öé*éöîêö$d

\0'2ò 8*' ûü $2ñìî$'c/î< $2ñìî$ ñò ûøòéûê î9îìíé$î/

÷2ñìî$ øðìí2ñ$îö <éò2 #ñ$2 ìîíîé*îö ðøûê î9îìíé$î d 0

cëìûøûìòéûê ûü ÿìd]

14.

Net Profit Margin =/îò úêíûõî

)î*îêðî

15.

Gross Profit Margin =ýìû$$ ëìûüéò

)î*îêðî

16. Comprehensive EPS = EPS + Other

Comprehensive Income per share

Reading 26: Understanding Balance Sheets

1. Percentage of A/C Receivable estimated to

be uncollectible =8ùùû<ñêíî üûì ôûð,òüðù 8v#

ýìû$$ ñõûðêò ûü 8v# )îíîé*ñ,ùî

2. Net Identifiable Assets = Fair value of

identifiable assets – Fair value of liabilities

& contingent liabilities




3. Amortized cost of PPE = Historical cost –

Accumulated depreciation – Impairment

losses

4.

Carrying value for PPE under revaluation

model

= Fair value at date of revaluation –

Accumulated depreciation (if any)

5. Amortized cost of PPE = Historical cost –

Accumulated depreciation – Impairment

losses

6.

Carrying value for PPE under revaluation

model

= Fair value at date of revaluation –Accumulated depreciation (if any)

7. Deferred tax liability = Taxable income <

Reported Financial Statement Income

before taxes

8. Deferred tax liability = Actual income tax

payable in a period < Income tax expense

9. Vertical common-size balance-sheet =^ñùñêíî $2îîò 8õûðêò

!ûòñù 8$$îò$

10.

Current ratio =#ðììîêò 8$$îò$

#ðììîêò -éñ,éùéòéî$

11.

Quick (acid test) =#ñ$2'&ñì1îòñ,ùî $îíðìéòéî$')îíîé*ñ,ùî$


12. Cash ratio =#ñ$2'&ñì1îòñ,ùî $îíðìéòéî$


13. Long-term debt-to-equity =!ûòñù ùûê'/òîìõ öî,ò

!ûòñù 7Cðéòó

14. Debt-to-Equity =!ûòñù ôî,ò


15. Total Debt =!ûòñù ôî,ò

!ûòñù 8$$îò$

16.

Financial Leverage =!ûòñù 8$$îò$


Reading 27: Understanding Cash Flow

Statements

1. End Cash = Beg cash + Cash receipts

(from operating, investing, and financing

activities) – Cash payments (for operating,

investing, and financing activities)

2.

End A/c Receivable = Beg A/c Receivable

+ Revenues – Cash collected from

customers

3.

Cash received from customers = Revenue – Increase in a/c receivable

4. Purchases from suppliers = COGS +

Increase in inventory

5.

Cash paid to suppliers = Cogs + Increase

in inventory – Increase in a/c payable

6. End Inventory = Beg inventory +

Purchases – COGS

7. End a/c payable = Beg a/c payable +

Purchases – Cash paid to suppliers

8. Cash paid to employees = Salary and

wages expense – Increase in salary and

wages payable

9. End salary and wages payable = Beg salary

and wages payable + Salary and wages

expense – cash paid to employees

10.

Cash paid for other operating expenses =

Other operating expenses – Decrease in prepaid expenses – Increase in other

accrued liabilities

11.

Cash paid for interest = Interest expense +

Decrease in interest payable

12. End Interest Payable = Beg interest

payable + Interest expense – Cash paid for

interest

13.

Cash paid for income taxes = Income tax

expense – Increase in income tax payable

14.

Historical cost of equipment sold = Beg

balance equipment + Equipment purchased

– End balance equipment




17. Total Asset Turnover =)î*îêðî

8*' !ûòñù 8$$îò$

18. Pretax margin =7ñìêéê'$ ,îüûìî òñ9 ,ðò ñüòîì éêòîìî$ò

)î*îêðî

19.

Return on Total Capital =7^ú!

÷2ûìò ñêö ùûê' òîìõ öî,ò ñêö îCðéòó

20. ROE =/îò úêíûõî

8*' !ûòñù 7Cðéòó

• ROE = ROA ! Leverage

•

ROE = Tax Burden ! Interest Burden

! EBIT Margin ! Total Asset

Turnover ! Leverage

21. Return on Common Equity =/îò úêíûõî/ëìîüîììîö ôé*éöîêö$

8*' #ûõõûê 7Cðéòó

22. Coefficient of Variation of Operating

Income =÷•ô ûü .øîìñòéê' úêíûõî

8*' .øîìñòéê' úêíûõî

23. Coefficient of Variation of Net Income =÷•ô ûü /îò úêíûõî

8*' /îò úêíûõî

24. Coefficient of Variation of Revenues =÷•ô ûü )î*îêðî

8*' )î*îêðî

25. Monetary Reserve Requirement (Cash

Reserve Ratio) =)î$îì*î$ 2îùö ñ$ #îêòìñù ^ñê1

÷øîíéüéîö ôîøû$éò -éñ,éùéòéî$

26. Liquid Asset Requirement =)îñöéùó &ñì1îòñ,ùî ÷îíðìéòéî$

÷øîíéüéîö ôîøû$éò -éñ,éùéòéî$

27. Net Interest Margin =/îò úêòîìî$ò úêíûõî

!ûòñù úêòîìî$ò 7ñìêéê' 8$$îò$

28. Sales per Square Meter =)î*îêðî

!ûòñù )îòñéù ÷øñíî éê ÷Cðñìî &îòîì$

29.

Average Daily Rate =)ûûõ )î*îêðî

/û ûü )ûûõ$ $ûùö

30. Occupancy Rate =/û ûü )ûûõ$ ÷ûùö

/û ûü )ûûõ$ ñ*ñéùñ,ùî

31. EBIT Interest Coverage =7^ú!

ýìû$$ úêòîìî$ò

32. EBITDA Interest Coverage =7^ú!ô8


33. FFO Interest Coverage =VV.'úêòîìî$ò ëñéö/.øîìñòéê' -îñ$î 8ömð$òõîêò$


34. Return on Capital =7^ú!

8*' #ñøéòñù

=

7^ú!

8*' c7Cðéòó'/ûê íðììîêò öîüîììîö òñ9î$'öî,òd

35. FFO to Debt =VV.

!ûòñù ôî,ò

36. Free Operating CF to Debt =#V./#ñø 79ø

!ûòñù ôî,ò

37. Discretionary CF to Debt =#V./#ñø î9ø/ôé*éöîêö$ øñéö

!ûòñù öî,ò

38.

Net CF to Capital expenditures =VV./ôé*éöîêö$

#ñø î9ø

39.

Debt to EBITDA =!ûòñù öî,ò

7^ú!ô8

40.

Total Debt to total debt plus Equity =!ûòñù öî,ò

!ûòñù öî,ò'7Cðéòó

41.

Z-Score = 1.2 ! #8/#-

!8 + 1.4 !

)•7

!8 +

3.3 ! 7^ú!

!8 + 0.6 !

&+ ûü $òûí1

^+ ûü ùéñ,éùéòéî$ + 1.0

! ÷ñùî$

!8

42. Segment margin =÷î'õîêò ëìûüéò c-û$$d

÷î'õîêò )î*îêðî

43. Segment turnover =÷î'õîêò )î*îêðî

÷î'õîêò 8$$îò$

44. Segment ROA =÷î'õîêò ëìûüéò c-û$$d


45. Segment Debt Ratio =÷î'õîêò -éñ,éùéòéî$


Reading 29: Inventories

1. NRA = Estimated Selling Price –

Estimated Costs of completion and

disposal




2. Inventory amount net of valuation

allowance = Carrying amount of Inventory

– Write downs

3.

(NRA – Normal Profit Margin) ( MV (

NRA

Reading 30: Long-Lived Assets

1. Dep Exp under Straight-line Method =ôîøìîíéñ,ùî #û$ò

7$òéõñòîö "$îüðù -éüî =

né$òûìéíñù #û$ò/7$òéõñòîö )î$éöðñù $ñù*ñ'î + ñùðî

7$òéõñòîö "$îüðù -éüî

2. Dep Exp under Units-of-Production

Method = Depreciable Cost ! ëìûöðíòéûê éê ò2î ëîìéûö

7$òéõñòîö ëìûöðíòé*î #ñøñíéòó

3. Carrying amount under cost model =

Historical Cost – Accumulated Dep or

Amortization

4. Carrying amount under revaluation model

= Fair value at the date of revaluation –

Any subsequent Accumulated Dep or

Amortization

5. Impairment Loss (IFRS) = Recoverable

Amount – Net Carrying Amount

Where, Recoverable amount = Max [(Fair

value – Costs to sell); Value in Use)] and

Value in use = PV of Expected Future CFs

6. Impairment Loss (US GAAP) = Asset’s

Fair Value – Carrying Amount …….If

Carrying amount > Undiscounted Expected

Future Cash Flows

Reading 31: Income Taxes

1. Deferred tax asset = Company’s taxable

income > Accounting profit

2. Tax base of revenue received in advance =

Carrying amount – Any amount of revenue

that will not be taxed at a future date

3.

Reported Effective Tax Rate =úêíûõî !ñ9 î9øîê$î

ëìî òñ9 éêíûõî ûì 8ííûðêòéê' ëìûüéò

4. Deferred tax liability = Carrying amount

of asset > Tax base of asset

5.

Deferred tax asset = Carrying amount of

asset < Tax base of asset

6. Deferred tax asset = Carrying amount of

liability > Tax base of asset

7.

Deferred tax liability = Carrying amount ofliability < Tax base of asset

8. Company’s tax expense (or credit)

reported on its income statement = Income

tax liability currently payable + è in

deferred tax asset / liability

Where,

• Income Tax liability currently

payable = Taxable income ! Tax

rate

•

èin deferred tax asset / liability =

Diff b/w the balance of the

deferred tax asset / liability for the

current period and the balance of

the previous period.

9. The company’s tax expense (or credit)

reported on its income statement = Taxes

payable + (* Deferred tax liability - *

Deferred tax asset)

Where,

• Income Tax liability currently

payable = Taxable income ! Taxrate

• Deferred tax liability = (carrying

amount – tax base) ! tax rate

• Deferred tax asset = (tax base –

carrying amount) ! tax rate

10. Tax base of a liability = Carrying amount

of the liability – Amounts that will be

deductible for tax purposes in the future

Reading 32: Non-current (Long-term)

Liabilities

1. Annual Interest Payment = Face Value !

Coupon Rate

2. Sale proceeds of bond = Sum of PV of

Interest Payments + PV of Face value of

Bond




3. When Face value - Sale proceed is > zero,

discount

4. When Face value – Sale proceed is < zero,

premium

5. Bond payable = Face value – (+) Discount

(Premium)

6. Total Interest Expense (in case of discount)

= Periodic interest payments +

Amortization of Discount

7.

Total Interest Expense (in case of

premium) = Periodic interest payments -

Amortization of Premium

8. Amount of Bonds payable reported on the

balance sheet = Historical cost +/-

Cumulative amortization (or amortization

cost)

9. Amount of Bonds payable initially

reported on the balance sheet under IFRS =

Sales proceeds – Issuance costs

10.

Amount of Bonds payable initially

reported on the balance sheet under US

GAAP = Sales proceeds

11. Bond i-exp. under effective i-rate method

= Carrying value of the bonds at the beg.

of the period ! Effective i-rate

12. Bond Interest Payment under effective

interest rate method = Face value of the

bonds ! Contractual (coupon) rate

13.

Amortization of the discount or premium

under effective interest rate method =

Bond interest expense – Bond interest

payment

14. Bond Discount/Premium Amortization

under Straight-line Method =^ûêö ôé$íûðêò ûì øìîõéðõ

/û ûü úêòîìî$ò ëîìéûö$

15. No of shares subscribed when warrants are

exercised =8''ìî'ñòî øìéêíéøñù ñõûðêò ûü öî,ò

ëñì *ñùðî ûü ñ ùûò

! shares subscribed per lot

16. Carrying amount of the leased asset =

Initial recognition amount – Accumulated

depreciation

17. Accumulated depreciation = Prior year’s

accumulated depreciation + Current year’s

depreciation expense

18.

Interest expense = Lease liability at the beg

of the period ! interest rate implicit in thelease

19. Sales revenue = lower of the fair value of

the asset and PV of the min lease payments

20. Cost of sales = Carrying amount of the

leased asset – PV of the estimated

unguaranteed residual value

21. Interest Revenue = Lease receivable at the

beg of the period ! Interest rate

22. Net interest expense = Beg Net pension

liability ! Discount rate

23. Net Interest income = Beg Net Pension

asset ! Discount rate

24. Reported pension expense = Pension costs

– Expected return on Pension plan assets

25. Funded Status = PV of the Defined benefit

obligations – Fair value of the plan assets

Reading 33: Financial Reporting Quality

Reading 34: Financial Statement Analysis:

Applications

1.

Company’s sales = Projected market share

! Projected total industry sales

2. Forecast amount of profit for a given

period = Forecasted amount of sales !

Forecast of the selected profit margin

3. Retained CF (RCF) / Total debt =

cûøîìñòéê' #V ,îüûìî 0# í2ñê'î$ o öé*éöîêö$d

òûòñù öî,ò

4. )îòñéêîö #V/#ñø î9ø

!ûòñù ôî,ò




5. Inventory value adjusted to FIFO basis =

End Inventory value under LIFO + End

LIFO reserve balance

6.

COGS adjusted to a FIFO basis = COGS

under LIFO – (End LIFO reserve – Beg

LIFO reserve)

7. Useful life of the company’s overall asset

base that has passed =8ííðõðùñòîö ôîø

ýìû$$ ëë7

8. Avg age of the asset base =8ííðõðùñòîö ôîø

8êêðñù ôîø î9øîê$î

9.

Remaining useful life of the asset =/îò ëë7 cêîò ûü ñííðõðùñòîö öîød

8êêðñù öîø î9øîê$î

10. Avg depreciable life of the assets at

installation =ýìû$$ ëë7

8êêðñù ôîø î9øîê$î

11. % of asset base that is being renewed

through new capital investment =#ñøî9

ýìû$$ ëë7' #ñøî9

12. Adjusted BV = Total stockholders’ equity

– Goodwill

13. Adjusted Price to BV ratio =ëìéíî õñì1îò íñøéòñùépñòéûê

8ömð$òîö ^+

14.

Tangible B.V = Total stockholders’ equity

– Goodwill – Other intangible assets

15. Price to tangible BV ratio =ëìéíî

!ñê'é,ùî ^+

16. Adjusted debt-to-equity ratio =)îøûìòîö öî,ò'ë+ ûü ûøîìñòéê' ùîñ$î

)îøûìòîö 7Cðéòó

17. Adjusted debt-to-asset ratio =)îøûìòîö öî,ò'ë+ ûü ûøîìñòéê' ùîñ$î

)îøûìòîö 8$$îò' ë+ ûü ûøîìñòéê' ùîñ$î

18. Adjusted Asset Turnover ratio =÷ñùî$

)îøûìòîö 8*' òûòñù ñ$$îò$'ë+ ûü ûøîìñòéê' ùîñ$î

19. PV of future operating lease payments =ë+ ûü íñøéòñù ùîñ$î øñóõîêò$

!ûòñù #ñøéòñù -îñ$î øñóõîêò$! Total Future

Operating Lease Payments

20. Interest expense = Interest ! PV of the

lease payments

21.

Depreciation expense estimated on

straight-line basis =ë+ ûü ò2î ùîñ$î øñóõîêò$

/û ûü óì$ ûü üðòðìî ùîñ$î øñóõîêò$

22.

Adjusted Interest Coverage ratio =

Qqrs , §6B? 6OG Ë ?t6G 6OG Ë

> GN@A6B?J , > 6OG6BJ6 Ë

* associated with the operating lease

obligations

Reading 35: Capital Budgeting

1.

Incremental CF = CF with a decision - CF

without that decision

2. NPV = PV of cash inflows - IO =

NPV =

t =1

n

!AT CFs at time t

1+Req RoR( )t " IO

3.

Avg Accounting RoR (AAR) =8*' /ú ñüòîì öîø u òñ9î$ ,îüûìî éêòîìî$ò

8*' ^+ ûü úê*$ò

4. PI =ë+ ûü üðòðìî #V$

ú. = 1 +

/ë+

ú.

5.

Value of a company = Value of company’s

existing invst + Net PV of all of

company’s future invst

Reading 36: Cost of Capital

1. WACC = wdr d (1 – t) + w pr p + wer e

2. Debt-to-Equity Ratio conversion into

weight (i.e. Debt / (Debt + Equity) =jcvw

xyzew{

&'jcvw

xyzew{

3. Optimal Capital Budget is the point where

MC of capital = Marginal return from

investing

4. After-tax cost of debt = Before-tax

Marginal Cost of Debt ! (1 – firm’s

marginal tax rate)

5. Preferred Stock Price per Share

=ëìîü ÷òûí1 ôé* øîì ÷2ñìî

#û$ò ûü ëìîü ÷òûí1




6. Expected Return on Stock I (under CAPM)

= E (R i) = R F + ,i [E (R M) – R F]

7. Expected Return on Stock I = E (R i) = R F +

,i1 (Factor risk premium)1 + ,i2 (Factor

risk premium)2+…..+,i j (Factor risk

premium) j

8. Cost of Equity = |} 8 ô%

ëh, F

9.

Expected Growth Rate of Dividends

g = (1 -ô

7ë÷) ! ROE

g = retention rate ! ROE

10.

Company’s stock returns = Méò 8 N ,~Mõò

11. Unlevered • of Comparable Company =

•"– íûõøñ 8€

– ‚aƒb„d„v…c

&' &/ò‚aƒb„d„v…c

j‚aƒb„d„v…cx‚aƒb„d„v…c

12. Levered • of Project =

†B– R(O” 8 †Ý– aO.R + , + ? :R(O”

‡R(O”

“R(O”

13. †H77IG 8 ˆ‰Š‹ƒZŒ

&' &/G r

14. †I}SMG` 8 †H77IG + , + ? : i

15. Sovereign yield spread = Govt bond yield

(denominated in developed country’s

currency) – T.B yield on a similar maturity

bond in developed country

16.

Country equity premium = Sovereign yield

spread ! 8êê ÷•ô ûü 7Cðéòó éêöî9

8êê ÷•ô ûü $û*îìîé'ê ,ûêö &1ò éê

òîìõ$ ûü öî*îùûøîö õ1ò íðììîêíó

17.

Cost of equity = K e= R F + ,[(E(R M)-R F) +

CRP]

18. Breakpoint =8õûðêò ûü íñøéòñù ñò <2éí2 $ûðìíî_$ íû$ò ûü íñø è

ëìûø ûü êî< íñø ìñé$îö üìûõ ò2î $ûðìíî

19. Cost of Capital (hen flotation costs are in

monetary terms = §î 8 ô%

ëh/V , F

20. When FC are in terms of % of the share

price: Cost of Equity = §î 8 ô%

ëh/V , F

21.

If FC are not tax deductible: NPV = PV of

Cash Inflows – IO – (FC in % ! New

Equity Capital)

22. If FC are tax deductible: NPV = PV of

Cash Inflows – IO – [(FC in % ! New

Equity Capital) ! (1 – Marginal Tax Rate)]

23. Asset • = (Debt • ! Proportion of Debt) +

(Equity • ! Proportion of Equity)

Reading 37: Measures of Leverage

1. Contribution Margin (CM) = (# of units

sold) ! [(price per unit) - (variable cost per

unit)]

2.

Per unit CM = Price per unit - Variable

cost per unit

3. Operating income = CM – Fixed Operating

Costs

4. DOL =Þ è éê .øîìñòéê' úêíûõî 7^ú!

Þ è éê "êéò$ ÷ûùö

or

DOL=#&

#&/ Vé9îö .øîìñòéê' #û$ò

5. DFL =Þ è éê /îò úêíûõî

Þ è éê .øîìñòéê' úêíûõî or

#&/ Vé9îö .ø #û$ò

#&/Vé9îö .ø #û$ò/Vé9îö Véê #û$ò

6.

DTL=Þ è éê /îò úêíûõî

Þ è éê /û ûü "êéò$ ÷ûùö = DOL ! DFL =

#&

#&/Vé9îö .ø #û$ò/Vé9îö Véê #û$ò

7. Break-even Revenue = (Variable cost per

unit ! Break-even Number of Units) +

Fixed Operating costs + Fixed Financial

Cost

8. Breakeven Number of units = QBE =Vé9îö .øîìñòéê' #û$ò$'Vé9îö Véêñêíéñù #û$ò$

ëìéíî øîì ðêéò/+ñìéñ,ùî íû$ò øîì ðêéò

9. Operating Breakeven = QOBE =!MŸIJ URI(HGMLT QO7G

$(MaI RI( SLMG/"H(MH|wI aO7G RI( SLMG




Reading 38: Dividends & Share Repurchases:

Basics

1. Company’s payout for the year = Cash

dividends + Value of shares repurchased in

any given year

2. Dividend Payout ratio =#ûõõûê $2ñìî íñ$2 öé*éöîêö$

/îò úêíûõî ñ*ñéùñ,ùî òû íûõõûê $2ñìî$

3. EPS after Dividend = EPS before Dividend

! ÷2ñìî$ ûv$ ,îüûìî ôé*éöîêö

÷2ñìî$ ûv$ ñüòîì ôé*éöîêö

4.

Stock Price after Dividend = Stock Price

before Dividend ! EPS after Dividend

5.

Total Market Value after Dividend =

Shares outstanding after Dividend ! Stock

price after Dividend

6. Stock price after 2-for-1 stock split =÷òûí1 øìéíî ,îüûìî $òûí1 $øùéò

k

7. EPS after 2-for-1 stock split =7ë÷ ,îüûìî $òûí1 $øùéò

k

8.

DPS after 2-for-1 stock split =ôë÷ ,îüûìî $òûí1 $øùéò

k

9. EPS after buyback =7ñìêéê'$/8üòîì òñ9 #û$ò ûü Vðêö$

÷2ñìî$ .ðò$òñêöéê' ñüòîì ^ðó,ñí1

10. Ex-dividend value of share = Stock price –

Dividend per share

11. Market value of Equity after distribution of

cash dividends =

\cŽ ûü $2ñìî$ ûv$d 0 c&+ $2ñìîd o #ñ$2 öé*]

Ž ûü $2ñìî$ ûv$

12. Post-repurchase share price =

Žûü $2ñìî$ ûv$ 0 c&+ $2ñìî o

<ûìò2 ûü ÷2ñìî ìîøðìí2ñ$î]

c Ž ûü $2ñìî$ ûv$/Ž ûü $2ñìî$ cíñê ,î ìîøðìí2ñ$îö ,ó ñ #û

Reading 39: Working Capital Management

1.

Operating cycle = No of days of inventory

+ No of days of receivables

2. Net operating cycle = No of days of

inventory + No of days of receivables – No

of days payables

3.

Money Market Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî

ëðìí2ñ$î øìéíî 0

opf

/û ûü öñó$ òû õñòðìéòó

4. Bond Equivalent Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî

ëðìí2ñ$î øìéíî0

opu


5. Discount-basis Yield =Vñíî *ñùðî/ëðìí2ñ$î øìéíî

Vñíî +ñùðî0

opf


6. Wght Avg collection period = wghts !

Avg no of days to collect accounts within

each aging category

Where, Weights = % of total receivables in

each category

7.

Float Factor =8*' ôñéùó Vùûñò

8*' ôñéùó ôîøû$éò =

8*' ôñéùó Vùûñò

aw„… ƒaz‘w aR ’“c‚”f jcbafewcS

`a aR j„{f

Where, Float =Amount of money that is in

transit b/w payments (by customers) and

funds (usable by co)

8.

Value of stretching payment = A/c payable

! Co's opportunity cost for ST funds

9. Cost of Trade Credit = + ,

ôé$íûðêò

&/ôé$íûðêò

ghi

‘? +

where n = days beyond discount period

10.

Cost of Line of Credit =úêòîìî$ò'#ûõõéòõîêò üîî

-ûñê 8õûðêò

11. Bankers Acceptance Cost =úêòîìî$ò

/îò øìûíîîö$ =

úêòîìî$ò

-ûñê ñõûðêò/úêòîìî$ò

12. Commercial Paper Cost =úêòîìî$ò'ôîñùîì_$ íûõõé$$éûê'^ñí1ðø íû$ò$

-ûñê ñõûðêò/úêòîìî$ò

13. Annualized cost = Cost ! 12




Reading 40: The Corporate Governance of

Listed Companies

Reading 41: Portfolio Management: An

Overview

1. NAV of bond mutual fund =c*ñùðî ûü îñí2 ,ûêö éê ò2î øûìòüûùéûd

/û ûü $2ñìî$

2. New Shares that need to be created =8õûðêò òû ,î úê*î$òîö éê ò2î Vðêö

/8+ ûì !ûòñù *ñùðî ûü ñ &ðòðñù Vðêö

3. New NAV of the Fund = NAV or Total

value of a Mutual Fund + Amount to beinvested in the Fund

4. No of shares need to be retired =8õûðêò òû ,î <éò2öìñ<ê üìûõ ò2î Vðêö

/8+ ûì !ûòñù *ñùðî ûü ñ &ðòðñù Vðêö

Reading 42: Risk Management: An

Introduction

Reading 43: Portfolio Risk & Return: Part I

1. Total Return = Capital Gain (or Loss) +

Dividend Yield

2. Capital Gain =ëw/ëwÒ%

ëwÒ%

3. Dividend Yield =ô

ëh? +

4. 3-Yr HPR = [(1 + R 1) ! (1 + R 2) ! (1 +

R 3)]1/3 – 1

5. Arithmetic mean (AM) R = YM 8Nƒ%'Nƒ‰'µ'Nƒ•Ò%'Nƒ

*

8 &

*

YMG*G[&

6. Geometric R for n periods = MDM 8

+ , Y& + , Yk l + , YL&

L ? +

7. IRR =#V ñò !éõî ò

&'ú)) w 8 j!

ò[f

8. Annual Return (Ann R):

• Ann R = (1 + Quarterly R) 4 – 1

• Ann R = (1 + Monthly R) 12 – 1

•

Ann R = (1 + Weekly R) 52 – 1

• Ann R = (1 + Daily R) 365 – 1

• Weekly R = (1 + Daily R) 5 – 1

• Weekly R = (1 + Annual R) 1/52 – 1

9. Portf R (for Two Assets) = (Wght of Asset

1 ! R of Asset 1) + (Wght of Asset 2 ! R

of Asset 2)

10. Gross R = R – Trading exp – other exp

directly related to the generation of returns.

11. Net R = Gross R - All managerial and

administrative exp

12. After-tax nominal R = Total R - Any

allowance for taxes on realized gains

13. (1 + Nominal R) = (1 + Real Rf R) ! (1 +

Inf) ! (1 + RP)

14. (1 + Real R) = (1 + Real Rf R) ! (1 + RP)

15.

(1 + Real R) = c&'/ûõéêñù )d

c&'úêüd

16. Var of a Single Asset = Šk 8 NZ/ˆ ‰

ƒ„%

*

17. Sample Variance = Jk 8 )w/) ‰

e„%

!/&

18.

Cov of R b/w two assets = Cov (Ri,Rj) =

-ij! %i ! % j

19. Portfolio Var = –ëk 8 —&

k–&k , —k

k–kk ,

«—&—kT¦H M&– Mk 8 —&k–&k , —kk–kk ,«—&—k˜&k–&–k

20. Portfolio S.D. = 3¦§? ¥¦>4¦ =N§4NB56

21. Cov b/w asset 1 & asset 2 = Correlation of

Return b/w two assets ! S.D. of asset 1 !

S.D. of asset 2

22. Correlation of Return b/w two assets =#û*ñìéñêíî ûü )îòðìê ,v< ò<û ñ$$îò$

÷•ô•ûü ñ$$îò & 0 ÷•ô•ûü ñ$$îò k

23. 1 + Expected Return =+ , Q M 8

+ , §ìü 0 + , Q ™ 0 + , Q M3

24. Utility of an Invest = Expected Return -&

k 0M4Jš ›H6§J4¦B T¦6¥¥ 4546B? 0

=N§ ¦¥ rBH6J?




Remaining Equity = Proceeds on sale –

Payoff loan – Margin i paid + Div received

– Sales commission paid

2.

ROE (based on leverage alone)

= Leverage (in times) ! stock price return

(in %)

3. Price of stock below which a margin call

will take place (P):úêéòéñù õñì'éê ª 'cë/ úêéòéñù ÷òûí1 ëìéíîd

ë8

ŸN4B?6BNB56 ŸN§F4B M6«K4§6A6B? cÞd

4. Total cost of placement to the issuing firm

in IPO ($)

= Gross proceeds received by the issuing

firm – Net proceeds received by the issuing

firm

5. Total cost of placement to the issuing firm

in IPO (%) =

cýìû$$ øìûíîîö$ ìîíîé*îö ,ó úV/

/îò øìûíîîö$ ìîíîé*îö ,ó úV

/îò øìûíîîö$ ìîíîé*îö ,ó úV

where IF = Issuing firm

6. Max leverage ratio =&ffÞ

Þ ûü 7Cðéòó

7. Max leverage ratio for position financed by

min margin requirement =&

&éê õñì'éê ìîCðéìîõîêò

Reading 47: Security Market Indices

1. Value of a price return index =

VPRI = D

P n

N

i

ii!=1

For Single Period:

2. % Change in value of Price return of

index Portfolio = PR I = 0

01

PRI

PRI PRI

V

V V !

3. Price Return (Ind constituent security):PR I

=

0

01

i

ii

P

P P !

4. Price return of the index: PR I =

!=

""#

$%%&

' ( N

i i

ii

i

P

P P w

1 0

01

5. % èin value of Total return of Index

0

01

PRI

I PRI PRI

V

IncV V +!

6. Total return of each security = TR i =

i

iii

P

Inc P P

0

01 +!

TotalRe turn wi

P1i ! P

0i + Inc

i

P0i

"

#$

%

&'

i=1

N

(

Over Multiple Time Periods:

7. Value of Price Return index at time t =

VPRIT = VPRI0 (1 + PR I1) (1 + PR I2) … (1 +

PR IT)

8.

Value of Total Return index at time t =

VTRIT = V TRI0 (1 + TR I 1) (1 + TR I 2) … (1 +

TR I T)

9. Weight of security i under price weighting

=ëìéíî ûü $îíðìéòó é

÷ðõ ûü ñùù øìéíî$ ûü íûê$òéòðîêò $îíðìéòéî$

10. Weight of security i under equal weighting

=&

/û ûü $îíðìéòéî$ éê ò2î éêöî9

11. Weight of security i under market-cap

weighting =/f ûü $2ñìî$ ûv$ ûü ÷é 0 ÷2ñìî øìéíî ûü ÷é

/û ûü $2ñìî$ ûv$ ûü ÷é 0 ÷2ñìî øìéíî ûü ÷é`e

Where Si = Security i

12. Weight of Si under Mkt Cap weighting =Vìñíòéûê ûü $2ñìî$ ûv$ õ1ò üùûñò 0 ûü $2ñìî$ ÷é 0

÷2ñìî øìéíî ûü $îíðìéòó é

cVìñíòéûê ûü $2ñìî$ ûv$ &1ò üùûñò 0 ûü $2ñìî$ ûv$ ûü ÷é 0

÷2ñìî øìéíî ûü $îíðìéòó éd

13.

Fundamental weight on security i =Vðêöñõîêòñù $épî õîñ$ðìî ûü íûõøñêó éË

cVðêöñõîêòñù$épî õîñ$ðìî ûü íûõøñêó éd`e

*Book value, cash flow, revenues, earnings,

dividends, & number of employees.

Reading 48: Market Efficiency




Reading 49: Overview of equity Securities

1. Equity security’s Total Return =÷ñùî ë ûü ñ $2ñìî/ëðì2ñ$î ëûü ñ $2ñìî'íñ$2v$òûí1 ôé*

ëðìí2ñ$î øìéíî ûü ñ $2ñìî

2. ROE in yr t =/ú cüûì .ìöéêñìó ÷2ñìî2ûùöîì$d éê óì ò

8*' !ûòñù ^+ ûü 7Cðéòó

OR

ROE =/ú cüûì .ìöéêñìó ÷2ñìî2ûùöîì$d éê óì ò

÷2ñìî2ûùöîì$_îCðéòó ñò ,î' ûü óì ò

3. MV of equity = Mkt price per share !

Shares O/s

4.

BV of equity per share =

!ûòñù ÷n_îCðéòó

÷2ñìî$ ûv$

5. Price-to-book ratio =&ñì1îò øìéíî øîì $2ñìî

^+ ûü îCðéòó øîì $2ñìî

6. ROE = Net profit margin ! Asset turnover

! Financial leverage =/îò îñìêéê'$

/îò $ñùî$ 0

/îò $ñùî$

8*' òûòñù ñ$$îò$ 0

8*' òûòñù ñ$$îò$

8*' íûõõûê îCðéòó

Reading 50: Introduction to Industry &

Company Analysis

Reading 51: Equity Valuation: Concepts &

Basic Tools

1. Value of a share of stock today =79øîíòîö öé*éöîêö éê óì ò

c&'ìîCðéìîö ).) ûê $òûí1d¬ò

ò[&

If an investor intends to buy and hold a share

for 1 yr:

2. Value of a share of stock today =79øîíòîö ôé* éê & óì '79øîíòîö $îùùéê' øìéíî éê & óîñì

c&'ìîC )û) ûê $òûí1d¬&

3. Value of a share of stock for n holding

period or investment horizon =79øîíòîö ôé* éê óì ò

&'ìîC ) ûê $òûí1 w ,L

G[&

79øîíòîö øìéíî éê ê øîìéûö$

&'ìîC ) ûê $òûí1 ‘

4. CFO = NI + Non-cash exp – Invst in WC

5. FCFE = CFO – FCInv + Net Borrowing

6.

Value of a share for a non-div-paying

stock =V#V7 éê óîñì ò

&'ìîC ) ûê $òûí1 wò[&

7. Req RoR on sharei = Current expected Rf

rate + Beta i [MRP]

8.

Value of a pref stock (non-callable, non-

convertible) =

( ) ( )r

D

r

D

g r

g DV

000

0

0

011=

!

+

=

!

+

=

9. Value of a pref stock (non-callable, non-

convertible) with maturity at time n =

Af 8‡f

c + , 5 dG ,

L

G/&

Ô

+ , 5 L

Gordon Growth Model:

10. Value of a share of stock =

( )r g

g r

D

g r

g DV <

!

=

!

+

= ,1

10

0

11.

Sustainable dividend growth rate =

g = ROE ! b

where b = earnings retention rate = (1 -

Dividend payout ratio)

Two-stage valuation model:

12. Value of share today = V0 =

Af 8‡f + , Ž7

G

c + , 5 dG ,

AL

c + , 5 dL

L

M[&

AL 8‡L'&

5 ? ŽB

‡L'& 8 ‡fc + , Ž7dL + , ŽB

13. Justified P/E =ëf

7&8

ô%v7%

ì/' 8

ø

ì/'

14. EV = MV of stock + MV of debt – Cash

and cash Equivalents

15. Asset-based value = Value of Equipment

and inventory – Value of Liabilities

Reading 52: Fixed Income Securities: Defining

Elements

1. Inf adj Principal amount of a zero-coupon-

indexed bond

= [Par value ! (1 + CPI)]

2.

Inf adj coupon payment for an interest-

indexed bond

= [(coupon rate ! Par value) ! (1+CPI)]




3. Inf adj Principal amount of a capital-

indexed bond

= [Par value ! (1 + CPI)]

4.

Inflation adjusted coupon payment for a

capital-indexed bond

= [Par value ! (1 + CPI)] ! coupon rate

Reading 53: Fixed Income Markets: Issuance,

Trading & Funding

Reading 54: Introduction to Fixed Income

Valuation

1.

Amount of discount below par value =Present value of deficiency

2. Present value of deficiency =#ûðøûê ìñòî/&ñì1îò öé$íûðêò ìñòî 0ëñì *ñùðî

&'&ñì1îò öé$íûðêò ìñòî wêò[&

3. Bond price =

PV =PMT

(1+ r)1 +

PMT

(1+ r)2 +...+

PMT + FV

(1+ r) N

4. % Price change =/î< øìéíî/.ùö øìéíî

.ùö øìéíî

5. Bond price (given sequence of spot rates)

= PV =

PMT

(1+ Z 1)1 +

PMT

(1+ Z 2 )2 +...+

PMT + FV

(1+ Z N ) N

6. Full price of bond = Flat price of bond +

Accrued interest

7. Accrued interest = ›r 8G

*0@\]

8. Full price of a fixed-rate bond between

coupon payments = PVFull

=

PMT

(1+ r)1!t /T

+

PMT

(1+ r)2!t /T

+...+PMT + FV

(1+ r) N !t /T

9. Full price of a fixed-rate bond between

coupon payments

PV ! (1+ r)t /T

10.

Interpolated yield (say for 3-year, givenmarket discount rates for 2 and 5 yrs) =

(Average yield for 2 year bonds) +o/k

u/k !

(average yield for 5 year bonds – average

yield for 2 year bonds)

11.

1+ APR

m

m

!

"#

$

%&

m

= 1+ APR

n

n

!

"#

$

%&

n

12.

Current yield =÷ðõ ûü íûðøûê øñóõîêò$ ìîíîé*îö û*îì ò2î óîñì

Vùñò øìéíî

13. Price of Floating-rate note = PV=

( I +Qm)!FV

m

1+

I + DM

m

"

#$

%

&'1 +

( I +QM )!FV

m

1+

I + DM

m

"

#$

%

&'2 +...+

( I +QM )!FV

m+FV

1+

I + DM

m

"

#$

%

&' N

14. Price of Money Market Instrument =

PV = FV ! 1" Days

Year! DR

#

$%

&

'(

15. Market Discount Rate =

DR = Year Days( )! FV " PV

FV

#

$%

&

'(

16. Price of Money Market Instrument =

PV = FV

1+ Days

Yr! AOR

"

#$

%

&'

17.

Add-on rate =

AOR =Yr

Days

!

"#

$

%&'

FV ( PV

PV

!

"#

$

%&

Relation b/w two spot rates and Implied

Forward Rate:

18. (1 + zA)A ! (1 + IFR A,B-A)B-A = (1 + zB)B

Z-spread over the benchmark spot curve:

Price of a bond =

PV =PMT

(1+ z1+ Z )

1 +

PMT

(1+ z2 + Z )

2 + ...+

PMT + FV

(1+ z N + Z )

N




19. OAS = Z-spread – Option value (bps per

year)

20. G-spread = Yield-to-maturity on Corporate

bond – Yield-to-maturity on a government

bond

21. Interpolated Spread = I-spread = YTM of

the bond - Linearly interpolated yield to

the same maturity on an appropriate

reference curve

Reading 55: Introduction to Asset Backed

Securities

1.

Loan-to-value ratio (LTV) =8õûðêò ûü &ûìò'ñ'î

ëìûøîìòó +ñùðî

2. Monthly CF for a MPS = Monthly CF of

underlying pool of mortgages - Servicing

fee - Other fees

3. Pass-through rate = Mortgage rate on the

underlying pool of mortgages – Servicing

Fee - Other fees

4. SMM = Pre-pmt for month ÷ (Beg

mortgage balance for month – Scheduled

principal re-pmt for month)

5. CPR = 1 0 (1 0 SMM)12

6. CF Construction (Monthly CF for MPS):

• Net interest = (Beg mortgage

balance ! Pass-through rate) / 12

•

Scheduled principal re-pmt =

Mortgage pmt – Gross i- pmt

• Gross i- pmt = (Beg mortgage

balance ! WAC) / 12

• Pre-pmt for month = SMM !

(Beg mortgage balance for month

– Scheduled principal re-pmt for

month)

•

Total principal re-pmt =

Scheduled principal re-pmt +

Prepayment

• Beg mortgage balance for the

following month = Beg mortgage

balance for the month – TotalPrincipal Pmt

• Projected CF for MPS = Net i-

pmt + Total principal re-pmt

7. DSC ratio =ëìûøîìòó®$ ñêêðñù /.ú

ôî,ò $îì*éíî

Reading 56: Understanding Fixed Income Risk

& Return

1.

Interest-on-interest gain fromcompounding = Future value of reinvested

coupons - Total amount of coupon

payments

Where,

FV of Reinvested Coupons = [CR !(1+

RR)n-1

] + [CR !(1+RR)n-2

] +…+ [CR !(1+

RR)n-n

]

Total Amount of Coupon Pmt = CR ! Par

value ! No of periods

RR = Re-invstmnt rate per period

CR = coupon rate

2. Realized RoR on Bond=

÷ðõ ûü )îéê*î$òîö #ûðøûê$'

)îöîõøòéûê ûü ëìéêíéøñù ñò &ñòðìéòó

^ûêö ëìéíî

%

m

? +

3. Carrying value of bond (if bond purchased

below par) = Purchase price + Amortized

amount of Discount

4.

Carrying value of a bond (if bond purchased above par) = Purchase price –

Amortized amount of Premium

5. Amortized amount for 1st year = Bond

Price after 1-yr - Initial bond price

6. Capital g / (l) = Sale price of Bond after n

years – Carrying value of Bond after n

years

7.

Macaulay Duration =

MacDur = 1! t / T ( )

PMT

1+ r( )1!t /T

PV Full

"

#

$$$$

%

&

''''

+ 2! t / T ( )

PMT

1+ r( )2!t /T

PV Full

"

#

$$$$

%

&

''''

+...+ N ! t /T ( )

PMT + FV

1+ r( ) N !t /T

PV Full

"

#

$$$$

%

&

''''

(

)

**

+

**

,

-

**

.

**

OR

MacDur =1+ r

r!

1+ r+ N " c! r( )#$ %&

c" 1+ r( ) N

!1#$

%&+ r

'

()

*)

+

,)

-)! (t /T )




8. Modified D =&ñíôðì

&'ì

9. Annualized Modified D =&ûöéüéîö ôðìñòéûê

ëîìéûöéíéó ûü øñóõîêò éê ñ óîñì

10.

% 1 PVFull = - AnnModDur ! 1Yield

11. Approx Modified D =

(PV ! )! (PV

+)

2" (#Yield )" (PV 0 )

12. Approx Mac Dur = Approx Mod Dur ! (1

+ r)

13. Effective D =(PV

! )! (PV

+)

2" (#Curve)" (PV 0 )

14. Macaulay D for a Zero-coupon bond =1/G

*

15. Macaulay D for a Perpetual bond = (1+ r) /

r

16. Avg Mod D for the Portf =

Ÿ¦I t ¦¥ q¦BI + 0&+ ûü ^ûêö &

!ûòñù &+ûü ëûìòü

+ Ÿ¦I t ¦¥ q¦BI « 0&+ ûü ^ûêö k

!ûòñù &+ ûü ëûìòü +

…+ Ÿ¦I t ¦¥ q¦BI ¯ 0&+ ûü ^ûêö /

!ûòñù &+ ûü ëûìòü

17. Money D = Annualized Mod D ! Full

Bond Price

18. * Full price of Bond (in currency units) # -

Money D ! è in annual YTM

19. PVBP =

(PV !

)! (PV +)

2

20.

Basis Point Value (BPV) = Money

duration ! 0.0001 (1 bp)

21. Bloomberg’s Risk Statistic = PVBP ! 100

22. %*PV Full = (-AnnModDur ! *Yield) +&

k 0==W=4¢>:° 0cèt>4²<dk

Or%*PV Full = (-AnnModDur ! *Yield) +

&

k 0==W=4¢>:° 0cèt>4²<dk

23. Approx. Convexity Adjustment =

(PV !)+ (PV

+)![2" (PV 0 )]

(#Yield )2" (PV 0 )

24.

Convexity of a zero coupon bond =

N ! (t /T )[ ]" N +1! (t /T )[ ](1+ r)

2

25. Money Convexity vs Money Duration =

*PV Full # - (MoneyDur ! *Yield) + [&

k !

MoneyCon ! (*Yield)2]

26. Money Convexity of bond = Annual

Convexity ! Full Price

27. Effective Convexity =

PV !( )+ PV +

( )! 2" (PV 0 )[ ]#$ %&

'Curve( )2" PV 0 )( )

28.

Duration Gap = Bond’s Macaulay

Duration – Investment Horizon

Reading 57: Fundamentals of Credit Analysis

1. Expected Loss = Default Probability !

Loss Severity given Default

2. Operating Profit Margin =.øîìñòéê' úêíûõî

)î*îêðî

3.

EBITDA = Operating Income + Dep +

Amort

4.

FCF = CFO – Cap exp– Div

5. Capital expenditures = Additions to P&E +

Additions to product rights & intangibles –

Proceeds of sale of P&E

6.

Total debt = ST debt + Current portion of

LT debt + LT debt

7.

Capital = Debt + Equity

8. Yield on Corp Bond = Rf rate + Expected

Inf rate + Maturity P + Liquidity P+ Credit

spread

9. Yield spread = Liquidity P + Credit spread




10. Return impact for smaller spread *# % *

in price # -Modified Duration ! *Spread

11. Return impact for larger spread * # % * in

price # - (Modified D ! *Spread) +

&kConvexity ! (*Spread)2

12.

Secured debt leverage =!ûòñù $îíðìîö öî,ò

7^ú!ô8

13. Senior unsecured leverage =÷îíðìîö öî,ò'÷îêéûì ðê$îíðìîö öî,ò

7^ú!ô8

14. Total Leverage =!ûòñù öî,ò

7^ú!ô8

15. Net Leverage =!ûòñù öî,ò/#ñ$2

7^ú!ô8

Reading 58: Derivatives Markets and

Instruments

1.

Value of the contract to the ‘Long’ at

expiration = ST – F0(T)

2. Value of the contract to the ‘Short’ at

expiration = F0(T) – ST

3. Margin % in stock market =&+ ûü ÷òûí1/&+ ûü ôî,ò

&+ ûü ÷òûí1

4.

Margin Call:

• Long position: Price ± that would

trigger a margin call = IM req – MM

req

• Short position: Price( that would

trigger a margin call = IM req – MM

req

5. TED spread = LIBOR – T-Bill rate

6. At expiration (for option Buyer):

• Value of Call option =

CT = Max (0, ST - X)

• Profit from Call option =

Max (0, ST - X) – C0

•

Value of Put option = P0 =

Max (0, X- ST)

• Profit from Put option =

Max (0, X- ST) – P0

7.

At expiration (for option Seller):

• Profit from Call option =

– Max (0, ST - X) + C0

•

Profit from Put option =

– Max (0, X- ST) + P0

8. To eliminate arbitrage opportunity:

Forward Price should be = Spot Price

0 + , > 5;:4 Þ G

Reading 59: Basics of Derivative Pricing &

Valuation

1.

Pricing of risky assets = S0 =7 c÷!d

&'ì'²

2. Commodity = F 0, T = S0 e(r – 2)T

where, 2 = Convenience yield 0 Cost of

carry

3. S0 =7 c÷!d

&'ì'² – 3 + 4

where, 3 (theta) = PV of the costs and 4

(gamma) = PV of benefits

4.

Arbitrage and Derivatives = Underlyingasset + Opposite position in derivative =

Underlying payoff – Derivative payoff =

Rf return

5. Pricing and Valuation of Forward

Contracts:

• At Expiration F (0, T) = S0 (1 + r)

Tor

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

• Value of forward (long) during

contract life (where t < T) = Vt (0, T)

= St – F (0, T) / (1 + r) (T – t)

• Value of forward (short) during

contract life (where t < T ) = Vt

(0, T) = F (0, T) / (1 + r) (T – t) - St

• Value of forward (long) at expiration

(where t = T) = VT (0, T) = ST - F (0,

T)

•

Value of forward (long) at initiation

(where t = 0) = Vt (0, T) = S0 – F (0,

T) / (1 + r) T

= 0

•

Forward price of an asset with benefitsand/or costs = (S0 – 4 + 3) (1 + r) T =

S0 (1 + r)T – (4 - 3) (1+ r)

T

• Value of Forward contract with

benefits and/or costs during the life of

the contract = St – (4 - 3) (1 + r) T - F

(T) / (1 + r) (T – t)




6. FRAs: An example of 3 ! 9 FRA (read as

three by nine):

• Contract expires in 90 days

•

Underlying loan settled in 270 days

• Underlying rate is 180-day LIBOR

•

For Synthetic FRA (take long position

in a 300-day Euro$ T.D and short

position in a 30-day Euro$ T.D

• For synthetic forward position in a 90-

day zero-coupon that begins in 30 day

(buy 120 day & sell 30 day (zero

coupon bonds)

7. Pricing and Valuation of Swap Contract (a

fixed for floating swap contract):

•

Fixed Periodic rate =

RN =

1 - ZN

Z1+Z

2 + ....+Z

N

• Where Zn are n period zero coupon

bonds (i.e. $1 discount factors)

)360/(1

1Zn

days Ln !+

=

• Value of a fixed rate side (per $1 NP)

= V fixed rate = [Fixed payment ! (

Z1

+Z2

+ ....+ZN )] + ($1 ! Z N)

• Value of a floating rate side (per $ 1

NP) = V floating rate = ($1 + 1st floating

pmt) ! Z1

Pricing and valuation of Options:

8. Payoff of Call options:

• At expiration call option = c T = Max

(0, ST –X)

•

Profit (call buyer) = Max (0, ST – X) –

c0

• Profit (call seller) = -Max (0, ST – X)

+ c0

9. Payoff of Put options:

• p T = Max (0, X- ST)

•

Profit (put buyer) = Max (0, X-ST) – p0

• Profit (put seller) = - Max (0, X – ST) +

p0

10. Max Profit/Loss for Option writer/holder:

• Max profit of option seller/writer!

Option premium.

• Max loss of option seller/writer!

unlimited.

•

Max loss of option holder!Option

premium

Put-Call Parity

11.

Protective Put• Value PP = p0 + S0

• Payoff at expiration (put out-of-the-

money) = ST.

• Payoff at expiration (put in-the-

money) = (X-ST) + ST = X.

12.

Fiduciary Call

• Value FC = c0 + X / (1+r) T

• Payoff at expiration (when call out-of-

the-money) = X.

• Payoff at expiration (call in-the-

money) = X + (ST – X) = ST.

13. Put-Call Parity (to avoid arbitrage) = c0 +

X / (1+r) T = p0 + S0

• Synthetic long position in a call =

C = p 0+S 0!

X

(1+ r)T

• Synthetic long position in a put =

p0= c

0!S

0+

X

(1+ r)T

• Synthetic long position in an

underlying = S 0 = c 0+

X

(1+ r)T ! p0

•

Synthetic long position in a riskless

bond = X

(1+ r)T = p 0

+S 0 ! c0

14. Put-Call-Forward Parity = F0(T) / (1 + r)T

+ p0 = c0 + X/(1 + r) T 15. Valuing a callable bond using Binomial

Model:

•

R u = R d! e2% :

• Value at time 0 = V0 = hS0 0 c0

• Value at time 1 will either V1+ = hS1

+ -

c1+ or V1

- = hS1- - c1

-




• If the portfolio was hedged, then V+

would equal V-.

• Value of the call =

• Value of the put =

Reading 60: Risk Management Applications of

Option Strategies

1.

For Call Option Buyer•

cT = max (0, ST –X)

• When ST ( X"cT = 0

• When ST > X"cT = ST – X

• Value at expiration = cT

•

Profit = cT – c0

• Maximum profit = 5! no upper limit

• Maximum loss = c0

• Breakeven = ST* = X + c0

2. For Call Option Seller

•

cT = max (0, ST –X)

• When ST ( X"cT = 0

•

When ST > X"cT = ST –X

• Value at expiration = -cT

•

Profit = –cT+ c0

• Maximum profit = c0

• Maximum loss = 5! no upper limit

• Breakeven = ST* = X +c0

3. For Put Option Buyer

•

pT = max (0, X - ST)

•

When ST < X" pT = X - ST

• When ST " X" pT = 0

• Value at expiration = pT

•

Profit = pT – p0

• Maximum profit = X – p0

• Maximum loss = p0

• Breakeven = ST* = X –p0

4. For Put Option Seller

• pT = max (0, X –ST)

•

When ST < X" pT = X – ST • When ST " X" pT = 0

• Value at expiration = –pT

• Profit = –pT + p0

• Maximum profit = p0

• Maximum loss = X - p0

• Breakeven = ST* = X - p0

5. Covered Call = Long stock position +

Short call position

•

Value at expiration = VT = ST – max

(0, ST – X)

•

When ST ( X"VT = ST

• When ST > X"VT = ST - ST +X = X

•

Profit = VT – S0 + c0

• Maximum Profit = X – S0 + c0

• Maximum Loss = S0 – c0

• Breakeven =ST* = S0 – c0

6. Protective Put = Long stock position +

Long Put position

•

Value at expiration: VT = ST + max (0,X - ST)

• When ST ( X"VT = ST + X - ST = X

• When ST > X"VT = ST

•

Profit = VT – S0 - p0

• Maximum Profit = 5

•

Maximum Loss = S0 + p0 – X

• Breakeven =ST* = S0 + p0

Reading 61: Introduction to Alternative

Investments

1.

Total Return = Alpha R + Beta R

2. Asset Based Valuation = Co value = Co’s

assets value – Co’s liabilities value

Real Estate Valuation




3. Direct Cap Approach " Valuation of a

property =1Ug

QHRMGHwM³HGMOL NHGI where

NOI = Gross potential income –Estimated

vacancy losses – Estimated collective

losses – Insurance – Property Taxes –Utilities – Repairs, maintenance exp.

4.

Income Based Approach" FFO = NI +

Dep exp on R.E + Def Tax charges – Gains

from sales of R.E + losses from sale of R.E

5. AFFO = FFO – Recurring Cap exp

6. Asset based Approach" REIT’s NAV =

Estimated MV of REIT’s total assets –

Value of REIT’s total liabilities.

7. Pricing of Commodity Futures Contracts:

Futures price # Spot price (1 +r) + Storage

costs – Convenience yield

8. Roll yield = Spot price of a commodity –

Futures contract price

or

Roll yield = Futures contract price with

expiration date ‘X’– Futures contract pricewith expiration date ‘Y.

9.

Returns on a passive investment in

commodity futures

= Return on the collateral + RP or

convenience yield net of storage costs.

10. Sharpe ratio = (Investment return – Rf

return) / S.D. of return

11. Sortino Ratio = (Annualized RoR –

Annualized Rfe rate)/Downside Deviation

l 1 Formula Sheet June 2016

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Transcript of l 1 Formula Sheet June 2016