finquiz formula sheet cfa level i 2015 · finquiz formula sheet cfa level i 2015 reading 5: time...

FinQuiz Formula Sheet CFA Level I 2015

Reading 5: Time Value of Money 1. Interest Rate (i)

• i = Real Rf + Inf P + Default Risk P + Liquidity P + Maturity P

• Nominal Rf i rate = Real Rf i Rate + Inf P

• i rate as a growth rate = g = !"#$"

%#-1

2. PV and FV of CF =

• PV = !"&'( #

• PV of Perpetuity = $)*(

• PV (for more than one Compounding

per year) = PV= FVN 1 +(-.

/.×1

𝑤ℎ𝑒𝑟𝑒 𝑟7 = 𝑠𝑡𝑎𝑡𝑒𝑑 𝑎𝑛𝑛 𝑖 − 𝑟𝑎𝑡𝑒 • FVN = 𝑃𝑉 1 + 𝑟 1 • FV (for more than one Compounding

per year) = FVN = PV 1 + (-.

.×1

• FV (for Continuous Compounding) = FVN = 𝑃𝑉𝑒(-×1

• Solving for N = B1 CD

ED(

(where LN =

natural log) 4. Stated & Effective Rates

• Periodic i Rate = FGHGIJ KLL M NHGI

1O. OQ RO.SOTLJMLU $I(MOJ7 ML VLI WIH(

• Effective (or Equivalent) Ann Rate (EAR = EFF%) = 1 +𝑃𝑒𝑟𝑖𝑜𝑑𝑖𝑐 𝑖 𝑅𝑎𝑡𝑒 . − 1

• EAR (with Continuous Compounding) = EAR = 𝑒(- − 1

5. PV & FV of Ordinary Annuity

• PVOA = $)*&'( [

LG\& = 𝑃𝑀𝑇

&/ %%_` #

(

• FVOA = ( )[ ]tNt rPMT −+1L

G\& =

𝑃𝑀𝑇 &'( #/&(

• Size of Annuity Payment = PMT = $"

$" OQ KLLTMGa !HbGO(

• PV of Annuity Factor = &/ %

%_ `-c

c×#

`-c

6. PV & FV of Annuity Due

• PVAD = 𝑃𝑀𝑇&/ %

%_` #

( + PMT at t = 0

= PVOA + PMT • FVAD =

( ) ( )NN

r1 r

1r1PMT +⎥⎦

⎤⎢⎣

⎡ −+=

FVOA ×(1+r)N Reading 6: Discounted Cash Flow Applications 1. NPV = R![

&'( [LG\d − 𝑐𝑓d

2. IRR (when project’s CFs are perpetuity) =

NPV = - IO + R!fNN

= 0

3. HPR = $% /$g' h%$g

4. MWR = R![

&'fNN [*M\d − 𝐶𝐹d = 0 (IRR

represents the MWR) 5. TWR:

• TWR (when no external CF) = rTWR = HPR = rt = )"%/)"g

)"g

• TWR (for more than one periods) = rTWR = [(1+rt,1)× (1+rt,2)×… (1+rt,n)] -1

• Annualized TWR (when investment is for more than one year) = 1 + 𝑅& 1 + 𝑅l …+

1 + 𝑅L%n_1

• TWR (for the year when valuation is daily) = rTWR = [(1+R1)× (1+R2)×… (1+R365)] -1 where R1 = )"%/)"g

)"g

6. Bank Discount Yield = BDY = rBD =

pqdL

$H(/$(MbI$H(

therefore Price = Par 1 −L × (rspqd

7. Holding Period Yield = HPY = $% /$g' h%$g

8. Effective Annual Yield = EAY = 1 +

𝐻𝑃𝑌 pqv/G − 1 (Rule: EAY > BDY) 9. Money Market Yield (or CD equivalent

Yield) rMM:

• rMM = HPY × pqdG


• rMM = (rBD) ×

!HbI "HxTI OQ GyI *(IH7T(a zMxx$T(byH7I $(MbI

• rMM = pqd (rspqd/ G (rs

(Rule: rMM>

rBD) 10. Bond Equivalent Yield = BEY =

Semiannual Yield × 2 Reading 7: Statistical Concepts & Market Returns 1. Range = Max Value – Min Value 2. Class Interval = i = {/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}7OxTGI !(I~TILba

*OGHx 1O OQ V}�7

5. Cumulative Absolute Frequency = Add up

the Absolute Frequencies 6. Cumulative Relative Frequency = Add up

the Relative Frequencies 7. Arithmetic Mean = FT. OQ O}�7 ML JHGH}H7I

1O.OQ O}�7 ML GyI JHGH}H7I

8. Median = Middle No (when observations are arranged in ascending/descending order)

• For Even no of obvs locate median at mean of L

l and

(L'l)l

𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛𝑠

• For Odd no. of obvs locate median at L'&

l position

9. Mode = obvs that occurs most frequently

in the distribution 10. Weighted Mean = 𝑋� = 𝑤M𝑋ML

M\& = (w1X1+ w2X2+….+ wnXn)

11. Geometric Mean = GM = 𝑋&𝑋l …𝑋Ln

with Xi≥0 for i = 1,2,…n. 12. Harmonic Mean = H.M = 𝑋{ =

L%��

n��%

13. Population Mean = µ = ��n�1

where N is the

number of observations in the entire population and Xi is the ith observation

14. Sample Mean = 𝑋 = ��n�L

where n = number of observation in the sample

15. Measures of Location:

• Quartiles = hM7G(M}TGMOL�

• Quintiles = hM7G(M}TGMOLv

• Deciles = hM7G(M}TGMOL&d

,

• Position of a percentile = Ly = 𝑛 + 1 a

&dd

16. Mean Absolute Deviation = MAD =

�[/�n��%

L

17. Population Var = σ2 = ��/� �#��%

1

18. Population S.D = 𝜎l= ��/� �#��%

1

19. Sample Var = s2 = ��/� �n��%

L/&

20. Sample S.D = s = ��/� �n��%

L/&

21. Semi-var = ��/� �

L/&!O( Hxx ��

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

𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = ��/� �

L/&!O( Hxx ��

23. Target Semi-var = ��/z �

L/&!O( Hxx ��z

where B = Target Value 24. Target Semi-Deviation =

𝑡𝑎𝑟𝑔𝑒𝑡 𝑠𝑒𝑚𝑖𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =

��/z �

L/&!O( Hxx ��z


25. Coefficient of Variation = CV = F

�

where s= sample S.D and 𝑋 = sample mean

26. Sharpe Ratio = )IHL $O(GQOxMO N/)IHL NQ N

F.h OQ $O(GQOxMO N

27. Excess Kurtosis = Kurtosis – 3

28. Geometric Mean R ≈

𝐴𝑟𝑖𝑡ℎ𝑚𝑒𝑡𝑖𝑐 𝑀𝑒𝑎𝑛 𝑅 − "H(MHLbI OQ Nl

Reading 8: Probability Concepts 1. Empirical Prob of an event E = P(E) =

$(O} OQ I�ILG �*OGHx $(O}

2. Odds for event E = $(O} OQ �

&/$(O} OQ �

3. Odds against event E = &/$(O} OQ �

$(O} OQ �

4. Conditional Prob of A given that B has

occurred = P(A|B) = $ Kz$ z

→ P(B) ≠ 0.

5. Multiplication Rule (Joint probability that

both events will happen): P(A and B) = P(AB) = P(A|B) × P(B) P(B and A) = P(BA) = P(B|A) × P(A)

6. Addition Rule (Prob that event A or B will occur):

P(A or B) = P(A) + P(B) – P(AB) P(A or B) = P(A) + P(B) (when events are mutually exclusive because P(AB) = 0)

7. Independent Events: • Two events are independent if:

P(B|A) = P(B) or if P(A|B) = P(A)

• Multiplication Rule for two independent events = P(A & B) = P(AB) = P(A)× P(B)

• Multiplication Rule for three independent events = P(A and B and C) = P(ABC) = P(A) × P(B) × P(C)

8. Complement Rule (for an event S) = P(S)

+ P(SC) = 1 (where SC is the event not S) 9. Total Probability Rule:

P(A) = P(AS) + P(ASC) = P(A|S)×P(S) + P(A|SC)×P(SC) P(A) = P(AS1) + P(AS2) +….+ P(ASn) = P(A|S1)×P(S1) + P(A|S2)×P(S2)… + P(A|Sn)×P(Sn) (where S1, S2, …,Sn are mutually exclusive and exhaustive scenarios)

10. Expected R = E(wiRi) = wiE(Ri)

11. Cov (Ri Rj) = 𝐸 𝑅M − 𝐸𝑅M 𝑅� − 𝐸𝑅� Cov (Ri Rj) = Cov (Rj Ri) Cov (R, R) = σ2 (R)

12. Portfolio Var = σ2 (Rp) =

𝑤M𝑤�𝐶𝑜𝑣 𝑅M𝑅�L�\&

LM\& σ2 (Rp) = 𝑤&l𝜎l 𝑅& + 𝑤ll𝜎l 𝑅l + 𝑤pl𝜎l 𝑅p + 2𝑤&𝑤l𝐶𝑜𝑣 𝑅&, 𝑅l + 2𝑤&𝑤p𝐶𝑜𝑣 𝑅&, 𝑅p + 2𝑤l𝑤p𝐶𝑜𝑣 𝑅l, 𝑅p

13. Standard Deviation (S.D) = 𝜎l 𝑅$ 14. Correlation (b/w two random variables Ri,

Rj) = 𝜌 𝑅M𝑅� =RO� N�N��N�×�N�

15. Bayes’ Formula =

𝑃 𝐸𝑣𝑒𝑛𝑡|𝑁𝑒𝑤 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 = $ 1I� fLQO(.HGMOL|��ILG

$ 1I� fLQO(.HGMOL ×

𝑃 𝑃𝑟𝑖𝑜𝑟 𝑝𝑟𝑜𝑏. 𝑜𝑓 𝐸𝑣𝑒𝑛𝑡 16. Multiplication Rule of Counting = n

factorial = 𝑛! = n (n-1)(n-2)(n-3)…1. 17. Multinomial Formula (General formula for

labeling problem) = L!L%!L�!…L�!

18. Combination Formula (Binomial Formula)

= 𝐶(L = L( = L!

L/( !(!

where n = total no. of objects and r = no. of objects selected.

19. Permutation = 𝑃(L = L!L/( !


Reading 9: Common Probability Distributions 1. Probability Function (for a binomial

random variable) p(x) = p(X=x) = L� 𝑝

� 1 − 𝑝 L/� = = L!L/� !�!

𝑝� 1 −

𝑝 L/� (for x = 0,1,2….n) • 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)

= &

}/H0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

𝑓𝑜𝑟 𝑎 ≤ 𝑥 ≤ 𝑏 =

F(x) = �/H}/H

𝑓𝑜𝑟 𝑎 < 𝑥 < 𝑏(cumulative

distribution) 3. Normal Density Funct = 𝑓 𝑥 =

&� l£

𝑒𝑥𝑝 /(�/�)�

l��for − ∞ < 𝑥 < + ∞

4. Estimations by using Normal Distribution:

• Approximately 50% of all obsv fall in the interval 𝜇 ± l

p𝜎

• Approx 68% of all obvs fall in the interval 𝜇 ± 𝜎

• Approx 95% of all obvs fall in the interval 𝜇 ± 2𝜎

• Approx 99% of all obvs fall in the interval 𝜇 ± 3𝜎

• More precise intervals for 95% of the obvs are 𝜇 ± 1.96𝜎 and for 99% of the observations are 𝜇 ± 2.58𝜎.

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

mean the point x lies) 𝑧 =𝑠𝑡𝑎𝑛𝑑𝑎𝑟𝑑 𝑛𝑜𝑟𝑚𝑎𝑙 𝑟𝑎𝑛𝑑𝑜𝑚 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 = �/��

(when X is normally distributed) 6. Roy’s Safety-Frist Criterion = SF Ratio =

� NE /N²�E

7. Sharpe Ratio = = � NE /N³

�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 + 0.50σ2) 10. Variance (σL

2) of a lognormal random variable = exp (2µ+ σ2) × [exp (σ2) – 1].

11. Lognormal Price = ST = S0exp (r0,T)

Where, exp = e and r0,t = Continuously compounded return from 0 to T

12. Price relative = End price / Beg price = St+1/ St=1 + Rt, 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:

rt, t+1= ln(1 + holding period return) or rt, t+1 = ln(price relative) = ln (St+1 / St) = ln (1 + Rt,t+1)

14. Continuously compounded return

associated with a holding period from 0 to T: r0,T= ln (ST / S0) or 𝑟d,* = 𝑟*/&,* +𝑟*/l,*/& + ⋯+ 𝑟d,& Where, rT-I, T = One-period continuously compounded return

15. When one-period continuously compounded returns (i.e. r0,1) are IID random variables. 𝐸 𝑟d,* = 𝐸 𝑟*/&,* + 𝐸 𝑟*/l,*/& +⋯+ 𝐸 𝑟d,& = 𝜇𝑇And 𝑉𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = 𝜎l 𝑟d,* = 𝜎l𝑇 S.D. = σ (r0,T) = σ 𝑇


16. Annualized volatility = sample S.D. of

one period continuously compounded returns × 𝑇

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 (σ) is known = 𝜎� =

�L

• When the population S.D (σ) is not known = 𝑠� =

7L where s = sample

S.D estimate = 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 =

𝑠l 𝑤ℎ𝑒𝑟𝑒 𝑠l = ��/� �n��%

L/&

4. Finite Population Correction Factor = fpc

= 1/L1/&

where N= population size

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 = 𝑋 ± 𝑧H/l

�L

• CI for normally distributed population with unknown variance = 𝑋 ± 𝑧H/l

FL

where S = sample S.D. 7. Student’s t distribution

µ = 𝑋 ± 𝑡H/lFL

8. Z-ratio = n

Xzσ

µ−=

9. t-ratio = ns

Xt µ−=

Reading 11: Hypothesis Testing 1. Test Statistic =

𝑺𝒂𝒎𝒑𝒍𝒆𝑺𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 / 𝑯𝒚𝒑𝒐𝒕𝒉𝒆𝒔𝒊𝒛𝒆𝒅𝑽𝒂𝒍𝒖𝒆𝒐𝒇𝒑𝒐𝒑𝒑𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓𝒔𝒕𝒂𝒏𝒅𝒂𝒓𝒅𝒆𝒓𝒓𝒐𝒓𝒐𝒇𝒔𝒂𝒎𝒑𝒍𝒆𝒔𝒕𝒂𝒕𝒊𝒔𝒕𝒊𝒄 ∗

*when Pop S.D is unknown, the standard error of sample statistic is given by 𝑆� = FL

*when Pop S.D is known, the standard error of sample statistic is given by 𝜎� = �L

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

3. 𝑧 = �/�gÌn

(when sample size is large or

small but pop S.D is known)

4. 𝑧 = �/�g-n

(when sample size is large but

pop S.D is unknown where s is sample S.D)

5. 𝑡L/& = �/�g-n

(when sample size is large or

small and pop S.D is unknown and popsampled is normally or approximately normally distributed)

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

means (normally distributed, pop var unknown but assumed equal)

t = �%/�� / �%/��ÍÎ�

n%'ÍÎ�

n�

%/� where 𝑆Sl = pooled

estimator of common variance = L%/& F%�' L�/& F��

L%' L�/l where 𝑑𝑓 = 𝑛& + 𝑛l −

2.

7. Test Statistic for a test of diff b/w two pop means (normally distributed, unequal and unknown pop var)


t = �%/�� / �%/��

Í%�

n%'Í��

n�

%/� In this df calculated as

𝑑𝑓 = Í%�

n% 'Í�

�

n�

�

Í%�

n%

�

n%'

Í��

n�

�

n�

8. Test Statistic for a test of mean differences

(normally distributed populations, unknown population variances)

• 𝑡 = J/�ÏgFJ

• sample mean difference = 𝑑 = &L

𝑑MLM\&

• sample variance = 𝑆Jl = J�/J �n

��%L/&

• sample S.D = 𝑆Jl • sample error of the sample mean

difference = 𝑠J = FÏL

8. Chi Square Test Statistic (for test

concerning the value of a normal

population’s variance) χ l = L/& 7�

�g�

where 𝑛 − 1 = 𝑑𝑓 𝑎𝑛𝑑 𝑠l =

𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 = ��/� �n��%

L/&

9. Chi Square Confidence Interval for

variance

Lower limit = L = L/& F�

χÐ/�

� and Upper limit

= U = L/& F�

χ%ÑÐ/�

�

10. F-test (test concerning differences between

variances of two normally distributed

populations) F = F%�

F��

𝑆&l = 1𝑠𝑡 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟 𝑤𝑖𝑡ℎ 𝑛& 𝑜𝑏𝑠 & 𝑆&l

= 2𝑛𝑑 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑟 𝑤𝑖𝑡ℎ 𝑛l 𝑜𝑏𝑠 𝑑𝑓& = 𝑛& − 1 𝑛𝑢𝑚𝑒𝑟𝑎𝑡𝑜𝑟 𝑑𝑓 𝑑𝑓l = 𝑛l − 1 𝑑𝑒𝑛𝑜𝑚𝑖𝑛𝑎𝑡𝑜𝑟 𝑑𝑓

11. Relation between chi-square and F-

distribution = 𝐹 = �%� .�� L

where:

• 𝑋&l is one chi-square random variable with one m degrees of freedom

• 𝑋ll is another chi-square random variable with one n degrees of freedom

12. Spearman Rank Correlation = 𝑟7

= 1 −6 𝑑MlL

M\&

𝑛 𝑛l − 1

• For small samples rejection points for the test based on 𝑟7are found using table.

• For large sample size (e.g. n>30) t-test can be used to test the hypothesis i.e.

𝑡 = 𝑛 − 2 &/l𝑟71 − 𝑟7l &/l

Reading 12: Technical Analysis 1. Relative Strength Analysis =

𝑷𝒓𝒊𝒄𝒆𝒐𝒇𝒂𝒔𝒔𝒆𝒕𝑷𝒓𝒊𝒄𝒆𝒐𝒇𝒕𝒉𝒆𝑩𝒆𝒏𝒄𝒉𝒎𝒂𝒓𝒌𝑨𝒔𝒔𝒆𝒕

2. Price Target for the

• Head and Shoulders = Neckline – (Head – Neckline)

• Inverse Head and Shoulders = Neckline + (Neckline– Head)

3. Simple Moving Average = 𝑷𝟏'𝑷𝟐'𝑷𝟑….'𝑷𝒏

𝑵

4. Momentum Oscillator (or Rate of Change

Oscillator ROC):

• Momentum Oscillator Value M = (V-Vx) ×100 (where V = most recent closing price and Vx = closing price x days ago)

• Alternate Method to calculate M = ""Ü×100

5. Relative Strength Index = RSI = 100 −

&dd&'NF

where

RS = ÝS byHLUI7 JT(MLU bOL7MJI(IJ SI(MOJ hO�L byHLUI7 JT(MLU bOL7MJI(IJ SI(MOJ

6. Stochastic Oscillator (composed of two

lines - %K and %D):


• %𝐾 = 100 R/B&�

{&�/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) = 𝑽𝒐𝒍𝒖𝒎𝒆𝒐𝒇𝑷𝒖𝒕𝑶𝒑𝒕𝒊𝒐𝒏𝒔𝑻𝒓𝒂𝒅𝒆𝒅𝑽𝒐𝒍𝒖𝒎𝒆𝒐𝒇𝑪𝒂𝒍𝒍𝑶𝒑𝒕𝒊𝒐𝒏𝒔𝑻𝒓𝒂𝒅𝒆𝒅

8. Short Interest Ratio (Type of Sentiment

Indicators) = 𝑺𝒉𝒐𝒓𝒕𝑰𝒏𝒕𝒆𝒓𝒆𝒔𝒕𝑨𝒗𝒆𝒓𝒂𝒈𝒆𝑫𝒂𝒊𝒍𝒚𝑻𝒓𝒂𝒅𝒊𝒏𝒈𝑽𝒐𝒍𝒖𝒎𝒆

9. Arms Index or TRIN i.e. Trading Index

(Type of Flow of funds Indicator) = 𝐴𝑟𝑚 𝐼𝑛𝑑𝑒𝑥 𝑜𝑟 𝑇𝑅𝐼𝑁 = 1O.OQ KJ�HL f77TI7 ÷1O.OQ hIbxML f77TI7"OxT.I OQ KJ�HL f77TI7÷"OxT.I OQ hIbxML f77TI7

Reading 13: Demand & Supply Analysis: Introduction 1. Slope of the demand curve =

∆ éê ëìéíî∆ éê ïðñêòéòó ôîõñêöîö

2. Slope of the supply curve =

∆ éê ëìéíî∆ 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) = ½ (Base × Height) = ½ [Qd × (Price intercept – P1)]

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) = ½ (Base × Height) = ½ {(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 to buyers –

Total variable cost 7. Society Welfare =Consumer surplus +

Producer surplus 8. Own-Price Elasticity of Demand =

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛

ΔΔ

=ΔΔ

=xdx

x

xd

x

xd

pd

QP

PQ

PQE x %

%

9. Arc Elasticity of Demand = % ∆ éê ïðñêòéòó ôîõñêöîö

% ∆ éê ëìéíî

)(

)(P%Q%

2121

12

2121

12

PPPPQQQQ

+−+−

=Δ

Δ

10. Income Elasticity of Demand =

% ∆ éê ïðñêòéòó ôîõñêöîö% ∆ éê úêíûõî

=

II

QQxdxd

x

Δ

Δ

=ΔΔI%Q% d

11. Cross Elasticity =

% ∆éê ïðñêòéòó ôîõñêöîö ûü ýûûö þ% ∆ éê ëìéíî ûü ýûûö ÿ

Reading 14: Demand & Supply Analysis: Consumer Demand 1. Marginal Utility = ∆ éê !ûòñù "òéùéòó

∆ éê ïðñêòéòó #ûê$ðõîö

2. Equation of Budget Constraint Line = (PX

× QX) + (PY × QY) 3. Slope of Budget Constraint Line = − ë�

ë%,

where X and Y is measured on the horizontal and vertical axis, respectively.


4. Marginal Rate of Substitution = ∆ éê ï%

∆ 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

costs 5. 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 = Σ (Pi × Qi)

9. Average Revenue (AR) = !ûòñù )î*îêðî

ïðñêòéòó

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

∆ 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$òïðñêòéòó ëìûöðíîö

= Avg. Fixed Cost + Avg.

Variable Cost 14. Marginal cost (MC) = ∆ éê !ûòñù #û$ò

∆ éê ïðñêòéòó ëìûöðíîö

15. Marginal Variable Cost =

∆ éê !ûòñù +ñìéñ,ùî #û$ò∆ éê ïðñêòéòó ëìûöðíîö

16. Marginal revenue (in perfect competition)

= Avg. Revenue = Price regardless of 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 è Output level where Price = Average Revenue = Marginal Revenue = Average Total Cost è 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 revenueè 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 AND when Price = Marginal Revenue while losses are < fixed costs è firm will continue operating.

23. Losses are incurred when there are

Operating losses (Total Revenue < Variable Cost) AND when losses= fixed costs è firm will shut down.

24. Average Product = !ûòñù ëìûöðíò

ïðñêòéòó ûü -ñ,ûì

25. Marginal Product = ∆ éê !ûòñù ëìûöðíò

∆ éê ïðñêéòó ûü -ñ,ûì =

∆ éê !ûòñù .ðòøðò∆ éê /û ûü 0ûì1îì$


26. Least-cost optimization Rule:

&ñì'éêñù ëìûöðíò ûü -ñ,ûì ëìéíî ûü -ñ,ûì

=

&ñì'éêñù ëìûöðíò ûü ë2ó$éíñù #ñøéòñùëìéíî 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 = Value of the input to firm =

∆ éê !ûòñù )î*îêðî∆ 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 regardless of level of Demand

2. Marginal Revenue = Price × 1 −

&ëìéíî 7ùñ$òéíéòó ûü ôîõñêö

3. Concentration Ratio = ÷ðõ ûü $ñùî$ *ñùðî$ ûü ò2î ùñì'î$ò / üéìõ$

!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 ýôë ×100

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 – Investment) – 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. % ∆ in unit labor cost = % ∆ in nominal

wages - % ∆ in productivity 25. Economic growth = Annual % ∆ in real

GDP 26. Total Factor Productivity growth = Growth

in 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 =

"HxTI OQ GyI RO.7T.SGMOL zH7|IG HG G�"HxTI OQ GyI ROL7T.SGMOL zH7|IG HG G%

×100

Inflation Rate = ëìéíî úêöî9 ñò òéõî ò�&dd

− 1

2. Fisher Index = 𝐼𝑝 ×𝐼𝐿 (where, IL =

Laspeyres index and Ip = Paasche Index) 3. 𝑈𝑛𝑖𝑡 𝑙𝑎𝑏𝑜𝑟 𝑐𝑜𝑠𝑡 (𝑈𝐿𝐶) 𝑖𝑛𝑑𝑖𝑐𝑎𝑡𝑜𝑟 =

!ûòñù ùñ,ûì íûõøîê$ñòéûê øîì 2ûðì øîì <ûì1îì.ðòøðò øîì 2ûðì øîì <ûì1îì

4. Velocity of money = /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= notes and coins in circulation + other very highly liquid deposits

4. Broad money = M2 = M1 + entire range of

liquid assets available to make purchases 5. M3 = M2 + other liquid assets 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 = National Income – Net taxes = (1 – t) National 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 = &

&/)$R &/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 in consumption

11. Cumulative multiplier =

íðõðùñòé*î îüüîíò ûê ìîñù ýôë û*îì ò2î ò<û óîñì$% OQ Dh$

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 - Sp =Y+R-T-Sp And, CA = Sp- I+ Govt surplus (or Govt saving) = Sp- I+ (T- G- R) Restated differently, Sp + Sg = I + CA where, Sg = Govt savings Sp = I + CA – Sg

• Current Account Imbalance CA = Sp + Sg – I

Reading 21: Currency Exchange Rates 1. Foreign price level in domestic currency =

Sö/ü×Pü 2. Real exchange rate(ô/ü) = (Sö ü×Pü)/Pö =

Sö ü×(Pü/Pö) 3. Real Exchange Rate öûõî$òéí/üûìîé'ê =

Sö/ü×#ëúR#ëúS

4. Change in Real Exchange rate =

1 +∆÷S/R÷S/R

×&'

∆URUR

&'∆USUS

− 1

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$

&d,ddd

8. Forward premium/discount (in %) =

$øûò þ/ìñòî'(üûì<ñìö øûéêò$/&d,ddd)$øûò þ/ìñòî

− 1

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:

• 1 + 𝑖J = 𝑆³Ï1 + 𝑖Q

&!³Ï

• In case of indirect quote, Arbitrage relationship is: 1 + 𝑖J =1/𝑆Q/J 1 + 𝑖Q 𝐹Q/J

• 𝐹³Ï= 𝑆³

Ï

&'M³&'MÏ

• Forward rate as a % of spot rate = !³/ÏF³/Ï

=&'M³&'MÏ


11. Return on hedged foreign investment

(with a quoted forward rate) = 𝑆Q/J 1 +

𝑖Q&

!³/Ï

12. Expected % change in the spot rate =

F[_%F[− 1 = %∆𝑆G'& =

M³/MÏ&'MÏ

• Forward points: 𝐹Q/J − 𝑆Q/J =

𝑆Q/JM³/MÏ&'MÏX

𝜏 (where 𝜏 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 = Ԑ = % í2ñê'î éê Cðñêòéòó% í2ñê'î éê øìéíî

= –% ∆ ï% ∆ ë

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

Q • % ∆ in expenditure = % ∆ R = % ∆ P

+ % ∆ Q = (1- Ԑ) % ∆ P 16. Basic idea of Marshall-Lerner condition =

𝜔�𝜀� + 𝜔) 𝜀) − 1 > 0 where, ɷx=share of exports ԐX=price elasticity of foreign demand for domestic country exports

ɷM=share of imports ԐM =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 + non-operating

income – 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 under IFRS, Revenue= Contract costs incurred under US GAAP, no revenue reported until contract is complete

4. Revenue recognized under installment

method = ëìûüéò ÷ñùî$

× 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 +ñùðî7$òéõñòîö "$îüðù -éüî


9. Annual Depreciation Expense (Declining

balance method) = &dd%"$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 úêíûõî0'2ò 8*' /û ûü $2ñìî$ û/$'/î< íûõõûê $2ñìî$ ò2ñò

<ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê

12. Diluted EPS for convertible debt =

/îò úêíûõî '8! M ûêíûê*îìòé,ùî öî,ò/ëìîüîìì ôé*

0'2ò 8*' êû ûü $2ñìî$ û/$'8ööéòéûêñù íûõõûê $2ñìî$ ò2ñò <ûðùö 2ñ*î ,îîê é$$ðîö ñò íûê*îì$éûê

13. Diluted EPS using Treasury Stock Method

= (Net Income − Preferred dividends)

[Wght Avg No. of shares +(New shares at option exercise −

Shares purchased with Cash received upon exercise ) ×

(Proportion of Yr)]

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 8/#

ýìû$$ ñõûðêò ûü 8/# )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 = dñùñêíî $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$#ðììîêò -éñ,éùéòéî$

12. Cash ratio = #ñ$2'&ñì1îòñ,ùî $îíðìéòéî$ #ðììîêò -éñ,éùéòéî$

13. Long-term debt-to-equity =

!ûòñù ùûê'/òîìõ öî,ò!ûòñù 7Cðéòó

14. Debt-to-Equity = !ûòñù ôî,ò

!ûòñù 7Cðéòó

15. Total Debt = !ûòñù ôî,ò

!ûòñù 8$$îò$

16. Financial Leverage = !ûòñù 8$$îò$

!ûòñù 7Cðéòó

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

15. Accumulated Dep on equipment sold =

Beg. balance accumulated dep + Dep expense – End. balance accumulated dep

16. Cash received from sale of equipment =

Historical cost of equipment sold – Accumulated dep on equipment sold + gain on sale of equipment

17. Dividends paid = Beg balance of R.E +

Net income – End balance of R.E 18. FCFF = Net income + Non-cash charges +

Interest expense (1 – tax rate) – Cap exp – WC expenditures

19. FCFF = CFO + Interest expense (1 – Tax

rate) – Cap exp 20. FCFE = CFO – Cap exp + Net borrowing 21. CF to revenue = #V.

/îò )î*îêðî

22. Cash ROA = #V.

8*îìñ'î !ûòñù 8$$îò$

23. Cash ROE = #V.

8*îìñ'î $2ñìî2ûùöîì$eîCðéòó

24. Cash to income = #V.

.øîìñòéê' éêíûõî

25. Cash flow per share =

#V./ëìîüîììîö ôé*éöîêö$/û ûü íûõõûê $2ñìî$ û/$

26. Debt Coverage = #V.

!ûòñù ôî,ò

27. Interest Coverage = #V.'úêòîìî$ò øñéö'!ñ9î$ øñéö

úêòîìî$ò øñéö

28. Reinvestment = #V.#ñ$2 øñéö üûì ùûê'/òîìõ ñ$$îò$

29. Debt payment =

#V.#ñ$2 øñéö üûì -! öî,ò ìîøñóõîêò

30. Dividend payment = #V.

ôé*éöîêö$ øñéö

31. Investing and Financing =

#V. #ñ$2 ûðòüùû<$ üûì éê*î$òéê' ñêö üéêñêíéê' ñíòé*éòéî$

Reading 28: Financial Analysis Techniques 1. Compound Growth Rate =

7êö +ñùðîdî' +ñùðî

%fg gR hijkgSl − 1

2. Combined ratio = -û$$î$ ñêö 79øîê$î$

/îò ëìîõéðõö 7ñìêîö

3. Operating ROA = .øîìñòéê' úêíûõî

8*' !ûòñù 8$$îò$


4. ROA = /îò úêíûõî

8*' !ûòñù 8$$îò$ or

ROA = /îò úêíûõî'úêòîìî$ò 79øîê$î &/!ñ9 ìñòî

8*' !ûòñù 8$$îò$

5. Effective Tax Rate = úêíûõî !ñ9

7ñìêéê'$ ,îüûìî !ñ9

6. Vertical common size income statement =

úêíûõî $òñòîõîêò úòîõ)î*îêðî

7. Horizontal common size balance sheet =

dñùñêíî $2îîò éòîõ éê ÿîñì ldñùñêíî $2îîò éòîõ éê ÿîñì &

8. Inventory turnover =

#û$ò ûü $ñùî$ ûì íû$ò ûü 'ûûö$ $ûùö8*' úê*îêòûìó

9. Days of Inventory on Hand (DOH) =

/û ûü ôñó$ éê øîìéûöúê*îêòûìó !ðìêû*îì

10. Receivables Turnover = )î*îêðî

8*' )îíîé*ñ,ùî$

11. Days of Sales Outstanding (DSO)

= /û ûü ôñó$ éê ëîìéûö)îíîé*ñ,ùî$ òðìêû*îì

12. Avg A/c Receivable Balance = Avg Days’

Credit Sales × DSO or Avg A/c Receivable Balance =

÷ñùî$)îíîé*ñ,ùî$ !ðìêû*îì

= ÷ñùî$mnopqr

13. Payables turnover = ëðìí2ñî$

8*' òìñöî øñóñ,ùî$

14. No of Days of Payables = /û ûü ôñó$ éê øîìéûö

ëñóñ,ùî$ !ðìêû*îì

15. WC Turnover = )î*îêðî

8*' 0#

16. Fixed Asset Turnover = )î*îêðî

8*' /îò Vé9îö 8$$îò$

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 =

7dú!÷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' úêíûõî8*' .øîìñòéê' úêíûõî

23. Coefficient of Variation of Net Income =

÷.ô ûü /îò úêíûõî8*' /îò úêíûõî

24. Coefficient of Variation of Revenues =

÷.ô ûü )î*îêðî8*' )î*îêðî

25. Monetary Reserve Requirement (Cash

Reserve Ratio) = )î$îì*î$ 2îùö ñ$ #îêòìñù dñê1÷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 = 7dú!

ýìû$$ úêòîìî$ò

32. EBITDA Interest Coverage = 7dú!ô8

ýìû$$ úêòîìî$ò

33. FFO Interest Coverage =

VV.'úêòîìî$ò ëñéö/.øîìñòéê' -îñ$î 8ösð$òõîêò$ ýìû$$ úêòîìî$ò

34. Return on Capital = 7dú!

8*' #ñøéòñù =

7dú!8*' (7Cðéòó'/ûê íðììîêò öîüîììîö òñ9î$'öî,ò)


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

7dú!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 × 7dú!!8

+ 0.6 × &+ ûü $òûí1d+ ûü ùéñ,éùéòéî$

+ 1.0

× ÷ñùî$!8

42. Segment margin = ÷î'õîêò ëìûüéò (-û$$)÷î'õîêò )î*îêðî

43. Segment turnover = ÷î'õîêò )î*îêðî

÷î'õîêò 8$$îò$

44. Segment ROA = ÷î'õîêò ëìûüéò (-û$$)÷î'õîêò 8$$îò$

45. Segment Debt Ratio = ÷î'õîêò -éñ,éùéòéî$÷î'õîêò 8$$îò$

Reading 29: Inventories

1. NRV = Estimated Selling Price – Estimated Costs of completion and disposal

2. Inventory amount net of valuation

allowance = Carrying amount of Inventory – Write downs

3. (NRV – Normal Profit Margin) ≤ MV ≤

NRV Reading 30: Long-Lived Assets 1. Dep Exp under Straight-line Method =

ôîøìîíéñ,ùî #û$ò7$òéõñòîö "$îüðù -éüî

= té$òûìéíñù #û$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 of

liability < Tax base of asset 8. Company’s tax expense (or credit)

reported on its income statement = Income


tax liability currently payable + ∆ in deferred tax asset / liability Where,

• Income Tax liability currently payable = Taxable income × Tax rate

• ∆in 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 × Tax rate

• 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. Initial carrying amount = 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 interest expense under effective

interest rate method = Carrying value of

the bonds at the beginning of the period × Effective interest 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 = dûêö 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 the lease

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 (U.S. GAAP) =

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 = (ûøîìñòéê' #V ,îüûìî 0# í2ñê'î$ – öé*éöîêö$)

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 (êîò ûü ñííðõðùñòîö öîø) 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 íñøéòñùévñòéûê8ösð$òîö d+

14. Tangible B.V = Total stockholders’ equity – Goodwill – Other intangible assets

15. Price to tangible BV ratio = ëìéíî !ñê'é,ùî d+

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$î øñóõîêò$"êöé$íûðêòîö /ûêíðììîêò #ñøéòñù -îñ$î øñóõîêò$

× Undiscounted Noncurrent Operating Lease Payments

*If term structures of capital and operating leases are assumed to be similar 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 =


EBIT ∗ + rent exp ∗∗ −Dep exp ∗∗

𝑖 expense ∗ +𝑖 costs ∗∗

* Unadjusted **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 t1+Req RoR( )t

− IO

3. Avg Accounting RoR (AAR) =

8*' /ú ñüòîì öîø & GH�I7 ,îüûìî éêòîìî$ò8*' d+ ûü úê*$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 = wdrd (1 – t) + wprp + were 2. Debt-to-Equity Ratio conversion into

weight (i.e. Debt / (Debt + Equity) = piz{|}~k{�

&' piz{ |}~k{�

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 (Ri) = RF + βi [E (RM) – RF] 7. Expected Return on Stock I = E (Ri) = RF +

βi1 (Factor risk premium)1 + βi2 (Factor risk premium)2+…..+βij (Factor risk premium)j

8. Cost of Equity = 𝐫𝐞 =

ô%ëg+ g

9. Expected Growth Rate of Dividends

g = (1 - ô7ë÷

) × ROE

g = retention rate × ROE 10. Company’s stock returns = Réò = a +

bRõò 11. Unlevered β of Comparable Company =

β", íûõøñ =��, �g�h�j�z�i

&' &/ò�g�h�j�z�ip�g�h�j�z�i|�g�h�j�z�i

12. Levered β of Project =

𝛽B, S(O� = 𝛽Ý, bO.S 1 + 1 − 𝑡S(O�𝐷S(O�𝐸S(O�

13. 𝛽H77IG =��[�

&' &/G s�

14. 𝛽I~TMGa = 𝛽H77IG 1 + 1 − 𝑡 h�

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 éêöî98êê ÷.ô ûü $û*îìîé'ê ,ûêö &1ò éê òîìõ$ ûü öî*îùûøîö õ1ò íðììîêíó

17. Cost of equity = Ke= RF + β[(E(RM)-RF) +

CRP] 18. Breakpoint =

8õûðêò ûü íñøéòñù ñò <2éí2 $ûðìíîe$ íû$ò ûü íñø ∆ ëìûø ûü êî< íñø ìñé$îö üìûõ ò2î $ûðìíî

19. Cost of Capital when flotation costs are in

monetary terms= rî =ô%ëg/V

+ g

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

price: Cost of Equity = rî =ô%

ëg &/ü+ g

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 β = (Debt β × Proportion of Debt) +

(Equity β × 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 = % ∆ éê .øîìñòéê' úêíûõî 7dú!% ∆ éê "êéò$ ÷ûùö

or DOL= #&

#&/ Vé9îö .øîìñòéê' #û$ò

5. DFL = % ∆ éê /îò úêíûõî

% ∆ éê .øîìñòéê' úêíûõîor

#&/ Vé9îö .ø #û$ò #&/Vé9îö .ø #û$ò$/Vé9îö Véê #û$ò

6. DTL= % ∆ éê /îò úêíûõî

% ∆ 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 = Vé9îö .øîìñòéê' #û$ò$'Vé9îö Véêñêíéñù #û$ò$

ëìéíî øîì ðêéò/+ñìéñ,ùî íû$ò øîì ðêéò

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 Stock Dividend = EPS before

Dividend × ÷2ñìî$ û/$ ,îüûìî ôé*éöîêö÷2ñìî$ û/$ ñüòîì ôé*éöîêö

4. Stock Price after Stock Dividend = Stock

Price before Dividend × EPS after Dividend

5. Total Market Value after Stock Dividend =

Shares outstanding after Dividend × Stock price after Dividend

6. Stock price after 2-for-1 stock split =

÷òûí1 øìéíî ,îüûìî $òûí1 $øùéòl

7. EPS after 2-for-1 stock split =

7ë÷ ,îüûìî $òûí1 $øùéòl

8. DPS after 2-for-1 stock split =

ôë÷ ,îüûìî $òûí1 $øùéòl

9. EPS after buyback =

7ñìêéê'$/8üòîì òñ9 #û$ò ûü Vðêö$÷2ñìî$ .ðò$òñêöéê' ñüòîì dðó,ñí1

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

Dividend per share 11. Market value of Equity after distribution of

cash dividends = [(# ûü $2ñìî$ û/$) × (&+ $2ñìî) – #ñ$2 öé*]

# ûü $2ñìî$ û/$

12. Post-repurchase share price = #ûü $2ñìî$ û/$ × (&+ $2ñìî – <ûìò2 ûü ÷2ñìî ìîøðìí2ñ$î]

( # ûü $2ñìî$ û/$/# ûü $2ñìî$ ìîøðìí2ñ$îö (íñê ,î ìîøðìí2ñ$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$î øìéíîëðìí2ñ$î øìéíî

×pqd

/û ûü öñó$ òû õñòðìéòó

4. Bond Equivalent Yield =

Vñíî *ñùðî/ëðìí2ñ$î øìéíîëðìí2ñ$î øìéíî

×pqv



5. Discount-basis Yield =

Vñíî *ñùðî/ëðìí2ñ$î øìéíîVñíî +ñùðî

×pqd


6. Wght Avg collection period = wghts ×

Avg no of days to collect accounts within each age category Where, Weights = % of total receivables in each category

7. Float Factor = 8*' ôñéùó Vùûñò8*' ôñéùó ôîøû$éò

= 8*' ôñéùó Vùûñò

�g{�� g~�{ gR ��i��l pihglk{iSfg gR p��l

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 = 1 +

ôé$íûðêò&/ôé$íûðêò

mno� − 1

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$ò'ôîñùîìe$ íûõõé$$éûê'dñí1ðø 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 =

(*ñùðî ûü îñí2 ,ûêö éê ò2î øûìòüûùéû)/û ûü $2ñìî$

2. New Shares that need to be created =

8õûðêò òû ,î úê*î$òîö éê ò2î Vðêö/8+ øîì $2ñìî ûì !ûòñù *ñùðî øîì $2ñìî ûü ñ &ðòðñù Vðêö

3. New NAV of the Fund = NAV or Total

value of a Mutual Fund + Amount to be invested in the Fund

4. No of shares need to be retired =

8õûðêò òû ,î <éò2öìñ<ê üìûõ ò2î Vðêö/8+ øîì $2ñìî ûì !ûòñù *ñùðî øîì $2ñìî ûü ñ &ðòðñù Vðêö

Reading 42: Portfolio Risk & Return: Part I 1. Total Return = Capital Gain (or Loss) +

Dividend Yield 2. Capital Gain = ë{/ë{Ñ%

ë{Ñ%

3. Dividend Yield = ô{ë{Ñ%

4. 3-Yr HPR = [(1 + R1) × (1 + R2) × (1 +

R3)]– 1 5. Arithmetic mean (AM) R = 𝑅M =

N�%'N��'⋯'N�.�Ñ%'N��*

= &*

𝑅MG*G\&

6. Geometric R for n periods = RDM =

1 + 𝑅& 1 + 𝑅l … 1 + 𝑅L&* − 1

7. IRR = #V ñò !éõî ò

&'ú)) { = 0!ò\d

8. Annualized 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) =(&'/ûõéêñù ))

(&'úêü)

16. Var of a Single Asset = 𝜎l = N[/� ��%

*

17. Sample Variance = sl = ){/) ��{�%

!/&

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

ρij× σi × σj

19. Portfolio Var = σël = w&lσ&l + wllσll +

2w&wlCov R&,Rl = w&lσ&l + wllσll +

2w&wlρ&lσ&σl 20. Portfolio S.D. = Portfolio Variance 21. Correlation of Return b/w two assets =

#û*ñìéñêíî ûü )îòðìê ,/< ò<û ñ$$îò$÷.ô.ûü ñ$$îò & × ÷.ô.ûü ñ$$îò l

22. 1 + Expected Return =1 + E R =

1 + rìü × 1 + E π × 1 + E RP 23. Utility of an Invest = Expected Return -

&l×Risk Aversion Coefficient ×

Var of Invest

24. Expected R of Portfolio = E Rø = w&Rü +

1 − w& E Ré 25. Risk of Portfolio = σøl = w&lσül +

(1 − w&)lσél + 2w& 1 − w& ρ&lσüσé =1 − w& lσél&σp = (1 – w1) σi,

Where σü = S.D. of risk − free asset 26. Capital Allocation Line (CAL) = E Rë =

Rü +7 )k /)R

�kσë

27. In portfolio of many risky assets =

• E Rø = ωéE Ré/é\&

• σël =��

/+ (//&)

/Cov

• σë =��

/+ (//&)

/ρσl

28. New Asset should be included in the Portf

only if 7 )�i /)R��i

> 7 )h /)R�h

×ρêî<,ø

Reading 43: Portfolio Risk & Return: Part II 1. Total Risk = Systematic risk +

Nonsystematic risk = β2i σ2m + σ2e 2. Total risk of for a well-diversified portfolio

= Systematic risk = βi×σm 3. Multi-Factor Model: 𝐸 𝑅M − 𝑅Q =

βM�𝐸(𝐹�)|�\& = βMù 𝐸 𝑅. − 𝑅Q +

βM�𝐸(𝐹�)|�\l

4. Single-Index Model (based on realized

returns): Ri – Rf = βi(Rm – Rf) + ei 5. Factor weight associated with each factor =

!ûòñù ÷îíðìéòó )é$1!ûòñù &ñì1îò )é$1

6. 𝐸 𝑅S = 𝑅Q + 𝛽S 𝐸 𝑅. − 𝑅Q =

= Rü + w&β& + wlβl E Rõ − Rü

7. Asset’s Beta = #ûììîùñòéûê ,îò<îîê ñ$$îò ñêö õñì1îò ×÷.ô.ûü 8$$îò

÷.ô.ûü &ñì1îò

8. Portfolio Beta = βø =wéβé; wé

êé\&

êé\& = 1

9. Sharpe Ratio = )h/)R�h

10. Treynor Ratio = NÎ/N³�Î

11. Ml = R$ − RQ�c�Î− 𝑅. − 𝑅Q

12. Jansen’s Alpha = 𝛼S = 𝑅S −

𝑅Q + 𝛽S 𝑅. − 𝑅Q 13. Security Characteristic Line (SCL) = Ré −

Rü = αé + βé Rõ − Rü 14. Weight in Nonmarket security should be

proportional to 8ùø2ñ ûü ÷îíðìéòó é

/ûê$ó$òîõñòéí *ñìéñêíî ûü ÷îíðìéòó é = αi / σ2

ei


15. Total Weight of Nonmarket securities in

portfolio should be proportional to = ��¥�

#��%

��

�#��%

16. Information Ratio =

8ùø2ñ ûü ÷îíðìéòó é/ûê$ó$òîõñòéí )é$1 ûü ÷îíðìéòó é

17. Expected Return of Portfolio (under

Arbitrage Pricing Model) = E Rø = RV +λùβø,ú + ⋯+ λ1βø,1

18. Return on an Asset in excess of 1-Month

T-Bill Return (under four factor model) = E Réò = αé + βé,&§!MKTò +βé,÷&dSMBò + βé,t&-HMLò + βé,"&ôUMDò

Reading 44: Basics of Portfolio Planning & Construction 1. Investor’s Expected Utility from Portfolio

= Up = E (Rp) – λσ2p

2. Tactical Asset Allocation (TAA) Return

contribution = Actual return of the portfolio – Return that would have been earned if the asset class weights were equal to the policy weights

Reading 45: Market Organization & Structure 1. Total return to a Leveraged Stock Purchase

= )îõñéêéê' 7Cðéòó/ú. ú.

where,

Remaining Equity = IO – Purchase commission + (-) Trading g(l) – Margin i paid + Div received – Sales commission paid

OR 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): Initial margin $ + (P − Initial Stock Price)

P= Maintenance Margin Requirement (%) 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 (%) = (ýìû$$ 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 = &dd%

% ûü 7Cðéòó

7. Max leverage ratio for position financed by min margin requirement =

&&éê õñì'éê ìîCðéìîõîêò

Reading 46: Security Market Indices 1. Value of a price return index =

VPRI = D

PnN

iii∑

=1

For Single Period:

2. % Change in value of Price return index

Portfolio = PR I = 0

01

PRI

PRIPRI

VVV −

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

= 0

01

i

ii

PPP −

4. Price return of the index: PR I =

∑=

⎟⎟⎠

⎞⎜⎜⎝

⎛ −N

i i

iii P

PPw1 0

01


5. Total return of Index Portfolio:

0

01

PRI

IPRIPRI

VIncVV +−

6. Total return of each security = TRi =

i

iii

PIncPP

0

01 +−

∑=

⎟⎟⎠

⎞⎜⎜⎝

⎛ +−=

N

i i

iiii P

IncPPwturnTotal1 0

01Re

Over Multiple Time Periods: 7. Value of Price Return index at time t =

VPRIT = VPRI0 (1 + PRI1) (1 + PRI2) … (1 + PRIT)

8. Value of Total Return index at time t =

VTRIT = V TRI0 (1 + TRI1) (1 + TRI2) … (1 + TRIT)

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 =

/d ûü $2ñìî$ û/$ ûü ÷é × ÷2ñìî øìéíî ûü ÷é/û ûü $2ñìî$ û/$ ûü ÷é × ÷2ñìî øìéíî ûü ÷éf

®�%

Where Si = Security i

12. Weight of Si under Float-Adjusted Mkt Cap weighting =

Vìñíòéûê ûü $2ñìî$ û/$ õ1ò üùûñò × ûü $2ñìî$ ÷é ×÷2ñìî øìéíî ûü $îíðìéòó é

(Vìñíòéûê ûü $2ñìî$ û/$ &1ò üùûñò × ûü $2ñìî$ û/$ ûü ÷é ×÷2ñìî øìéíî ûü $îíðìéòó é)

13. Fundamental weight on security i =

Vðêöñõîêòñù $évî õîñ$ðìî ûü íûõøñêó é∗(Vðêöñõîêòñù $évî õîñ$ðìî ûü íûõøñêó é)f

®�%

*Book value, cash flow, revenues, earnings, dividends, & number of employees. Reading 47:Market Efficiency Reading 48: Overview of equity Securities 1. Equity security’s Total Return =

÷ñùî ë ûü ñ $2ñìî/ëðì2ñ$î ë ûü ñ $2ñìî'íñ$2/$òûí1 ôé*ëðìí2ñ$î øìéíî ûü ñ $2ñìî

2. ROE in yr t =

/ú (üûì .ìöéêñìó ÷2ñìî2ûùöîì$) éê óì ò8*' !ûòñù d+ ûü 7Cðéòó

OR

ROE = /ú (üûì .ìöéêñìó ÷2ñìî2ûùöîì$) éê óì ò÷2ñìî2ûùöîì$eîCðéòó ñò ,î' ûü óì ò

3. MV of equity = Mkt price per share ×

Shares O/s

4. BV of equity per share = !ûòñù ÷te$ îCðéòó

÷2ñìî$ û/$

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

d+ ûü îCðéòó øîì $2ñìî

6. ROE = Net profit margin × Asset turnover

× Financial leverage = /îò îñìêéê'$/îò $ñùî$

×/îò $ñùî$

8*' òûòñù ñ$$îò$× 8*' òûòñù ñ$$îò$

8*' íûõõûê îCðéòó

Reading 49: Introduction to Industry & Company Analysis Reading 50: Equity Valuation: Concepts & Basic Tools 1. Value of a share of stock today =

79øîíòîö öé*éöîêö éê óì ò(&'ìîCðéìîö ).) ûê $òûí1){

¯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(&'ìîC )û) ûê $òûí1)%

3. Value of a share of stock for n holding

periods or investment horizon = 79øîíòîö ôé* éê óì ò&'ìîC ) ûê $òûí1 { +

LG\&

79øîíòîö øìéíî éê ê øîìéûö$&'ìîC ) ûê $òûí1 �

4. CFO = NI + Non-cash exp – Inv 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 {

¯ò\&


7. ReqRoR on sharei = Current expected Rf

rate + Beta i [MRP]

8. Value of a pref stock (non-callable, non-convertible) =

( ) ( )rD

rD

grgD

V 0000 0

011=

−

+=

−

+=

9. Value of a pref stock (non-callable, non-convertible) with maturity at time n =

𝑉d =𝐷d

(1 + 𝑟)G+

L

G\&

𝐹1 + 𝑟 L

Gordon Growth Model: 10. Value of a share of stock =

( )rg

grD

grgD

V <−

=−

+= ,

1 100

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 =

𝑉d =𝐷d 1 + 𝑔7 G

(1 + 𝑟)G+

𝑉L(1 + 𝑟)L

L

G\&

𝑉L =𝐷L'&𝑟 − 𝑔B

𝐷L'& = 𝐷d(1 + 𝑔7)L 1 + 𝑔B 13. Justified P/E = ëd

7& = ô%/7%

ì/'= ø

ì/'

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

and cash Equivalents

15. Asset-based value = Value of Assets – Value of Liabilities

Reading 51: 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 52: Fixed Income Markets: Issuance, Trading & Funding Reading 53: 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 ×ëñì *ñùðî

&'&ñì1îò öé$íûðêò ìñòî {êò\&

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+ Z1)

1 +PMT(1+ Z2 )

2 +...+PMT +FV(1+ ZN )

N

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

Accrued interest

7. Accrued interest = AI = G* ×𝑃𝑀𝑇

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, given market discount rates for 2 and 5 yrs) =

(Average yield for 2 year bonds) + p/lv/l

×


(average yield for 5 year bonds – average yield for 2 year bonds)

11. 1+ APRmm

!

"#

$

%&m

= 1+ APRnn

!

"#

$

%&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 +DMm

"

#$

%

&'1 +

(I +QM )×FVm

1+ I +DMm

"

#$

%

&'2 +...+

(I +QM )×FVm

+FV

1+ I +DMm

"

#$

%

&'N

14. Price of Money Market Instrument (on a

discount-rate basis) =

PV = FV × 1− DaysYear

×DR#

$%

&

'(

15. Market Discount Rate =

DR = YearDays( )× FV −PV

FV#

$%

&

'(

16. Price of Money Market Instrument (on an

add-on rate basis)=

PV =FV

1+ DaysYr

× AOR"

#$

%

&'

17. Add-on rate =

AOR = YrDays!

"#

$

%&×

FV −PVPV

!

"#

$

%&

Relation b/w two spot rates and Implied Forward Rate: 18. (1 + zA)A × (1 + IFRA,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+ zN + 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 = Yield to maturity of the bond - Standard swap rate in that currency of the same tenor

Reading 54: Introduction to Asset Backed Securities 1. Loan-to-value ratio (LTV) =

ëìûøîìòóe$ øðìí2ñ$î øìéíî8õûðêò ûü &ûìò'ñ'î

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 − (1 − 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 – Total Principal Pmt

• Projected CF for MPS = Net i- pmt + Total principal re-pmt

7. DSC ratio = ëìûøîìòó’$ ñêêðñù /.úôî,ò $îì*éíî


Reading 55: Understanding Fixed Income Risk & Return 1. Interest-on-interest gain from

compounding = 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

dûêö ëìéíî

%n

− 1

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( )

PMT1+ r( )1−t/T

PV Full

"

#

$$$$

%

&

''''

+ 2− t /T( )

PMT1+ r( )2−t/T

PV Full

"

#

$$$$

%

&

''''

+...+ N − t /T( )

PMT +FV1+ r( )N−t/T

PV Full

"

#

$$$$

%

&

''''

(

)**

+**

,

-**

.**

OR

MacDur = 1+ rr

−1+ r + N × c− r( )#$ %&

c× 1+ r( )N −1#$

%&+ r

'

()

*)

+

,)

-)− (t /T )

8. Modified D = &ñíôðì

&'ì

9. Annualized Modified D =

&ûöéüéîö ôðìñòéûêëîìéûöéíéó ûü øñóõîêò éê ñ óîñì

10. % Δ PVFull = - AnnModDur × ΔYield 11. Approx Modified D =

(PV− )− (PV+ )2× (ΔYield)× (PV0 )

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

+ r)

13. Effective D = (PV− )− (PV+ )

2× (ΔCurve)× (PV0 )

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 =

Mod D of Bond 1 × &+ ûü dûêö &!ûòñù &+ûü ëûìòü

+ Mod D of Bond 2 × &+ ûü dûêö l!ûòñù &+ ûü ëûìòü

+

…+ Mod D of Bond N × &+ ûü dûêö /!ûòñù &+ ûü ëûìòü

17. Money D = Annualized Mod D × Full

Bond Price

18. ∆ Full price of Bond (in currency units) ≈ -Money D × ∆ 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) +

&l ×𝐴𝑛𝑛𝐶𝑜𝑛𝑣𝑒𝑥𝑖𝑡𝑦 ×(∆𝑌𝑖𝑒𝑙𝑑)l

23. Approx. Convexity Adjustment =

(PV− )+ (PV+ )−[2× (PV0 )](ΔYield)2 × (PV0 )


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) + [&l ×

MoneyCon × (∆Yield)2] 26. Money Convexity of bond = Annual

Convexity × Full Price 27. Effective Convexity =

PV−( )+ PV+( )− 2× (PV0 )[ ]#$ %&

ΔCurve( )2 × PV0 )( )

28. Duration Gap = Bond’s Macaulay

Duration – Investment Horizon Reading 56: Fundamentals of Credit Analysis 1. Expected Loss = Default Probability ×

Loss Severity given Default 2. Funds From Operations = NI +Dep +

Amor+ Deferred income taxes noncash items Where NI = Net Income

3. FCF Before Div = NI – Cap exp. – (+) Inc (dec) in Non-cash WC – Non-recurring items

4. FCF After Div = FCF Before Div – Div 5. Operating Profit Margin = .øîìñòéê' úêíûõî

)î*îêðî

6. EBITDA = Operating Income + Dep +

Amort 7. FCF = CFO – Cap exp– Div 8. Capital expenditures = Additions to P&E +

Additions to product rights & intangibles – Proceeds of sale of P&E

9. Total debt = ST debt + Current portion of

LT debt + LT debt 10. Capital = Debt + Equity 11. Yield on Corp Bond = Real Rf rate +

Expected Inf rate + Maturity P + Liquidity P+ Credit spread

12. Yield spread = Liquidity P + Credit spread 13. Return impact for smaller spread ∆≈ % ∆

in price ≈ -Modified Duration × ∆Spread 14. Return impact for larger spread ∆ ≈ % ∆ in

price ≈ - (Modified D × ∆Spread) + &lConvexity × (∆Spread)2

15. Secured debt leverage = !ûòñù $îíðìîö öî,ò

7dú!ô8

16. Senior unsecured leverage =

÷îíðìîö öî,ò'÷îêéûì ðê$îíðìîö öî,ò7dú!ô8

17. Total Leverage = !ûòñù öî,ò7dú!ô8

18. Net Leverage = !ûòñù öî,ò/#ñ$2

7dú!ô8

Reading 57: 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 = pT = 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 × 1 + 𝑖 𝑟𝑎𝑡𝑒 % G

Reading 58: Basics of Derivative Pricing & Valuation 1. Pricing of risky assets = S0 = 7 (÷!)

&'ì'³ �

2. Commodity = F 0, T = S0 e (r – δ)T where, δ = Convenience yield − Cost of carry

3. S0 = 7 (÷�)

&'ì'´ � – θ + γ

where, θ (theta) = Present value of the costs and γ (gamma) = Present value of benefits

4. Arbitrage and Derivatives = Underlying

asset + Opposite position in derivative = Underlying payoff – Derivative payoff = Rf return

5. Pricing and Valuation of Forward

Contracts:

• At Expiration F0 ( T) = S0 (1 + r) T or S0 = F0 (T) / (1 + r) T

• Value of forward (long) during contract life (where t < T) = Vt (T) = St – F0 (T) / (1 + r)(T – t)

• Value of forward (short) during contract life (where t < T ) = Vt (T) = F0 (T) / (1 + r) (T – t) - St

• Value of forward (long) at expiration (where t = T) = VT (T) = ST - F0 (T)

• Value of forward (long) at initiation (where t = 0) = Vt (0, T) = S0 – F0 (T) / (1 + r) T = 0

• Forward price of an asset with benefits and/or costs = (S0 – γ + θ) (1 + r) T = S0 (1 + r) T – (γ - θ) (1+ r) T

• Value of Forward contract with benefits and/or costs during the life of the contract = St – (γ - θ) (1 + r) t - F0 (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 270-day Euro$ T.D and short position in a 90-day Euro$ T.D

• For synthetic forward position in a 90-day zero-coupon that begins in 30 days (buy 120-day & sell 30-day zero coupon bonds)

7. 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

8. 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

9. Max Profit/Loss for Option writer/holder: • Max profit of option seller/writer è

Option premium. • Max loss of option seller/writer è

unlimited in case of calls; large in case of puts (bounded by zero).

• Max loss of option holder èOption premium

Put-Call Parity 10. 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.


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

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

• Synthetic long position in a call =

TrXSpc)1(000 +

−+=

• Synthetic long position in a put =

p 0= c 0−S 0+X

(1+ r)T

• Synthetic long position in an

underlying = S0 = c 0+X

(1+ r)T− p0

• Synthetic long position in a riskless

bond = X

(1+ r)T= p 0+S0 − c0

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

+ p0 = c0 + X/(1 + r) T 14. Valuing a callable bond using Binomial

Model:

• 0

1

0

1 ,SSd

SSu

−+

==

• Value at time 0 = V0 = hS0 − 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 59: Risk Management Applications of Option Strategies 1. For Call Option Buyer

• cT = max (0, ST –X) • When ST ≤ X àcT = 0 • When ST> X àcT = ST – X • Value at expiration = cT • Profit = cT – c0 • Maximum profit = ∞è no upper limit • Maximum loss = c0

• Breakeven = ST* = X + c0 2. For Call Option Seller

• cT = max (0, ST –X) • When ST ≤ X àcT = 0 • When ST> X àcT = ST –X • Value at expiration = -cT • Profit = –cT+ c0 • Maximum profit = c0 • Maximum loss = ∞è no upper limit • Breakeven = ST* = X +c0

3. For Put Option Buyer

• pT = max (0, X - ST) • When ST< X àpT = X - ST • When ST ≥ X àpT = 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 àpT = X – ST • When ST ≥ X àpT = 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 àVT = ST • When ST> X àVT = 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 àVT = ST + X - ST = X • When ST> X àVT = ST • Profit = VT – S0 - p0 • Maximum Profit = ∞ • Maximum Loss = S0 + p0 – X • Breakeven =ST* = S0 + p0

Reading 60: 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 = 1Vf

RHSMGHxMµHGMOL 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 price with 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

finquiz formula sheet cfa level i 2015 · finquiz formula sheet cfa level i 2015 reading 5: time...

Documents