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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%$g
8. Effective Annual Yield = EAY = 1 +
𝐻𝑃𝑌 pqv/G − 1 (Rule: EAY > BDY) 9. Money Market Yield (or CD equivalent
Yield) rMM:
• rMM = HPY × pqdG
FinQuiz Formula Sheet CFA Level I 2015
• rMM = (rBD) ×
!HbI "HxTI OQ GyI *(IH7T(a zMxx$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
FinQuiz Formula Sheet CFA Level I 2015
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/( !
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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)
FinQuiz Formula Sheet CFA Level I 2015
t = �%/�� / �%/��
Í%�
n%'��
n�
%/� In this df calculated as
𝑑𝑓 = Í%�
n% '�
�
n�
�
Í%�
n%
�
n%'
��
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):
FinQuiz Formula Sheet CFA Level I 2015
• %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$ðõîö
2. Equation of Budget Constraint Line = (PX
× QX) + (PY × QY) 3. Slope of Budget Constraint Line = − ë�
ë%,
where X and Y is measured on the horizontal and vertical axis, respectively.
FinQuiz Formula Sheet CFA Level I 2015
4. Marginal Rate of Substitution = ∆ éê ï%
∆ éê ï�=
&ñì'éêñù "òéùéòó ûü ýûûö þ&ñì'éêñù "òéùéòó ûü ýûûö ÿ
Reading 15: Demand & Supply Analysis: The Firm 1. Profit = Total revenue – Total cost 2. Accounting Profit = Total Revenue –
Explicit Costs(or Accounting costs) 3. Economic Profit
• = Total Revenue – Explicit Costs – Implicit Costs or
• = Accounting Profit – Implicit Costs or
• = Total Revenue – Total Economic Costs
4. Economic costs = Explicit costs + Implicit
costs 5. Normal Profit = Accounting Profit –
Economic Profit 6. Accounting profit = Economic Profit +
Normal Profit 7. Economic rent = (New “Higher” Price
after ↑ in Demand – Previous Price before ↑ in Demand) × QS before ↑ in Demand
8. Total Revenue (TR):
• = Price × Quantity or
• = Sum of individual units sold × Respective prices of individual Units sold = Σ (Pi × Qi)
9. Average Revenue (AR) = !ûòñù )î*îêðî
ïðñêòéòó
10. Marginal Revenue (MR) = ∆ éê !ûòñù )î*îêðî
∆ éê ïðñêòéòó
11. Total Variable Cost = Variable Cost per
unit × Quantity Produced 12. Total Cost = Total Fixed + Total Variable 13. Average total cost (ATC) =
!ûòñù #û$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$
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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$îì*î ìñòéû
3. Narrow money = M1= notes and coins in circulation + other very highly liquid deposits
4. Broad money = M2 = M1 + entire range of
liquid assets available to make purchases 5. M3 = M2 + other liquid assets 6. Quantity Theory of Money = M × V = P ×
Y where, M = Quantity of money V = Velocity of circulation of money P = Average price level Y = Real output
7. Neutral Rate = Trend Growth + Inflation Target
8. Impact of Taxes and Government
Spending: The Fiscal Multiplier The net impact of the government sector on AD: • G – T + B = Budget surplus or Budget
deficit where, G = government spending , T =taxes, B =transfer benefits
• Disposable income = National Income – Net taxes = (1 – t) National Income where, Net taxes = taxes – transfer payments, t = net tax rate
9. Fiscal Multiplier (in the absence of taxes) = 1/(1 - MPC) • MPS = 1 – MPC.
FinQuiz Formula Sheet CFA Level I 2015
• Total increase in income and spending
= Fiscal multiplier × G 10. Fiscal Multiplier (in the presence of taxes)
• MPC (with taxes) = MPC × (1 - t) • Fiscal multiplier = &
&/)$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
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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$
FinQuiz Formula Sheet CFA Level I 2015
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)
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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 =
FinQuiz Formula Sheet CFA Level I 2015
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 $ûðìíî
19. Cost of Capital when flotation costs are in
monetary terms= rî =ô%ëg/V
+ g
20. When FC are in terms of % of the share
price: Cost of Equity = rî =ô%
ëg &/ü+ g
21. If FC are not tax deductible: NPV = PV of
Cash Inflows – IO – (FC in % × New Equity Capital)
FinQuiz Formula Sheet CFA Level I 2015
22. If FC are tax deductible: NPV = PV of
Cash Inflows – IO – [(FC in % × New Equity Capital) × (1 – Marginal Tax Rate)]
23. Asset β = (Debt β × Proportion of Debt) +
(Equity β × Proportion of Equity) Reading 37: Measures of Leverage 1. Contribution Margin (CM) = (# of units
sold) × [(price per unit) - (variable cost per unit)]
2. Per unit CM = Price per unit - Variable cost per unit
3. Operating income = CM – Fixed Operating
Costs
4. DOL = % ∆ éê .øîìñòéê' úêíûõî 7dú!% ∆ éê "êéò$ ÷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
/û ûü öñó$ òû õñòðìéòó
FinQuiz Formula Sheet CFA Level I 2015
5. Discount-basis Yield =
Vñíî *ñùðî/ëðìí2ñ$î øìéíîVñíî +ñùðî
×pqd
/û ûü öñó$ òû õñòðìéòó
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
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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\&
FinQuiz Formula Sheet CFA Level I 2015
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
×
FinQuiz Formula Sheet CFA Level I 2015
(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
FinQuiz Formula Sheet CFA Level I 2015
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 )
FinQuiz Formula Sheet CFA Level I 2015
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)
FinQuiz Formula Sheet CFA Level I 2015
• 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.
FinQuiz Formula Sheet CFA Level I 2015
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
FinQuiz Formula Sheet CFA Level I 2015
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