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CFA Level 1, June, 2016 - Formula Sheet

the best cfa® instruction spring 2019

CFA Singapore Research Programme Level 1 2 are accredited *All the information above are extracted from the CFA June 2016 exam candidates survey and are accurate at time of summarises key formulas, definitions, and concepts Sep 27, 2018 Next course

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Description

FinQuiz

Formula Sheet

Reading 5: Time Value of Money

  Interest Rate (i) •   i = Rf + Inf P + Default Risk P + Liquidity P + Maturity P •   Nominal Rf i rate = Real Rf i Rate + Inf P •  

PV (for more than one Compounding

? 1 FV (for more than one Compounding per year) = FVN = 1 +

FV (for Continuous Compounding) = FVN =

Solving for N =

natural log) Stated & Effective Rates •   Periodic i Rate = FGHGIJ  KLL  M  NHGI

PV of Annuity Factor =

HPR = rt =

  HPR =

  IRR (when project’s CFs are perpetuity) = NPV =

  Bank Discount Yield = BDY = rBD = &'( # /&

Reading 6: Discounted Cash Flow Applications 1

  NPV =

TWR (for the year) = rTWR = [(1+R1)× (1+R2)×… (1+R365)]

FVOA ×(1+r)

!Z L'G[& &'( Z

PVOA + PMT •  

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

PV & FV of Annuity Due

1O  OP  QO

ROSLJMLT  $I(MOJ7  ML  ULI  VIH(

Effective (or Equivalent) Ann Rate (EAR = EFF%) = 1 +

  TWR: •   TWR (when no external CF) = rTWR =

Size of Annuity Payment = PMT = &/

PV of Perpetuity =

  MMWR =

EAR (with Continuous Compounding) = EAR =

PV & FV of Ordinary Annuity •  

  PV and FV of CF =

CFA Level I 2016

$H( L' ×  (qr

  Holding Period Yield = HPY =

  Effective Annual Yield = EAY = 1 +

? opu/G − 1 (Rule: EAY > BDY) 9

  Money Market Yield (or CD equivalent Yield) rMM: •  

rMM = HPY ×  

rMM = (rBD) ×

!HaI  "HwSI  OP  GxI  *(IH7S(`  yMww $S(axH7I  $(MaI

FinQuiz

Formula Sheet

(Rule: rMM>

rBD) 10

  Bond Equivalent Yield = BDY = Semiannual Yield × 2 Reading 7: Statistical Concepts & Market Returns 1

  Range = Max Value – Min Value 2

  Class Interval = i ≥ •   •   •  

i = class interval H = highest value L'= lowest value,

  Absolute Frequency = Actual No of Observations (obvs) in a given class interval 4

  Relative Frequency =

K|7OwSGI  

  Cumulative Relative Frequency = Add up the Relative Frequencies 7

  Arithmetic Mean =

  Population Var = σ2 =

For Odd no

  Population S

 OP  O|~7  ML  JHGH|H7I 1O

OP  O|~7  ML  GxI  JHGH|H7I

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

  Mode = obvs that occurs most frequently in the distribution

  Sample S

D = s'= L'M[&

  Weighted Mean =

  Geometric Mean = GM = with Xi≥0 for i = 1,2,…n

!O(  Hww  …ƒ ‹…

  Semi-deviation (Semi S

!O(  Hww  …ƒ ‹…

  Target Semi-var = 13

  Population Mean = µ =

  Semi-var =

  Harmonic Mean = H

!O(  Hww  …ƒ ‹y

  Target Semi-Deviation =

  Sample Mean =

  where n =

number of observation in the sample 15

  Measures of Location: Quartiles =

Quintiles =

Deciles =

Percentiles = Ly =

!O(  Hww  …ƒ ‹y

  Coefficient of Variation = CV =

iM7G(M|SGMOL

  Mean Absolute Deviation = MAD = m ƒ„% …Z /…

  Sample Var = s2 =

For Even no of obvs locate L'median at

*OGHw  1O  OP  U|~7

  Cumulative Absolute Frequency = Add up the Absolute Frequencies

CFA Level I 2016

  Sharpe Ratio =

)IHL  $O(GPOwMO  N /)IHL  NP  N F

  Excess Kurtosis = Kurtosis – 3

FinQuiz

Formula Sheet

  Geometric Mean R ≈

"H(MHLaI  OP  N

Reading 8: Probability Concepts 1

  Empirical Prob of an event E = P(E) = $(O|  OP  I~ILG  •

CFA Level I 2016

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)

*OGHw  $(O|

  Odds for event E =

$(O|  OP  • &/$(O|  OP  •

  Odds against event E =

&/$(O|  OP  • $(O|  OP  •  

  Conditional Prob of A given that B has occurred = P(A|B) =

  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)

  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,

…,Sn are mutually exclusive and exhaustive scenarios)

  Correlation (b/w two random variables Ri,

?” Cov (Ri Rj) = Cov (Rj Ri) Cov (R,

R) = σ2 (R) 12

  Portfolio Var = σ2 (Rp) = L'L M[& ”[&

QO~   Nƒ N˜ ™Nƒ ×™N˜

  Bayes’ Formula =

HGMOL|•~ILG

  Multiplication Rule of Counting = n factorial =

  Multinomial Formula (General formula for labeling problem) =  

  Combination Formula (Binomial Formula) = L' 

  Expected R = E(wiRi) = wiE(Ri) 11

  Cov (Ri Rj) =

  Standard Deviation (S

  Permutation = L' 

Reading 9: Common Probability Distributions 1

  Probability Function (for a binomial random variable) p(x) = p(X=x) = L'Ÿ

?Ÿ 1 −

FinQuiz

Formula Sheet

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

•   •   •   •   •  

  Roy’s Safety-Frist Criterion = SF Ratio = • NE /N´ ™E

  Sharpe Ratio = =

  Probability Density Function (pdf) = f(x) &

  Normal Density Funct =

  Estimations by using Normal Distribution: •  

Approximately 50% of all obsv fall in k

Approx 68% of all obvs fall in the interval

? Approx 95% of all obvs fall in the interval

? Approx 99% of all obvs fall in the interval

? More precise intervals for 95% of the obvs are

? and for 99% of the observations are

  Z-Score (how many S

Ds away from the mean the point x lies)

(when X is normally distributed)

  Value at Risk = VAR = Minimum $ loss expected over a specified period at a specified prob level

  Mean (µL) of a lognormal random variable = exp (µ + 0

50σ2) 10

  Variance (σL2) of a lognormal random variable = exp (2µ+ σ2) × [exp (σ2) – 1]

CFA Level I 2016

  Continuously compounded return associated with a holding period from 0 to T: R0,T= ln (ST / S0) or

?*/&,* +

T = One-period continuously compounded returns 15

  When one-period continuously compounded returns (i

r0,1) are IID random variables

?*/&,* +

?*/k,*/& +

  Log Normal 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 = holding period return on the stock from t to t + 1

  Continuously compounded return associated with a holding period from t to t + 1:

  Annualized volatility = sample S

of one period continuously compounded returns ×

? Reading 10: Sampling and Estimation 1

  Var of the distribution of the sample mean =

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

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

D of the distribution of the sample mean =

FinQuiz

Formula Sheet

  Standard Error of the sample mean: •   When the population S

D (σ) is known =

L% '  L‰ /k

‰ %/‰ ω % ' ω m% m‰

Power of Test = 1-Prob of Type II Error

D is known)

CI for normally distributed population F L

(when sample size is large but

D is unknown where s'is sample S

  Student’s t distribution F L

?L/& =  

D is unknown and pop

Test Statistic for a test of diff b/wn two pop means (normally distributed,

unequal and unknown pop var unknown) t=

?Rk = pooled

D is unknown,

the standard error of sample statistic is give by

L% /& F%‰ '   L‰ /& F‰‰

estimator of common variance =

D is unknown,

the standard error of sample statistic is give by

CI for normally distributed population ™ with known variance =

…% /…‰ / ˆ% /ˆ‰ m% m‰

  Construction of Confidence Interval (CI) = Point estimate ± (Reliability factor × Standard error)

Test Statistic for a test of diff b/w two pop means (normally distributed,

pop var unknown but assumed equal) t=

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

  Test Statistic =

  Finite Population Correction Factor = fpc 1/&

Reading 11: Hypothesis Testing

sampled is normally or approximately normally distributed)

D estimate of s'=  

  t-ratio =

When the population S

D (σ) is not

  Z-ratio =

CFA Level I 2016

In this df calculated as

‰ ‰ ω %  ' ω m% m‰ ‰ ‰ ω ω % ‰ m% m‰ ' m% m‰

Test Statistic for a test of mean differences (normally distributed populations,

unknown population variances) J/ˆÑh

?Jk =  

FinQuiz

Formula Sheet

?Jk sample error of the sample mean difference =

L/& F ‰ ™h‰

Chi Square Confidence Interval for variance Lower limit = L'= =U==

Spearman Rank Correlation =

?7 6 LM[&

?k − 1 •   For small samples rejection points for the test based on

•   For large sample size (e

n>30) t-test can be used to test the hypothesis i

?7k &/k

F%‰ F‰‰

  Simple Moving Average =

Relation between Chi Square and F…%‰

?&k is one chi square random variable with one m degrees of freedom

  Momentum Oscillator (or Rate of Change Oscillator ROC): •  

Momentum Oscillator Value M = (VVx)  ×100

where ÝR  axHLTI7   iO•L  axHLTI7

  Stochastic Oscillator (composed of two lines %K and %D):

Reading 12: Technical Analysis

  Price Target for the •   Head and Shoulders = Neckline – (Head – Neckline) •   Inverse Head and Shoulders = Neckline + (Neckline– Head)

  Relative Strength Index = RSI = 100 −

  Relative Strength Analysis =

F-test (test concerning differences between variances of two normally distributed

L/& F ‰

(where V = most recent closing price and Vx = closing price x days ago) Alternate Method to calculate M = "

L/& F ‰

?kk is another chi square random variable with one n degrees of freedom

Chi Square Test Statistic (for test concerning the value of a normal

CFA Level I 2016

Q/B&‡ z&‡/B&‡

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

Put/Call Ratio (Type of Sentiment Indicators) =

  Short Interest Ratio (Type of Sentiment Indicators) =

  Arms Index TRIN i

Trading Index (Type of Flow of funds Indicator) =

OP  KJ~HL  g77SI7  ÷1O

OP  iIawML  g77SI7 "OwS

I  OP  KJ~HL  g77SI7÷"OwS

I  OP  iIawML  g77SI7

FinQuiz

Formula Sheet

Reading 13: Demand & Supply Analysis: Introduction

  Total Surplus = Total value – Total variable cost

  Slope of the demand curve =

  Society Welfare = Consumer surplus + Producer surplus

∆  éê  ëìéíî ∆  éê  ïðñêòéòó  ôîõñêöîö

  Slope of the supply curve =

  Price Elasticity of Demand = %  ∆  éê  ïðñêòéòó  ôîõñêöîö

  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 (Q0 × P 0)

Q2 − Q1 (Q1 + Q2 ) %ΔQ = P2 − P1 %ΔP 1 2 ( P1 + P2 ) 1 2

  Income Elasticity of Demand = %  ∆  éê  ïðñêòéòó  ôîõñêöîö %  ∆  éê  úêíûõî  

Total revenue = Total quantity sold × Price per unit Area (for calculating Producer Surplus) = ½ (Base × Height) = ½ {(Q0) × (P0 – intercept point on yaxis**)} **where supply curve intersects y-axis

  Total Surplus = Consumer surplus + Producer surplus

Q2 − Q1 (Q1 + Q2 ) %ΔQ = I 2 − I1 %ΔI 1 2 ( I1 + I 2 )

  Producer Surplus = Total revenue received from selling a given amount of a good – Total variable cost of producing that amount

  Cross Elasticity = %  ∆éê  ïðñêòéòó  ôîõñêöîö  ûü  ýûûö  þ %  ∆  éê  ëìéíî  ûü  ýûûö  ÿ

Reading 14: Demand & Supply Analysis: Consumer Demand 1

  Marginal Utility = 2

  Slope of Budget Constraint Line =

∆  éê  ï% ∆  éê  ï‚

ë‚   ë%

  Marginal Rate of Substitution =

∆  éê  ï% ∆  éê  ï‚

&ñì'éêñù  "òéùéòó  ûü  ýûûö  þ &ñì'éêñù  "òéùéòó  ûü  ýûûö  ÿ

%  ∆    éê  ëìéíî

∆  éê  ïðñêòéòó  ÷ðøøùéîö

CFA Level I 2016

!ûòñù  "òéùéòó ∆  éê  ïðñêòéòó  #ûê$ðõîö

Equation of Budget Constraint Line = (PX × QX ) + (PY × QY)

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

FinQuiz

Formula Sheet

  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) =

ïðñêòéòó ∆  éê  

!ûòñù  )î*îêðî ∆  éê  ïðñêòéòó

  Total Variable Cost = Variable Cost per unit × Quantity Produced 12

  Total Cost = Total Fixed + Total Variable 13

  Average total cost (ATC) =

!ûòñù  #û$ò

Fixed Cost + Avg

Variable Cost 14

  Marginal cost (MC) =

!ûòñù  #û$ò ∆  éê  ïðñêòéòó  ëìûöðíîö

  Marginal Variable Cost = ∆  éê  

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

  Marginal revenue (in perfect competition) = Avg

Revenue = Price = Demand

  Marginal Product =

!ûòñù  ëìûöðíò ∆  éê  ïðñêéòó  ûü  -ñ,ûì

!ûòñù  

ðòøðò ∆  éê  /û  ûü  0ûì1îì$

  Profit can be increased by decreasing output when MR< MC

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

  Break-even price: P = ATC è Output level where Price = Average Revenue = Marginal Revenue = Average Total Cost è where,

Total Revenue = Total Cost

!ûòñù  )î*îêðî

  Marginal Revenue (MR) =

ïðñêòéòó  ëìûöðíîö

  Profit can be increased by increasing output when MR> MC

CFA Level I 2016

  Firms earn Economic Profits when Price > Average Total Cost 21

  Profits occur when Total Revenue (TR) ≥ Total Cost (TC) & when Price = Marginal Costè firm will continue operating

  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 Cost while losses are < fixed costs è firm will continue operating

  Losses are incurred when there are Operating losses (Total Revenue ≤ Variable Cost) AND when losses ≥ fixed costs è firm will shut down

  Average Product =

!ûòñù  ëìûöðíò ïðñêòéòó  ûü  -ñ,ûì

ëìéíî  ûü  -ñ,ûì   &ñì'éêñù  ëìûöðíò  ûü  ë2ó$éíñù  #ñøéòñù ëìéíî  ûü  ë2óéíñù  #ñøéòñù

  Profit is maximized when: MRP = Price or cost of the input for each type of resource that is used in the production process 28

  Marginal Revenue product = Marginal Product of an input unit × Price of the Product = Price of the input = ∆    éê  

!ûòñù  )î*îêðî ∆  éê  ïðñêòéòó  ûü  úêøðò  îõøùûóîö

  Surplus value or contribution of an input to firm’s profit = MRP – Cost of an input Reading 16: The firm & Market Structures 1

  In perfect competition,

Marginal revenue = Avg

Revenue = Price = Demand 2

  Marginal Revenue = Price  × 1 −  

& ëìéíî  7ùñ$òéíéòó  ûü  ôîõñêö

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

!ûòñù  &ñì1îò  ÷ñùî$

FinQuiz

Formula Sheet

  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$î  óì  øìéíî$

  Real GDP = [(Nominal GDP / GDP deflator) ÷ 100] 5

  GDP deflator =

/ûõéêñù  ýôë )îñù  ýôë  

 ×100

  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

CFA Level I 2016

  National Income = Compensation of employees + Corp & Govt enterprise profits before taxes + Interest income + unincorporated business net income + rent + indirect business taxes less subsidies

  Private Sector Saving = Household Saving + Undistributed Corporate Profits + Capital Consumption Allowance 18

  GDP = Household consumption + Private Sector Saving + Net Taxes

  Total Amount Earned by Capital = Profit + Capital Consumption Allowance

  Domestic saving = Investment + Fiscal balance + Trade balance

  PI = National income – Indirect business taxes – Corp income taxes – Undistributed Corp profits + Transfer payments

  Trade Balance = Exports – Imports

  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

  Business sector saving = Undistributed corporate profits + Capital consumption allowance 16

  Total Expenditure = Household consumption (C) + Investments (I) + Government spending (G) + Net exports (X-M)

  Fiscal balance = Government Expenditure – Taxes = (Savings – Investment) – Trade Balance 22

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

  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

  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)]

FinQuiz

Formula Sheet

CFA Level I 2016

  Money Multiplier = 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 =

Reading 18: Understanding Business Cycles 1

  Price index at time t2 = "HwSI  OP  GxI  QO

RGMOL  yH7{IG  HG  G  ‰

"HwSI  OP  GxI  QOL7S

RGMOL  yH7{IG  HG  G  % ëìéíî  úêöî9  ñò  òéõî  òk  

Inflation Rate =

 )î$îì*î  )îC  ûì  ìî$îì*î  ìñòéû  

  Narrow money = M1= currency held outside banks + checking accounts + traveller’s check 4

  Broad money = M2 = M1 + time deposits + saving deposits 5

  M3 = M2 + deposits with non-bank financial institution

7õøùûóîî  #ûõøîê$ñòéûê  

  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

  Fisher Index =

IL = Laspeyres index and Ip = Paasche Index)

  Neutral Rate = Trend Growth + Inflation Target

  Impact of Taxes and Government Spending: The Fiscal Multiplier The net impact of the government sector on AD: •   G – T + B = Budget surplus or Budget deficit where,

G = government spending ,

T =taxes,

B =transfer benefits •   Disposable income = Income – Net taxes = (1 – t) Income

!ûòñù  ùñ,ûì  íûõøîê$ñòéûê  øîì  2ûðì  øîì