CFA Level 1 Formulas Exam (Correct Answers)
Price change based on convexity Correct Answers-duration(change in yield)
+1/2(convexity)(change in yield)^2
Effective Duration Correct AnswersRequired if a bond has embedded options: [(v-)-
(v+)]/[2V0(change in curve)]
Modified Duration Correct Answers[(v-)-(v+)]/[2V0(change in yield)]
Future Value Correct AnswersPV(1+(I/Y)^N)
PV Correct AnswersFV/(1+r)^n
PV of perpetuity Correct AnswersPMT / discount rate
Approximate percentage price change of a bond Correct Answers(-)(modified duration)
(ΔYTM)
Nominal Risk Free Correct AnswersReal Risk Free + expected inflation
Required Return Correct AnswersNominal risk free + liquidity premiums + default risk
premium + maturity risk premium
EAR Correct Answers[(1+periodic rate)^N ] - 1
EAR continuous Correct Answerse^r - 1
Bank discount yield Correct Answers(FV - Price)/(FV) * (360/T)
HPY Correct Answers[(P1+D1)/P0] - 1
EAY Correct Answers(1+HPY)^(365/T) - 1
HPY (MMY equation) Correct AnswersMMY * (T/360)
MMY Correct AnswersHPY * (360/T)
Geometric return Correct Answers[(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return Correct Answers[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean Correct Answers[N/(sum of (1/sample means))]
Position of observation Correct Answers(n+1)*(k/100)
Excess kurtosis Correct AnswersSample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation Correct Answerssum of: (mean - sample mean)/n-1
Variance Correct Answers(x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation Correct AnswersSample standard deviation/sample mean
Sharpe Ratio Correct AnswersRisk of portfolio - risk free / Standard deviation of portfolio
Joint Probability Correct AnswersP(AB) = P(A|B) * P(B)
Addition rule Correct AnswersP(A or B) = P(A) + P(B) - P(AB)
Multiplication rule Correct AnswersP(A and B) = P(A)*P(B)
Total Probability Rule Correct AnswersP(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value Correct AnswersP(x)*(x)
Covariance Correct AnswersP[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that
sum to 1 OR [SDa*SDb*correlation)
Correlation Correct AnswersCovariance(A,B) / SDa*SDb
Portfolio expected return Correct Answersweight times the E(R) of each stock
Portfolio variance Correct AnswersWa^2*SDa^2 + Wb^2*SDb^2 +
2WaWb*SDa*SDb*Corr(a,b)
Baye's formula Correct AnswersP(new info) / unconditional probability of new info*prior
prob of event
Combination binomial Correct AnswersnCr - order doesn't matter
Permutation binomial Correct AnswersnPr - order matters
, Binomial probability Correct AnswersnCx * p^x * (1-p)^(n-x)
Binomial Expected value Correct AnswersnP
Binomial variance Correct Answersnp(1-p)
90% confidence interval Correct Answers+/- 1.645 SDs
95% confidence interval Correct Answers+/- 1.96 SDs
99% confidence interval Correct Answers+/- 2.58 SDs
Z score Correct Answers(x-mean)/SD
Roy's safety first ratio Correct Answers(E(Rp) - Rtarget)/SD
Mean sampling error Correct Answersmean - miu
Standard error Correct AnswersSD/ sqrt (n)
Confidence interval Correct Answersx+/- z*(SD/sqrt(n))
Type 1 error Correct Answersrejection of null hypothesis when it is actually true
Type 2 error Correct AnswersAccepting the null when it is false
t-stat Correct Answerst-statistic for tests involving the population mean (location of
mean, difference in means, paired comparisons)
chi square test Correct AnswersUse chi-square statistic for tests of a single population
variance ([(n-1)SD^2]/Variance - observed)
F stat Correct AnswersUse F-statistic for tests comparing two population variances.
(SD1/SD2)
Price elasticity of demand Correct Answers%Δ Qd/Δ% price
Income elasticity Correct Answers%Δ Qd/%Δ income
Accounting profit Correct AnswersTotal revenue - total explicit/acctg costs
Economic profit Correct AnswersTotal revenue - explicit costs - implicit
costs(opportunity costs)
Normal profit Correct AnswersAcctg profit - economic profit (equals 0)
Total revenue Correct AnswersPrice * quantity
Avg total revenue Correct AnswersTR/Q
Marginal revenue Correct AnswersΔTR/ΔQ
Marginal cost Correct AnswersΔTC/ΔQ
Avg total cost Correct Answerstotal costs/total product
Avg variable cost Correct Answerstotal VC/total product
Shutdown point Correct AnswersTR < TVC
HHI Correct AnswersSum of market shares of each firms squared
GDP Deflator Correct AnswersNominal GDP/Real GDP * 100
Fiscal Multiplier Correct Answers1/[(1-Marginal propensity to consume)(1-t)
Money multiplier Correct Answers1/Reserve Requirement
GDP Correct Answersconsumption spending + investment + government spending +
net exports (C+I+G+NX)
FX formula layout Correct AnswersFX rates are expressed as price currency / base
currency and interpreted as the number of units of the price currency for each unit of the
base currency.
CPI Correct Answers(basket of good prices)/(basket of goods base year)*100
Real FX rate Correct AnswersNominal FX rate * (base currency CPI/price currency CPI)
No-Arbitrage Forward Exchange Rate Correct Answers(forward/sport) = (1+price
currency interest rate)/(1+base currency interest rate)
Equation of exchange Correct Answersmoney supply * velocity = Price * real output
Price change based on convexity Correct Answers-duration(change in yield)
+1/2(convexity)(change in yield)^2
Effective Duration Correct AnswersRequired if a bond has embedded options: [(v-)-
(v+)]/[2V0(change in curve)]
Modified Duration Correct Answers[(v-)-(v+)]/[2V0(change in yield)]
Future Value Correct AnswersPV(1+(I/Y)^N)
PV Correct AnswersFV/(1+r)^n
PV of perpetuity Correct AnswersPMT / discount rate
Approximate percentage price change of a bond Correct Answers(-)(modified duration)
(ΔYTM)
Nominal Risk Free Correct AnswersReal Risk Free + expected inflation
Required Return Correct AnswersNominal risk free + liquidity premiums + default risk
premium + maturity risk premium
EAR Correct Answers[(1+periodic rate)^N ] - 1
EAR continuous Correct Answerse^r - 1
Bank discount yield Correct Answers(FV - Price)/(FV) * (360/T)
HPY Correct Answers[(P1+D1)/P0] - 1
EAY Correct Answers(1+HPY)^(365/T) - 1
HPY (MMY equation) Correct AnswersMMY * (T/360)
MMY Correct AnswersHPY * (360/T)
Geometric return Correct Answers[(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return Correct Answers[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean Correct Answers[N/(sum of (1/sample means))]
Position of observation Correct Answers(n+1)*(k/100)
Excess kurtosis Correct AnswersSample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation Correct Answerssum of: (mean - sample mean)/n-1
Variance Correct Answers(x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation Correct AnswersSample standard deviation/sample mean
Sharpe Ratio Correct AnswersRisk of portfolio - risk free / Standard deviation of portfolio
Joint Probability Correct AnswersP(AB) = P(A|B) * P(B)
Addition rule Correct AnswersP(A or B) = P(A) + P(B) - P(AB)
Multiplication rule Correct AnswersP(A and B) = P(A)*P(B)
Total Probability Rule Correct AnswersP(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value Correct AnswersP(x)*(x)
Covariance Correct AnswersP[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that
sum to 1 OR [SDa*SDb*correlation)
Correlation Correct AnswersCovariance(A,B) / SDa*SDb
Portfolio expected return Correct Answersweight times the E(R) of each stock
Portfolio variance Correct AnswersWa^2*SDa^2 + Wb^2*SDb^2 +
2WaWb*SDa*SDb*Corr(a,b)
Baye's formula Correct AnswersP(new info) / unconditional probability of new info*prior
prob of event
Combination binomial Correct AnswersnCr - order doesn't matter
Permutation binomial Correct AnswersnPr - order matters
, Binomial probability Correct AnswersnCx * p^x * (1-p)^(n-x)
Binomial Expected value Correct AnswersnP
Binomial variance Correct Answersnp(1-p)
90% confidence interval Correct Answers+/- 1.645 SDs
95% confidence interval Correct Answers+/- 1.96 SDs
99% confidence interval Correct Answers+/- 2.58 SDs
Z score Correct Answers(x-mean)/SD
Roy's safety first ratio Correct Answers(E(Rp) - Rtarget)/SD
Mean sampling error Correct Answersmean - miu
Standard error Correct AnswersSD/ sqrt (n)
Confidence interval Correct Answersx+/- z*(SD/sqrt(n))
Type 1 error Correct Answersrejection of null hypothesis when it is actually true
Type 2 error Correct AnswersAccepting the null when it is false
t-stat Correct Answerst-statistic for tests involving the population mean (location of
mean, difference in means, paired comparisons)
chi square test Correct AnswersUse chi-square statistic for tests of a single population
variance ([(n-1)SD^2]/Variance - observed)
F stat Correct AnswersUse F-statistic for tests comparing two population variances.
(SD1/SD2)
Price elasticity of demand Correct Answers%Δ Qd/Δ% price
Income elasticity Correct Answers%Δ Qd/%Δ income
Accounting profit Correct AnswersTotal revenue - total explicit/acctg costs
Economic profit Correct AnswersTotal revenue - explicit costs - implicit
costs(opportunity costs)
Normal profit Correct AnswersAcctg profit - economic profit (equals 0)
Total revenue Correct AnswersPrice * quantity
Avg total revenue Correct AnswersTR/Q
Marginal revenue Correct AnswersΔTR/ΔQ
Marginal cost Correct AnswersΔTC/ΔQ
Avg total cost Correct Answerstotal costs/total product
Avg variable cost Correct Answerstotal VC/total product
Shutdown point Correct AnswersTR < TVC
HHI Correct AnswersSum of market shares of each firms squared
GDP Deflator Correct AnswersNominal GDP/Real GDP * 100
Fiscal Multiplier Correct Answers1/[(1-Marginal propensity to consume)(1-t)
Money multiplier Correct Answers1/Reserve Requirement
GDP Correct Answersconsumption spending + investment + government spending +
net exports (C+I+G+NX)
FX formula layout Correct AnswersFX rates are expressed as price currency / base
currency and interpreted as the number of units of the price currency for each unit of the
base currency.
CPI Correct Answers(basket of good prices)/(basket of goods base year)*100
Real FX rate Correct AnswersNominal FX rate * (base currency CPI/price currency CPI)
No-Arbitrage Forward Exchange Rate Correct Answers(forward/sport) = (1+price
currency interest rate)/(1+base currency interest rate)
Equation of exchange Correct Answersmoney supply * velocity = Price * real output
