CFA Level 1 Formulas || With 100%
Accurate Formulas
Conceptial Researchers 2024
, CFA Level 1 Formulas || With 100%
Accurate Formulas
Sharpe Ratio - ANSWER - Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability - ANSWER - P(AB) = P(A|B) * P(B)
Addition rule - ANSWER - P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule - ANSWER - P(A and B) = P(A)*P(B)
Total Probability Rule - ANSWER - P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - ANSWER - P(x)*(x)
Covariance - ANSWER - P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that
sum to 1 OR [SDa*SDb*correlation)
Correlation - ANSWER - Covariance(A,B) / SDa*SDb
Portfolio expected return - ANSWER - weight times the E(R) of each stock
Portfolio variance - ANSWER - Wa^2*SDa^2 + Wb^2*SDb^2 +
2WaWb*SDa*SDb*Corr(a,b)
Baye's formula - ANSWER - P(new info) / unconditional probability of new info*prior
prob of event
Combination binomial - ANSWER - nCr - order doesn't matter
Permutation binomial - ANSWER - nPr - order matters
Binomial probability - ANSWER - nCx * p^x * (1-p)^(n-x)
Binomial Expected value - ANSWER - nP
Binomial variance - ANSWER - np(1-p)
90% confidence interval - ANSWER - +/- 1.645 SDs
95% confidence interval - ANSWER - +/- 1.96 SDs
99% confidence interval - ANSWER - +/- 2.58 SDs
Z score - ANSWER - (x-mean)/SD
Roy's safety first ratio - ANSWER - (E(Rp) - Rtarget)/SD
,Mean sampling error - ANSWER - mean - miu
Standard error - ANSWER - SD/ sqrt (n)
Confidence interval - ANSWER - x+/- z*(SD/sqrt(n))
Price change based on convexity - ANSWER - -duration(change in yield)
+1/2(convexity)(change in yield)^2
Effective Duration - ANSWER - Required if a bond has embedded options: [(v-)-
(v+)]/[2V0(change in curve)]
Modified Duration - ANSWER - [(v-)-(v+)]/[2V0(change in yield)]
Future Value - ANSWER - PV(1+(I/Y)^N)
PV - ANSWER - FV/(1+r)^n
PV of perpetuity - ANSWER - PMT / discount rate
Approximate percentage price change of a bond - ANSWER - (-)(modified duration)
(ΔYTM)
Nominal Risk Free - ANSWER - Real Risk Free + expected inflation
Required Return - ANSWER - Nominal risk free + liquidity premiums + default risk
premium + maturity risk premium
EAR - ANSWER - [(1+periodic rate)^N ] - 1
EAR continuous - ANSWER - e^r - 1
Bank discount yield - ANSWER - (FV - Price)/(FV) * (360/T)
HPY - ANSWER - [(P1+D1)/P0] - 1
EAY - ANSWER - (1+HPY)^(365/T) - 1
HPY (MMY equation) - ANSWER - MMY * (T/360)
MMY - ANSWER - HPY * (360/T)
Geometric return - ANSWER - [(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return - ANSWER - [(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - ANSWER - [N/(sum of (1/sample means))]
Position of observation - ANSWER - (n+1)*(k/100)
, Excess kurtosis - ANSWER - Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation - ANSWER - sum of: (mean - sample mean)/n-1
Variance - ANSWER - (x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation - ANSWER - Sample standard deviation/sample mean
Type 1 error - ANSWER - rejection of null hypothesis when it is actually true
Type 2 error - ANSWER - Accepting the null when it is false
t-stat - ANSWER - t-statistic for tests involving the population mean (location of
mean, difference in means, paired comparisons)
chi square test - ANSWER - Use chi-square statistic for tests of a single population
variance ([(n-1)SD^2]/Variance - observed)
F stat - ANSWER - Use F-statistic for tests comparing two population variances.
(SD1/SD2)
Price elasticity of demand - ANSWER - %Δ Qd/Δ% price
Income elasticity - ANSWER - %Δ Qd/%Δ income
Accounting profit - ANSWER - Total revenue - total explicit/acctg costs
Economic profit - ANSWER - Total revenue - explicit costs - implicit costs(opportunity
costs)
Normal profit - ANSWER - Acctg profit - economic profit (equals 0)
Total revenue - ANSWER - Price * quantity
Avg total revenue - ANSWER - TR/Q
Marginal revenue - ANSWER - ΔTR/ΔQ
Marginal cost - ANSWER - ΔTC/ΔQ
Avg total cost - ANSWER - total costs/total product
Avg variable cost - ANSWER - total VC/total product
Shutdown point - ANSWER - TR < TVC
HHI - ANSWER - Sum of market shares of each firms squared
GDP Deflator - ANSWER - Nominal GDP/Real GDP * 100
Accurate Formulas
Conceptial Researchers 2024
, CFA Level 1 Formulas || With 100%
Accurate Formulas
Sharpe Ratio - ANSWER - Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability - ANSWER - P(AB) = P(A|B) * P(B)
Addition rule - ANSWER - P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule - ANSWER - P(A and B) = P(A)*P(B)
Total Probability Rule - ANSWER - P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - ANSWER - P(x)*(x)
Covariance - ANSWER - P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that
sum to 1 OR [SDa*SDb*correlation)
Correlation - ANSWER - Covariance(A,B) / SDa*SDb
Portfolio expected return - ANSWER - weight times the E(R) of each stock
Portfolio variance - ANSWER - Wa^2*SDa^2 + Wb^2*SDb^2 +
2WaWb*SDa*SDb*Corr(a,b)
Baye's formula - ANSWER - P(new info) / unconditional probability of new info*prior
prob of event
Combination binomial - ANSWER - nCr - order doesn't matter
Permutation binomial - ANSWER - nPr - order matters
Binomial probability - ANSWER - nCx * p^x * (1-p)^(n-x)
Binomial Expected value - ANSWER - nP
Binomial variance - ANSWER - np(1-p)
90% confidence interval - ANSWER - +/- 1.645 SDs
95% confidence interval - ANSWER - +/- 1.96 SDs
99% confidence interval - ANSWER - +/- 2.58 SDs
Z score - ANSWER - (x-mean)/SD
Roy's safety first ratio - ANSWER - (E(Rp) - Rtarget)/SD
,Mean sampling error - ANSWER - mean - miu
Standard error - ANSWER - SD/ sqrt (n)
Confidence interval - ANSWER - x+/- z*(SD/sqrt(n))
Price change based on convexity - ANSWER - -duration(change in yield)
+1/2(convexity)(change in yield)^2
Effective Duration - ANSWER - Required if a bond has embedded options: [(v-)-
(v+)]/[2V0(change in curve)]
Modified Duration - ANSWER - [(v-)-(v+)]/[2V0(change in yield)]
Future Value - ANSWER - PV(1+(I/Y)^N)
PV - ANSWER - FV/(1+r)^n
PV of perpetuity - ANSWER - PMT / discount rate
Approximate percentage price change of a bond - ANSWER - (-)(modified duration)
(ΔYTM)
Nominal Risk Free - ANSWER - Real Risk Free + expected inflation
Required Return - ANSWER - Nominal risk free + liquidity premiums + default risk
premium + maturity risk premium
EAR - ANSWER - [(1+periodic rate)^N ] - 1
EAR continuous - ANSWER - e^r - 1
Bank discount yield - ANSWER - (FV - Price)/(FV) * (360/T)
HPY - ANSWER - [(P1+D1)/P0] - 1
EAY - ANSWER - (1+HPY)^(365/T) - 1
HPY (MMY equation) - ANSWER - MMY * (T/360)
MMY - ANSWER - HPY * (360/T)
Geometric return - ANSWER - [(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return - ANSWER - [(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - ANSWER - [N/(sum of (1/sample means))]
Position of observation - ANSWER - (n+1)*(k/100)
, Excess kurtosis - ANSWER - Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation - ANSWER - sum of: (mean - sample mean)/n-1
Variance - ANSWER - (x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation - ANSWER - Sample standard deviation/sample mean
Type 1 error - ANSWER - rejection of null hypothesis when it is actually true
Type 2 error - ANSWER - Accepting the null when it is false
t-stat - ANSWER - t-statistic for tests involving the population mean (location of
mean, difference in means, paired comparisons)
chi square test - ANSWER - Use chi-square statistic for tests of a single population
variance ([(n-1)SD^2]/Variance - observed)
F stat - ANSWER - Use F-statistic for tests comparing two population variances.
(SD1/SD2)
Price elasticity of demand - ANSWER - %Δ Qd/Δ% price
Income elasticity - ANSWER - %Δ Qd/%Δ income
Accounting profit - ANSWER - Total revenue - total explicit/acctg costs
Economic profit - ANSWER - Total revenue - explicit costs - implicit costs(opportunity
costs)
Normal profit - ANSWER - Acctg profit - economic profit (equals 0)
Total revenue - ANSWER - Price * quantity
Avg total revenue - ANSWER - TR/Q
Marginal revenue - ANSWER - ΔTR/ΔQ
Marginal cost - ANSWER - ΔTC/ΔQ
Avg total cost - ANSWER - total costs/total product
Avg variable cost - ANSWER - total VC/total product
Shutdown point - ANSWER - TR < TVC
HHI - ANSWER - Sum of market shares of each firms squared
GDP Deflator - ANSWER - Nominal GDP/Real GDP * 100
