CFA LEVEL 1 FORMULAS OVER 240 APPLIED FOMULAS FOR
ECONOMICS GOOD PRACTICE MATERAIL FOR UPCOMING EXAMS
NEW UPDATE 2022
Price change based on convexity - -duration(change in yield)+1/2(convexity)(change in yield)^2
Effective Duration - Required if a bond has embedded options: [(v-)-(v+)]/[2V0(change in
curve)]
Modified Duration - [(v-)-(v+)]/[2V0(change in yield)]
Future Value - PV(1+(I/Y)^N)
PV - FV/(1+r)^n
PV of perpetuity - PMT / discount rate
Approximate percentage price change of a bond - (-)(modified duration)(ΔYTM)
Nominal Risk Free - Real Risk Free + expected inflation
Required Return - Nominal risk free + liquidity premiums + default risk premium + maturity risk
premium
EAR - [(1+periodic rate)^N ] - 1
EAR continuous - e^r - 1
Bank discount yield - (FV - Price)/(FV) * (360/T)
HPY - [(P1+D1)/P0] - 1
EAY - (1+HPY)^(365/T) - 1
HPY (MMY equation) - MMY * (T/360)
MMY - HPY * (360/T)
Geometric return - [(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return - [(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - [N/(sum of (1/sample means))]
, Position of observation - (n+1)*(k/100)
Excess kurtosis - Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation - sum of: (mean - sample mean)/n-1
Variance - (x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation - Sample standard deviation/sample mean
Sharpe Ratio - Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability - P(AB) = P(A|B) * P(B)
Addition rule - P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule - P(A and B) = P(A)*P(B)
Total Probability Rule - P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - P(x)*(x)
Covariance - P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation - Covariance(A,B) / SDa*SDb
Portfolio expected return - weight times the E(R) of each stock
Portfolio variance - Wa^2*SDa^2 + Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
Baye's formula - P(new info) / unconditional probability of new info*prior prob of event
Combination binomial - nCr - order doesn't matter
Permutation binomial - nPr - order matters
Binomial probability - nCx * p^x * (1-p)^(n-x)
Binomial Expected value - nP
Binomial variance - np(1-p)
ECONOMICS GOOD PRACTICE MATERAIL FOR UPCOMING EXAMS
NEW UPDATE 2022
Price change based on convexity - -duration(change in yield)+1/2(convexity)(change in yield)^2
Effective Duration - Required if a bond has embedded options: [(v-)-(v+)]/[2V0(change in
curve)]
Modified Duration - [(v-)-(v+)]/[2V0(change in yield)]
Future Value - PV(1+(I/Y)^N)
PV - FV/(1+r)^n
PV of perpetuity - PMT / discount rate
Approximate percentage price change of a bond - (-)(modified duration)(ΔYTM)
Nominal Risk Free - Real Risk Free + expected inflation
Required Return - Nominal risk free + liquidity premiums + default risk premium + maturity risk
premium
EAR - [(1+periodic rate)^N ] - 1
EAR continuous - e^r - 1
Bank discount yield - (FV - Price)/(FV) * (360/T)
HPY - [(P1+D1)/P0] - 1
EAY - (1+HPY)^(365/T) - 1
HPY (MMY equation) - MMY * (T/360)
MMY - HPY * (360/T)
Geometric return - [(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return - [(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - [N/(sum of (1/sample means))]
, Position of observation - (n+1)*(k/100)
Excess kurtosis - Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation - sum of: (mean - sample mean)/n-1
Variance - (x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation - Sample standard deviation/sample mean
Sharpe Ratio - Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability - P(AB) = P(A|B) * P(B)
Addition rule - P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule - P(A and B) = P(A)*P(B)
Total Probability Rule - P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - P(x)*(x)
Covariance - P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation - Covariance(A,B) / SDa*SDb
Portfolio expected return - weight times the E(R) of each stock
Portfolio variance - Wa^2*SDa^2 + Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
Baye's formula - P(new info) / unconditional probability of new info*prior prob of event
Combination binomial - nCr - order doesn't matter
Permutation binomial - nPr - order matters
Binomial probability - nCx * p^x * (1-p)^(n-x)
Binomial Expected value - nP
Binomial variance - np(1-p)
