CFA Level 1 Formulas
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)
90% confidence interval - ✔ +/- 1.645 SDs
95% confidence interval - ✔ +/- 1.96 SDs
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)
90% confidence interval - ✔ +/- 1.645 SDs
95% confidence interval - ✔ +/- 1.96 SDs
