CFA Level 1 Formulas with all Correct & 100% Verified
Answers |Latest Version |Already Graded A+
Price change based on convexity ✔Correct Answer--duration(change in yield)+1/2(convexity)
(change in yield)^2
Effective Duration ✔Correct Answer-Required if a bond has embedded options:
[(v-)-(v+)]/[2V0(change in curve)]
Modified Duration ✔Correct Answer-[(v-)-(v+)]/[2V0(change in yield)]
Future Value ✔Correct Answer-PV(1+(I/Y)^N)
PV ✔Correct Answer-FV/(1+r)^n
PV of perpetuity ✔Correct Answer-PMT / discount rate
Approximate percentage price change of a bond ✔Correct Answer-(-)(modified duration)(ΔYTM)
Nominal Risk Free ✔Correct Answer-Real Risk Free + expected inflation
Required Return ✔Correct Answer-Nominal risk free + liquidity premiums + default risk premium +
maturity risk premium
EAR ✔Correct Answer-[(1+periodic rate)^N ] - 1
EAR continuous ✔Correct Answer-e^r - 1
Bank discount yield ✔Correct Answer-(FV - Price)/(FV) * (360/T)
HPY ✔Correct Answer-[(P1+D1)/P0] - 1
EAY ✔Correct Answer-(1+HPY)^(365/T) - 1
HPY (MMY equation) ✔Correct Answer-MMY * (T/360)
MMY ✔Correct Answer-HPY * (360/T)
Geometric return ✔Correct Answer-[(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return ✔Correct Answer-[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean ✔Correct Answer-[N/(sum of (1/sample means))]
Position of observation ✔Correct Answer-(n+1)*(k/100)
Excess kurtosis ✔Correct Answer-Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation ✔Correct Answer-sum of: (mean - sample mean)/n-1
, Variance ✔Correct Answer-(x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation ✔Correct Answer-Sample standard deviation/sample mean
Sharpe Ratio ✔Correct Answer-Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability ✔Correct Answer-P(AB) = P(A|B) * P(B)
Addition rule ✔Correct Answer-P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule ✔Correct Answer-P(A and B) = P(A)*P(B)
Total Probability Rule ✔Correct Answer-P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value ✔Correct Answer-P(x)*(x)
Covariance ✔Correct Answer-P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation ✔Correct Answer-Covariance(A,B) / SDa*SDb
Portfolio expected return ✔Correct Answer-weight times the E(R) of each stock
Portfolio variance ✔Correct Answer-Wa^2*SDa^2 + Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
Baye's formula ✔Correct Answer-P(new info) / unconditional probability of new info*prior prob of
event
Combination binomial ✔Correct Answer-nCr - order doesn't matter
Permutation binomial ✔Correct Answer-nPr - order matters
Binomial probability ✔Correct Answer-nCx * p^x * (1-p)^(n-x)
Binomial Expected value ✔Correct Answer-nP
Binomial variance ✔Correct Answer-np(1-p)
90% confidence interval ✔Correct Answer-+/- 1.645 SDs
95% confidence interval ✔Correct Answer-+/- 1.96 SDs
99% confidence interval ✔Correct Answer-+/- 2.58 SDs
Z score ✔Correct Answer-(x-mean)/SD
Roy's safety first ratio ✔Correct Answer-(E(Rp) - Rtarget)/SD
Mean sampling error ✔Correct Answer-mean - miu
Answers |Latest Version |Already Graded A+
Price change based on convexity ✔Correct Answer--duration(change in yield)+1/2(convexity)
(change in yield)^2
Effective Duration ✔Correct Answer-Required if a bond has embedded options:
[(v-)-(v+)]/[2V0(change in curve)]
Modified Duration ✔Correct Answer-[(v-)-(v+)]/[2V0(change in yield)]
Future Value ✔Correct Answer-PV(1+(I/Y)^N)
PV ✔Correct Answer-FV/(1+r)^n
PV of perpetuity ✔Correct Answer-PMT / discount rate
Approximate percentage price change of a bond ✔Correct Answer-(-)(modified duration)(ΔYTM)
Nominal Risk Free ✔Correct Answer-Real Risk Free + expected inflation
Required Return ✔Correct Answer-Nominal risk free + liquidity premiums + default risk premium +
maturity risk premium
EAR ✔Correct Answer-[(1+periodic rate)^N ] - 1
EAR continuous ✔Correct Answer-e^r - 1
Bank discount yield ✔Correct Answer-(FV - Price)/(FV) * (360/T)
HPY ✔Correct Answer-[(P1+D1)/P0] - 1
EAY ✔Correct Answer-(1+HPY)^(365/T) - 1
HPY (MMY equation) ✔Correct Answer-MMY * (T/360)
MMY ✔Correct Answer-HPY * (360/T)
Geometric return ✔Correct Answer-[(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return ✔Correct Answer-[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean ✔Correct Answer-[N/(sum of (1/sample means))]
Position of observation ✔Correct Answer-(n+1)*(k/100)
Excess kurtosis ✔Correct Answer-Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation ✔Correct Answer-sum of: (mean - sample mean)/n-1
, Variance ✔Correct Answer-(x-mean)^2/N (population) and divided by (n-1) for a sample
Coefficient of Variation ✔Correct Answer-Sample standard deviation/sample mean
Sharpe Ratio ✔Correct Answer-Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability ✔Correct Answer-P(AB) = P(A|B) * P(B)
Addition rule ✔Correct Answer-P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule ✔Correct Answer-P(A and B) = P(A)*P(B)
Total Probability Rule ✔Correct Answer-P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value ✔Correct Answer-P(x)*(x)
Covariance ✔Correct Answer-P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation ✔Correct Answer-Covariance(A,B) / SDa*SDb
Portfolio expected return ✔Correct Answer-weight times the E(R) of each stock
Portfolio variance ✔Correct Answer-Wa^2*SDa^2 + Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
Baye's formula ✔Correct Answer-P(new info) / unconditional probability of new info*prior prob of
event
Combination binomial ✔Correct Answer-nCr - order doesn't matter
Permutation binomial ✔Correct Answer-nPr - order matters
Binomial probability ✔Correct Answer-nCx * p^x * (1-p)^(n-x)
Binomial Expected value ✔Correct Answer-nP
Binomial variance ✔Correct Answer-np(1-p)
90% confidence interval ✔Correct Answer-+/- 1.645 SDs
95% confidence interval ✔Correct Answer-+/- 1.96 SDs
99% confidence interval ✔Correct Answer-+/- 2.58 SDs
Z score ✔Correct Answer-(x-mean)/SD
Roy's safety first ratio ✔Correct Answer-(E(Rp) - Rtarget)/SD
Mean sampling error ✔Correct Answer-mean - miu
