CFA Level 1 Formulas Exam Questions
with Correct Answers
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
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
with Correct Answers
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
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
