CFA LEVEL 1 FORMULAS
QUESTIONS AND
CORRECT ANSWERS
GRADED A+ 2025-2026
Price change based on convexity - ANS--duration(change in
yield)+1/2(convexity)(change in yield)^2
Effective Duration - ANS-Required if a bond has embedded options: [(v-)-
(v+)]/[2V0(change in curve)]
Modified Duration - ANS-[(v-)-(v+)]/[2V0(change in yield)]
Future Value - ANS-PV(1+(I/Y)^N)
PV - ANS-FV/(1+r)^n
PV of perpetuity - ANS-PMT / discount rate
Approximate percentage price change of a bond - ANS-(-)(modified duration)(ΔYTM)
Nominal Risk Free - ANS-Real Risk Free + expected inflation
Required Return - ANS-Nominal risk free + liquidity premiums + default risk premium
+ maturity risk premium
,EAR - ANS-[(1+periodic rate)^N ] - 1
EAR continuous - ANS-e^r - 1
Bank discount yield - ANS-(FV - Price)/(FV) * (360/T)
HPY - ANS-[(P1+D1)/P0] - 1
EAY - ANS-(1+HPY)^(365/T) - 1
HPY (MMY equation) - ANS-MMY * (T/360)
MMY - ANS-HPY * (360/T)
Geometric return - ANS-[(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return - ANS-[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - ANS-[N/(sum of (1/sample means))]
Position of observation - ANS-(n+1)*(k/100)
Excess kurtosis - ANS-Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation - ANS-sum of: (mean - sample mean)/n-1
Variance - ANS-(x-mean)^2/N (population) and divided by (n-1) for a sample
, Coefficient of Variation - ANS-Sample standard deviation/sample mean
Sharpe Ratio - ANS-Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability - ANS-P(AB) = P(A|B) * P(B)
Addition rule - ANS-P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule - ANS-P(A and B) = P(A)*P(B)
Total Probability Rule - ANS-P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - ANS-P(x)*(x)
Covariance - ANS-P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation - ANS-Covariance(A,B) / SDa*SDb
Portfolio expected return - ANS-weight times the E(R) of each stock
Portfolio variance - ANS-Wa^2*SDa^2 + Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
Baye's formula - ANS-P(new info) / unconditional probability of new info*prior prob of
event
Combination binomial - ANS-nCr - order doesn't matter
Permutation binomial - ANS-nPr - order matters
QUESTIONS AND
CORRECT ANSWERS
GRADED A+ 2025-2026
Price change based on convexity - ANS--duration(change in
yield)+1/2(convexity)(change in yield)^2
Effective Duration - ANS-Required if a bond has embedded options: [(v-)-
(v+)]/[2V0(change in curve)]
Modified Duration - ANS-[(v-)-(v+)]/[2V0(change in yield)]
Future Value - ANS-PV(1+(I/Y)^N)
PV - ANS-FV/(1+r)^n
PV of perpetuity - ANS-PMT / discount rate
Approximate percentage price change of a bond - ANS-(-)(modified duration)(ΔYTM)
Nominal Risk Free - ANS-Real Risk Free + expected inflation
Required Return - ANS-Nominal risk free + liquidity premiums + default risk premium
+ maturity risk premium
,EAR - ANS-[(1+periodic rate)^N ] - 1
EAR continuous - ANS-e^r - 1
Bank discount yield - ANS-(FV - Price)/(FV) * (360/T)
HPY - ANS-[(P1+D1)/P0] - 1
EAY - ANS-(1+HPY)^(365/T) - 1
HPY (MMY equation) - ANS-MMY * (T/360)
MMY - ANS-HPY * (360/T)
Geometric return - ANS-[(1+r1)(1+r2)(1+r3)]^(1/n) - 1
Time weighted return - ANS-[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - ANS-[N/(sum of (1/sample means))]
Position of observation - ANS-(n+1)*(k/100)
Excess kurtosis - ANS-Sample kurtosis - 3 (3 is normal kurtosis)
Mean absolute deviation - ANS-sum of: (mean - sample mean)/n-1
Variance - ANS-(x-mean)^2/N (population) and divided by (n-1) for a sample
, Coefficient of Variation - ANS-Sample standard deviation/sample mean
Sharpe Ratio - ANS-Risk of portfolio - risk free / Standard deviation of portfolio
Joint Probability - ANS-P(AB) = P(A|B) * P(B)
Addition rule - ANS-P(A or B) = P(A) + P(B) - P(AB)
Multiplication rule - ANS-P(A and B) = P(A)*P(B)
Total Probability Rule - ANS-P(A) = P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - ANS-P(x)*(x)
Covariance - ANS-P[(Ra - E(Ra) * (Rb - E(Rb)] - sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation - ANS-Covariance(A,B) / SDa*SDb
Portfolio expected return - ANS-weight times the E(R) of each stock
Portfolio variance - ANS-Wa^2*SDa^2 + Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
Baye's formula - ANS-P(new info) / unconditional probability of new info*prior prob of
event
Combination binomial - ANS-nCr - order doesn't matter
Permutation binomial - ANS-nPr - order matters
