CFA Level 1 Exam - Formulas
Nominal Interest Rate - ANS Nominal Int. Rate =
Real Rf Rate + Expected Inflation Rate
Required Interest Rate - ANS Required Rate =
Nominal Rf Rate + Default premium + liquidity premium + tenor premium
Effective Annual Rate (EAR) - ANS EAR =
(1 + stated annual rate / m)^m - 1
m: # of compounding periods / yr
Future Value (FV) - ANS FV =
PV*(1 + I/Y)^N
PV: amounted invested today
I/Y: rate of return per compounding period
N: total # of compounding periods
Present Value (PV) - ANS PV =
FV / (1+I/Y)^N
I/Y: rate of return per compounding period
N: total # of compounding periods
PV of a Perpetuity - ANS PV of a Perpetuity =
PMT / (I/Y)
Holding Period Return (HPR) - ANS HPR =
(Ending Value (incl. an CFs) / Beginning Value)) - 1
Bank Discount Yield (BDY) - ANS BDY =
,(D / F)*(360 / t)
D: Dollar discount (difference between face value and purchase price)
F: face value (par value)
t: # of days remaining until maturity
Holding Period Yield (HPY) - ANS HPY =
((P1 - P0 + D1) / P0))
OR
((P1 + D1) / P0)) - 1
P0: Price paid for instrument
P1: Price to be received at maturity
D1: interest payment (distribution to holder of instrument)
Effective Annual Yield (EAY) - ANS EAY =
(1 + HPY)^(365 / t) - 1
EAY can be converted to HPY by using the reciprocal of the exponent and plugging EAY into
formula in place of HPY
Money Market Yield (CD Equivalent Yield) - ANS MMY =
HPY*(360 / t)
Bond Equivalent Yield (BEY) - ANS BEY =
[(1 + EAY)^(1/2) - 1] * 2
Geometric Mean - ANS Geometric Mean =
((1+R1)*(1+R2)....(1+R10))^(1/n) - 1
Harmonic Mean = N / (1/Xi)
Xi: Observation or data point, there are N values of Xi - ANS Harmonic Mean =
, N / Sum of (1/Xi)
Xi: Observation or data point, there are N values of Xi
Position of the observation at a given percentile (y) w/ n data points sorted in ascending order: -
ANS Position of the observation at a given percentile (y) w/ n data points sorted in ascending
order:
Ly = (n+1)*(y/100)
Chebyshev's Inequality - ANS % of observations that lie w/in k standard deviations of the mean
=
1 - 1 / K^2
k: # of standard deviations
Coefficient of Variation (CV) - ANS CV =
Standard Deviation of X / Avg. Value of X
Sharpe Ratio - ANS Sharpe Ratio =
(Rp - Rf) / Std. of Portfolio Returns
Rp: portfolio return
Rf: risk-free return
Excess Kurtosis - ANS Excess Kurtosis =
sample kurtosis - 3
*Kurtosis of a Normal Distribution has a value of 3
Addition Rule of Probability: P (A or B) - ANS Addition Rule of Probability: P (A or B) =
P(A) + P(B) - P(A*B)
*The addition rule of probability is used to determine the probability that at least one of the 2
events will occur
Total Probability Rule: P(A) - ANS Total Probability Rule: P(A) =
P (A | B1)*P(B1) + P (A | B2)*P(B2)...+......P (A | Bn)*P(Bn)
Nominal Interest Rate - ANS Nominal Int. Rate =
Real Rf Rate + Expected Inflation Rate
Required Interest Rate - ANS Required Rate =
Nominal Rf Rate + Default premium + liquidity premium + tenor premium
Effective Annual Rate (EAR) - ANS EAR =
(1 + stated annual rate / m)^m - 1
m: # of compounding periods / yr
Future Value (FV) - ANS FV =
PV*(1 + I/Y)^N
PV: amounted invested today
I/Y: rate of return per compounding period
N: total # of compounding periods
Present Value (PV) - ANS PV =
FV / (1+I/Y)^N
I/Y: rate of return per compounding period
N: total # of compounding periods
PV of a Perpetuity - ANS PV of a Perpetuity =
PMT / (I/Y)
Holding Period Return (HPR) - ANS HPR =
(Ending Value (incl. an CFs) / Beginning Value)) - 1
Bank Discount Yield (BDY) - ANS BDY =
,(D / F)*(360 / t)
D: Dollar discount (difference between face value and purchase price)
F: face value (par value)
t: # of days remaining until maturity
Holding Period Yield (HPY) - ANS HPY =
((P1 - P0 + D1) / P0))
OR
((P1 + D1) / P0)) - 1
P0: Price paid for instrument
P1: Price to be received at maturity
D1: interest payment (distribution to holder of instrument)
Effective Annual Yield (EAY) - ANS EAY =
(1 + HPY)^(365 / t) - 1
EAY can be converted to HPY by using the reciprocal of the exponent and plugging EAY into
formula in place of HPY
Money Market Yield (CD Equivalent Yield) - ANS MMY =
HPY*(360 / t)
Bond Equivalent Yield (BEY) - ANS BEY =
[(1 + EAY)^(1/2) - 1] * 2
Geometric Mean - ANS Geometric Mean =
((1+R1)*(1+R2)....(1+R10))^(1/n) - 1
Harmonic Mean = N / (1/Xi)
Xi: Observation or data point, there are N values of Xi - ANS Harmonic Mean =
, N / Sum of (1/Xi)
Xi: Observation or data point, there are N values of Xi
Position of the observation at a given percentile (y) w/ n data points sorted in ascending order: -
ANS Position of the observation at a given percentile (y) w/ n data points sorted in ascending
order:
Ly = (n+1)*(y/100)
Chebyshev's Inequality - ANS % of observations that lie w/in k standard deviations of the mean
=
1 - 1 / K^2
k: # of standard deviations
Coefficient of Variation (CV) - ANS CV =
Standard Deviation of X / Avg. Value of X
Sharpe Ratio - ANS Sharpe Ratio =
(Rp - Rf) / Std. of Portfolio Returns
Rp: portfolio return
Rf: risk-free return
Excess Kurtosis - ANS Excess Kurtosis =
sample kurtosis - 3
*Kurtosis of a Normal Distribution has a value of 3
Addition Rule of Probability: P (A or B) - ANS Addition Rule of Probability: P (A or B) =
P(A) + P(B) - P(A*B)
*The addition rule of probability is used to determine the probability that at least one of the 2
events will occur
Total Probability Rule: P(A) - ANS Total Probability Rule: P(A) =
P (A | B1)*P(B1) + P (A | B2)*P(B2)...+......P (A | Bn)*P(Bn)
