FORMULAS FOR THE WIN: A+ CFA
LEVEL 1 EQUATION MASTERY
GUIDE – 2026–2027
Time weighted return - THE CORRECT ANSWER-
[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - THE CORRECT ANSWER-[N/(sum of (1/sample
means))]
Position of observation - THE CORRECT ANSWER-(n+1)*(k/100)
Excess kurtosis - THE CORRECT ANSWER-Sample kurtosis - 3 (3 is
normal kurtosis)
Mean absolute deviation - THE CORRECT ANSWER-sum of: (mean -
sample mean)/n-1
Variance - THE CORRECT ANSWER-(x-mean)^2/N (population) and
divided by (n-1) for a sample
Coefficient of Variation - THE CORRECT ANSWER-Sample standard
deviation/sample mean
,Sharpe Ratio - THE CORRECT ANSWER-Risk of portfolio - risk free /
Standard deviation of portfolio
Joint Probability - THE CORRECT ANSWER-P(AB) = P(A|B) * P(B)
Addition rule - THE CORRECT ANSWER-P(A or B) = P(A) + P(B) -
P(AB)
Multiplication rule - THE CORRECT ANSWER-P(A and B) = P(A)*P(B)
Total Probability Rule - THE CORRECT ANSWER-P(A) =
P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - THE CORRECT ANSWER-P(x)*(x)
Covariance - THE CORRECT ANSWER-P[(Ra - E(Ra) * (Rb - E(Rb)] -
sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation - THE CORRECT ANSWER-Covariance(A,B) / SDa*SDb
Portfolio expected return - THE CORRECT ANSWER-weight times the
E(R) of each stock
Portfolio variance - THE CORRECT ANSWER-Wa^2*SDa^2 +
Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
, Baye's formula - THE CORRECT ANSWER-P(new info) / unconditional
probability of new info*prior prob of event
Combination binomial - THE CORRECT ANSWER-nCr - order doesn't
matter
Permutation binomial - THE CORRECT ANSWER-nPr - order matters
Binomial probability - THE CORRECT ANSWER-nCx * p^x * (1-p)^(n-
x)
Binomial Expected value - THE CORRECT ANSWER-nP
Binomial variance - THE CORRECT ANSWER-np(1-p)
90% confidence interval - THE CORRECT ANSWER-+/- 1.645 SDs
95% confidence interval - THE CORRECT ANSWER-+/- 1.96 SDs
99% confidence interval - THE CORRECT ANSWER-+/- 2.58 SDs
Z score - THE CORRECT ANSWER-(x-mean)/SD
Roy's safety first ratio - THE CORRECT ANSWER-(E(Rp) - Rtarget)/SD
Mean sampling error - THE CORRECT ANSWER-mean - miu
LEVEL 1 EQUATION MASTERY
GUIDE – 2026–2027
Time weighted return - THE CORRECT ANSWER-
[(1+HPY1)(1+HPY2)(1+HPY3)]^(1/n) - 1
Harmonic Mean - THE CORRECT ANSWER-[N/(sum of (1/sample
means))]
Position of observation - THE CORRECT ANSWER-(n+1)*(k/100)
Excess kurtosis - THE CORRECT ANSWER-Sample kurtosis - 3 (3 is
normal kurtosis)
Mean absolute deviation - THE CORRECT ANSWER-sum of: (mean -
sample mean)/n-1
Variance - THE CORRECT ANSWER-(x-mean)^2/N (population) and
divided by (n-1) for a sample
Coefficient of Variation - THE CORRECT ANSWER-Sample standard
deviation/sample mean
,Sharpe Ratio - THE CORRECT ANSWER-Risk of portfolio - risk free /
Standard deviation of portfolio
Joint Probability - THE CORRECT ANSWER-P(AB) = P(A|B) * P(B)
Addition rule - THE CORRECT ANSWER-P(A or B) = P(A) + P(B) -
P(AB)
Multiplication rule - THE CORRECT ANSWER-P(A and B) = P(A)*P(B)
Total Probability Rule - THE CORRECT ANSWER-P(A) =
P(A|B1)*P(B1)...+P(A|B2)*P(B2)
Expected Value - THE CORRECT ANSWER-P(x)*(x)
Covariance - THE CORRECT ANSWER-P[(Ra - E(Ra) * (Rb - E(Rb)] -
sum for all probabilities that sum to 1 OR
[SDa*SDb*correlation)
Correlation - THE CORRECT ANSWER-Covariance(A,B) / SDa*SDb
Portfolio expected return - THE CORRECT ANSWER-weight times the
E(R) of each stock
Portfolio variance - THE CORRECT ANSWER-Wa^2*SDa^2 +
Wb^2*SDb^2 + 2WaWb*SDa*SDb*Corr(a,b)
, Baye's formula - THE CORRECT ANSWER-P(new info) / unconditional
probability of new info*prior prob of event
Combination binomial - THE CORRECT ANSWER-nCr - order doesn't
matter
Permutation binomial - THE CORRECT ANSWER-nPr - order matters
Binomial probability - THE CORRECT ANSWER-nCx * p^x * (1-p)^(n-
x)
Binomial Expected value - THE CORRECT ANSWER-nP
Binomial variance - THE CORRECT ANSWER-np(1-p)
90% confidence interval - THE CORRECT ANSWER-+/- 1.645 SDs
95% confidence interval - THE CORRECT ANSWER-+/- 1.96 SDs
99% confidence interval - THE CORRECT ANSWER-+/- 2.58 SDs
Z score - THE CORRECT ANSWER-(x-mean)/SD
Roy's safety first ratio - THE CORRECT ANSWER-(E(Rp) - Rtarget)/SD
Mean sampling error - THE CORRECT ANSWER-mean - miu
