CFA LEVEL 1 FEB 2026 with all Correct & 100% Verified
Answers |Latest Version |Already Graded A+
Holding period return without dividends ✔Correct Answer-(New - Old) / Old
Holding period return with dividends ✔Correct Answer-(New - Old + Dividend) / Old
Annualized return ✔Correct Answer-(1 + HPR)^(365/days) - 1
Continuously compounded return ✔Correct Answer-ln(1+HPR)
Arithmetic mean ✔Correct Answer-"normal" mean
sum / number of numbers
Geometric mean ✔Correct Answer-[ (1+r1)*(1+r2)*...*(1+rn)]^(1/n) - 1
Harmonic mean ✔Correct Answer-N / [(1/X1)+(1/X2)+...+(1/Xn)]
Where n = sample mean
What is a harmonic mean used for ✔Correct Answer-it helps determine the average cost of shares
purchased over time
Trimmed mean (x%) ✔Correct Answer-When you exlude the highest (x/2)% and the lowest (x/2)%.
If it's a 5% trimmed mean, you exlude the highest 2.5% and lowest 2.5% of all your data
Winsorized mean (x%) ✔Correct Answer-Rather than eliminating the highest (x/2)% and the lowest
(x/2)%, you find the substitute the value at the highest and lowest (x/2) percentile of the data
Sample variance ✔Correct Answer-s² = Σ ( xi - x̄ )² / ( n - 1 )
Sample standard deviation ✔Correct Answer-Square root of sample variance
Intuitive definition of variance ✔Correct Answer-A variance measures the squared distance of how
far, on average, a group of observations lies from a mean
Intuitive definition of standard deviation ✔Correct Answer-Standard deviation is the square root of
variance, which gives us a result that is easier to interpret because the units of the result are the
same as the original units in the problem, as opposed to being square units. Both SD and variance
measure how far, on average, a group of observations is from a mean
Target downside semideviation ✔Correct Answer-SQRT ( [(X1 - target)^2 + (X2 - target)^2 +...+(Xn -
target)^2] / (n - 1))
Same formula as SD but instead of dispersion about a mean, we're looking for dispersion about some
target number that is pre-set
Coefficient of variation ✔Correct Answer-SD / Mean
,Intuitive definition of coefficient of variation ✔Correct Answer-A coefficient of variation expresses
how much dispersion exists relative to the mean of a distribution. This allows us for direct
comparison of dispersions across different data sets
Bayes' Forula ✔Correct Answer-P(A|B) = (P(B|A) / P(B)) * P(A)
Expected return ✔Correct Answer-E(X) = (P(X1) * X1) + (P(X2) * X2) +...+ (P(Xn) * Xn)
Think expected value
Correlation coefficient of A and B ✔Correct Answer-Corr(A,B) = Cov(A,B) / (SD(A)*SD(B))
Covariance of x and y ✔Correct Answer-((X1-Xm)(Y1-Ym) + (X2-Xm)(Y2-Ym) +...+(Xn-Xm)(Ym-Yn)) /
n-1
Change to n for population covariance
Expected return of a 2-stock portfolio ✔Correct Answer-E(Rp) = Wa*E(Ra) + Wb*E(Rb)
Variance of a 2-stock portfolio ✔Correct Answer-(w^2(A) * σ^2(A)) + (w^2(B) * σ^2(B)) +
2w(A)w(B)σ(A)σ(B)⍴(AB)
Roy's Safety First Ratio ✔Correct Answer-(expected return - target return) / SD
Normal distribution standard deviations ✔Correct Answer-68% of observation fall within +/- 1σ
90% of observations fall within +/- 1.65σ
95% of observations fall within +/- 1.96σ
99% of observations fall within +/- 2.58σ
Z-score ✔Correct Answer-(observation - population mean) / standard deviation
Intuitive definition of a z-score ✔Correct Answer-a measure of how many standard deviations you
are away from the norm (average or mean)
Central limit theorem ✔Correct Answer-The theory that, as sample size increases, the distribution
of sample means of size n, randomly selected, approaches a normal distribution.
Standard error ✔Correct Answer-SD / sqrt(n)
Intuitive definition of a standard error ✔Correct Answer-Standard error tells us how much a
sample mean would differ from the actual population mean. Smaller standard error implies that the
sample mean is close to the actual population mean
Jackknife resampling ✔Correct Answer-Calculate multiple sample means, each with one
observation removed, then calculate the SD of those sample means
,Bootstrap sampling ✔Correct Answer-Draw multiple samples of size n from the data set, taking the
mean of the samples each time and then taking a new sample of the same size, then find the
standard deviation of the sample means
Null hypothesis ✔Correct Answer-a statement or idea that can be falsified, or proved wrong
This one always has the equals sign in it - greater than or equal to, less than or equal to
Alternative hypothesis ✔Correct Answer-What we can conclude if there is sufficient evidence to
reject the null hypothesis
Test of mean - type of stat and degrees of freedom ✔Correct Answer-t or z
n-1
Test of difference in means - type of stat and degrees of freedom ✔Correct Answer-t
n1 + (n2 - 2)
Test of mean differences - type of stat and degrees of freedom ✔Correct Answer-t
n-1
Test of variance - type of stat and degrees of freedom ✔Correct Answer-chi square
n-1
Test of equal variances - type of stat and degrees of freedom ✔Correct Answer-F
(n1-1), (n2-1)
Test of correlation - type of stat and degrees of freedom ✔Correct Answer-t
n-2
Test of independence - type of stat and degrees of freedom ✔Correct Answer-chi square
(rows - 1) * (columns - 1)
Test of regression slope (significance) - type of stat and degrees of freedom ✔Correct Answer-F
1, n-2
Test of regression slope (value) - type of stat and degrees of freedom ✔Correct Answer-t
n-2
Linear regression ✔Correct Answer-y = b0 + b1X1 + e1
Y = dependent variable
b0 = y-intercept
, b1 = slope
X1 = independent variable
e1 = error term
estimated slope term ✔Correct Answer-Cov(X,Y) / var(x)
SST ✔Correct Answer-sum(actual - mean)^2
SSR ✔Correct Answer-sum(predicted - mean)^2
SSE ✔Correct Answer-sum(actual - predicted)^2
R^2 ✔Correct Answer-SSR / SST
Intuitive definition of R^2 ✔Correct Answer-Percentage of variation in the dependent variable
explained by the variation in the independent variable
Functional forms (log-lin, lin-log, log-log) ✔Correct Answer-the first one refers to the dependent
variable (Y) and the second one refers to the independent variable (X)
Confidence interval ✔Correct Answer-Y(hat) +/- (Crit Value * Standard Error of Forecast)
Intuitive definition of a confidence interval ✔Correct Answer-the range of values within which a
population parameter is estimated to lie
MSE ✔Correct Answer-Mean Squared Error
SSE / DoF
MSR ✔Correct Answer-Mean Squared Regression
SSR / number of independent variables
F-stat ✔Correct Answer-MSR/MSE
Assumptions of linear regressions ✔Correct Answer-There is a linear relationship between the
variables
Variance of the error terms is constant (homoskedasticity)
Error terms are not correlated with each other (independently distributed)
Error terms are normally distributed
Type I Error ✔Correct Answer-Reject a true null hypothesis
Type II Error ✔Correct Answer-Fail to reject a fale null hypothesis
Probability sampling ✔Correct Answer-When we know the probability in the population of each
sample member
Answers |Latest Version |Already Graded A+
Holding period return without dividends ✔Correct Answer-(New - Old) / Old
Holding period return with dividends ✔Correct Answer-(New - Old + Dividend) / Old
Annualized return ✔Correct Answer-(1 + HPR)^(365/days) - 1
Continuously compounded return ✔Correct Answer-ln(1+HPR)
Arithmetic mean ✔Correct Answer-"normal" mean
sum / number of numbers
Geometric mean ✔Correct Answer-[ (1+r1)*(1+r2)*...*(1+rn)]^(1/n) - 1
Harmonic mean ✔Correct Answer-N / [(1/X1)+(1/X2)+...+(1/Xn)]
Where n = sample mean
What is a harmonic mean used for ✔Correct Answer-it helps determine the average cost of shares
purchased over time
Trimmed mean (x%) ✔Correct Answer-When you exlude the highest (x/2)% and the lowest (x/2)%.
If it's a 5% trimmed mean, you exlude the highest 2.5% and lowest 2.5% of all your data
Winsorized mean (x%) ✔Correct Answer-Rather than eliminating the highest (x/2)% and the lowest
(x/2)%, you find the substitute the value at the highest and lowest (x/2) percentile of the data
Sample variance ✔Correct Answer-s² = Σ ( xi - x̄ )² / ( n - 1 )
Sample standard deviation ✔Correct Answer-Square root of sample variance
Intuitive definition of variance ✔Correct Answer-A variance measures the squared distance of how
far, on average, a group of observations lies from a mean
Intuitive definition of standard deviation ✔Correct Answer-Standard deviation is the square root of
variance, which gives us a result that is easier to interpret because the units of the result are the
same as the original units in the problem, as opposed to being square units. Both SD and variance
measure how far, on average, a group of observations is from a mean
Target downside semideviation ✔Correct Answer-SQRT ( [(X1 - target)^2 + (X2 - target)^2 +...+(Xn -
target)^2] / (n - 1))
Same formula as SD but instead of dispersion about a mean, we're looking for dispersion about some
target number that is pre-set
Coefficient of variation ✔Correct Answer-SD / Mean
,Intuitive definition of coefficient of variation ✔Correct Answer-A coefficient of variation expresses
how much dispersion exists relative to the mean of a distribution. This allows us for direct
comparison of dispersions across different data sets
Bayes' Forula ✔Correct Answer-P(A|B) = (P(B|A) / P(B)) * P(A)
Expected return ✔Correct Answer-E(X) = (P(X1) * X1) + (P(X2) * X2) +...+ (P(Xn) * Xn)
Think expected value
Correlation coefficient of A and B ✔Correct Answer-Corr(A,B) = Cov(A,B) / (SD(A)*SD(B))
Covariance of x and y ✔Correct Answer-((X1-Xm)(Y1-Ym) + (X2-Xm)(Y2-Ym) +...+(Xn-Xm)(Ym-Yn)) /
n-1
Change to n for population covariance
Expected return of a 2-stock portfolio ✔Correct Answer-E(Rp) = Wa*E(Ra) + Wb*E(Rb)
Variance of a 2-stock portfolio ✔Correct Answer-(w^2(A) * σ^2(A)) + (w^2(B) * σ^2(B)) +
2w(A)w(B)σ(A)σ(B)⍴(AB)
Roy's Safety First Ratio ✔Correct Answer-(expected return - target return) / SD
Normal distribution standard deviations ✔Correct Answer-68% of observation fall within +/- 1σ
90% of observations fall within +/- 1.65σ
95% of observations fall within +/- 1.96σ
99% of observations fall within +/- 2.58σ
Z-score ✔Correct Answer-(observation - population mean) / standard deviation
Intuitive definition of a z-score ✔Correct Answer-a measure of how many standard deviations you
are away from the norm (average or mean)
Central limit theorem ✔Correct Answer-The theory that, as sample size increases, the distribution
of sample means of size n, randomly selected, approaches a normal distribution.
Standard error ✔Correct Answer-SD / sqrt(n)
Intuitive definition of a standard error ✔Correct Answer-Standard error tells us how much a
sample mean would differ from the actual population mean. Smaller standard error implies that the
sample mean is close to the actual population mean
Jackknife resampling ✔Correct Answer-Calculate multiple sample means, each with one
observation removed, then calculate the SD of those sample means
,Bootstrap sampling ✔Correct Answer-Draw multiple samples of size n from the data set, taking the
mean of the samples each time and then taking a new sample of the same size, then find the
standard deviation of the sample means
Null hypothesis ✔Correct Answer-a statement or idea that can be falsified, or proved wrong
This one always has the equals sign in it - greater than or equal to, less than or equal to
Alternative hypothesis ✔Correct Answer-What we can conclude if there is sufficient evidence to
reject the null hypothesis
Test of mean - type of stat and degrees of freedom ✔Correct Answer-t or z
n-1
Test of difference in means - type of stat and degrees of freedom ✔Correct Answer-t
n1 + (n2 - 2)
Test of mean differences - type of stat and degrees of freedom ✔Correct Answer-t
n-1
Test of variance - type of stat and degrees of freedom ✔Correct Answer-chi square
n-1
Test of equal variances - type of stat and degrees of freedom ✔Correct Answer-F
(n1-1), (n2-1)
Test of correlation - type of stat and degrees of freedom ✔Correct Answer-t
n-2
Test of independence - type of stat and degrees of freedom ✔Correct Answer-chi square
(rows - 1) * (columns - 1)
Test of regression slope (significance) - type of stat and degrees of freedom ✔Correct Answer-F
1, n-2
Test of regression slope (value) - type of stat and degrees of freedom ✔Correct Answer-t
n-2
Linear regression ✔Correct Answer-y = b0 + b1X1 + e1
Y = dependent variable
b0 = y-intercept
, b1 = slope
X1 = independent variable
e1 = error term
estimated slope term ✔Correct Answer-Cov(X,Y) / var(x)
SST ✔Correct Answer-sum(actual - mean)^2
SSR ✔Correct Answer-sum(predicted - mean)^2
SSE ✔Correct Answer-sum(actual - predicted)^2
R^2 ✔Correct Answer-SSR / SST
Intuitive definition of R^2 ✔Correct Answer-Percentage of variation in the dependent variable
explained by the variation in the independent variable
Functional forms (log-lin, lin-log, log-log) ✔Correct Answer-the first one refers to the dependent
variable (Y) and the second one refers to the independent variable (X)
Confidence interval ✔Correct Answer-Y(hat) +/- (Crit Value * Standard Error of Forecast)
Intuitive definition of a confidence interval ✔Correct Answer-the range of values within which a
population parameter is estimated to lie
MSE ✔Correct Answer-Mean Squared Error
SSE / DoF
MSR ✔Correct Answer-Mean Squared Regression
SSR / number of independent variables
F-stat ✔Correct Answer-MSR/MSE
Assumptions of linear regressions ✔Correct Answer-There is a linear relationship between the
variables
Variance of the error terms is constant (homoskedasticity)
Error terms are not correlated with each other (independently distributed)
Error terms are normally distributed
Type I Error ✔Correct Answer-Reject a true null hypothesis
Type II Error ✔Correct Answer-Fail to reject a fale null hypothesis
Probability sampling ✔Correct Answer-When we know the probability in the population of each
sample member
