CFA Level 1 – 101 Questions and Answers
1. Addition Rule of Probability: ADDITION: P(A or B) = P(A) + P(B) - P(AB)
2. Roy's Safety First Criterion: Safety First Ratio =
(E(R) - Rₜ) / σ Larger ratio is better
If (Rₜ) is risk free rate, then it becomes Sharpe Ratio
3. Sharpe Ratio: Sharpe Ratio = (E(R) -
RFR) / σ Larger ratio is better
If (Rt) is higher than RFR, then it becomes Safety First Ratio
4. Central Limit Theorem: If we take samples of a population, with a large enough
sample size, the distribution of all sample means is normal with:
-A mean equal to the population mean
-A variance equal to the population variance divided by sample size (σ² / n)
5. Standard Error of Sample Mean: σ / n^½
6. Binomial Probability: One of two possible outcomes (i.e.
success/failure) Possible outcomes can be demonstrated in binomial
tree
Use "nCr" on calculator to solve:
,nCr = P(success)^x * P(failure)^(n-x)
7. P - Value: Based on a calculated test statistic, rather than a significance level
(which is chosen) p-value = smallest significance level at which an analyst can reject
the null hypothesis
one-tailed test - "less than or
equal to" two-tailed test - "equal
to"
8. Cumulative Distribution Function: Gives the probability that a random
variable will have an outcome less than or equal to a specific value (represented by F(x))
F(x) = probability of an outcome less than or equal to x
Standard normal table (z) shows cumulative probabilities
9. Effective Annual Yield: EAY = (1 +
(i/n))^n - 1 Stated Rate = (EAY^(1/n) - 1) * n
10. Continuous Compounding: ln(EAY) = continuously compounded stated rate
e^(continuously compounded stated rate) = EAY
11. Type I Error: Incorrectly rejecting a true null hypothesis
,(convicting an innocent person is Type I)
12. Type II Error: Failure to reject a false null hypothesis
(failure to convict a guilty person is Type II)
13. Significance Level / Power of a Test: Significance Level = Probability of Type I
Power of a Test = (1 - Probability of Type I)
14. Covariance (Probability Model): Covariance of random variables A and B from
probability model
On the calculator:
1) Enter returns for set A and joint probabilities for AB; find mean A
2) Enter returns for set B and joint probabilities for AB; find mean B
3) Multiply each joint probability AB by each set's returns minus means
(ex: P(AB1)(A1 - Mean A)(B1 - Mean B) + P(AB2)(A2 - Mean A)(B2 - Mean B) + ... + P(ABn)(An - Mean
A)(Bn - Mean B))
4) The summed total is your covariance
15. Covariance (Sample): Covariance of random variables A and B torical data
with n
from sample with his observations
, 16. Correlation Coefficient: COVab / σaσb
17. Bank Discount Yield (Discount basis): (Discount / Face Value) * (360 / Days)
18. Money Market Yield: (HPY) * (360 / Days)
19. Bond Equivalent Yield: (HPY) * (365 / Days)
Most appropriate for comparing yields!
1. Addition Rule of Probability: ADDITION: P(A or B) = P(A) + P(B) - P(AB)
2. Roy's Safety First Criterion: Safety First Ratio =
(E(R) - Rₜ) / σ Larger ratio is better
If (Rₜ) is risk free rate, then it becomes Sharpe Ratio
3. Sharpe Ratio: Sharpe Ratio = (E(R) -
RFR) / σ Larger ratio is better
If (Rt) is higher than RFR, then it becomes Safety First Ratio
4. Central Limit Theorem: If we take samples of a population, with a large enough
sample size, the distribution of all sample means is normal with:
-A mean equal to the population mean
-A variance equal to the population variance divided by sample size (σ² / n)
5. Standard Error of Sample Mean: σ / n^½
6. Binomial Probability: One of two possible outcomes (i.e.
success/failure) Possible outcomes can be demonstrated in binomial
tree
Use "nCr" on calculator to solve:
,nCr = P(success)^x * P(failure)^(n-x)
7. P - Value: Based on a calculated test statistic, rather than a significance level
(which is chosen) p-value = smallest significance level at which an analyst can reject
the null hypothesis
one-tailed test - "less than or
equal to" two-tailed test - "equal
to"
8. Cumulative Distribution Function: Gives the probability that a random
variable will have an outcome less than or equal to a specific value (represented by F(x))
F(x) = probability of an outcome less than or equal to x
Standard normal table (z) shows cumulative probabilities
9. Effective Annual Yield: EAY = (1 +
(i/n))^n - 1 Stated Rate = (EAY^(1/n) - 1) * n
10. Continuous Compounding: ln(EAY) = continuously compounded stated rate
e^(continuously compounded stated rate) = EAY
11. Type I Error: Incorrectly rejecting a true null hypothesis
,(convicting an innocent person is Type I)
12. Type II Error: Failure to reject a false null hypothesis
(failure to convict a guilty person is Type II)
13. Significance Level / Power of a Test: Significance Level = Probability of Type I
Power of a Test = (1 - Probability of Type I)
14. Covariance (Probability Model): Covariance of random variables A and B from
probability model
On the calculator:
1) Enter returns for set A and joint probabilities for AB; find mean A
2) Enter returns for set B and joint probabilities for AB; find mean B
3) Multiply each joint probability AB by each set's returns minus means
(ex: P(AB1)(A1 - Mean A)(B1 - Mean B) + P(AB2)(A2 - Mean A)(B2 - Mean B) + ... + P(ABn)(An - Mean
A)(Bn - Mean B))
4) The summed total is your covariance
15. Covariance (Sample): Covariance of random variables A and B torical data
with n
from sample with his observations
, 16. Correlation Coefficient: COVab / σaσb
17. Bank Discount Yield (Discount basis): (Discount / Face Value) * (360 / Days)
18. Money Market Yield: (HPY) * (360 / Days)
19. Bond Equivalent Yield: (HPY) * (365 / Days)
Most appropriate for comparing yields!
