CFA Level 1 - 101 -Complete Exam Study
Guide with Verified Answers |
Guaranteed A+
Addition Rule of Probability
ADDITION: P(A or B) = P(A) + P(B) - P(AB)
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
Sharpe Ratio
Sharpe Ratio = (E(R) - RFR) / σ
Larger ratio is better
If (Rt) is higher than RFR, then it becomes Safety First Ratio
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)
Standard Error of Sample Mean
σ / n^½
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)
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"
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
Effective Annual Yield
EAY = (1 + (i/n))^n - 1
Stated Rate = (EAY^(1/n) - 1) * n
Continuous Compounding
ln(EAY) = continuously compounded stated rate
e^(continuously compounded stated rate) = EAY
Type I Error
Incorrectly rejecting a true null hypothesis
(convicting an innocent person is Type I)
Type II Error
,Failure to reject a false null hypothesis
(failure to convict a guilty person is Type II)
Significance Level / Power of a Test
Significance Level = Probability of Type I
Power of a Test = (1 - Probability of Type I)
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
Covariance (Sample)
Covariance of random variables A and B from sample with historical data with n observations
Correlation Coefficient
COVab / σaσb
Bank Discount Yield (Discount basis)
(Discount / Face Value) * (360 / Days)
Money Market Yield
(HPY) * (360 / Days)
Bond Equivalent Yield
(HPY) * (365 / Days)
Most appropriate for comparing yields!
Technical Analysis Indicators
, Continuation:
TRIANGLE (or pennant) = Suggests a pause in the stock price movement that will be followed by
a continuation of the previous trend
Reversal:
HEAD AND SHOULDERS = Suggests a future decline in the stock price regardless of prior trend
DOUBLE BOTTOM = Increasing stock price in the future (reversal of a downtrend)
Trendlines:
SUPPORT / RESISTANCE = Range that stock price trades in based on supply/demand. Stock is
"supported" from going below a certain low price, and "resists" going above a certain high price
Price Elasticity
%ΔQuantity / %ΔPrice = (ΔQ / ΔP) * (P₀ / Q₀)
Demand is elastic if less than -1
Demand is inelastic if 0 to -1
Income Elasticity
%ΔQuantity / %ΔIncome
Positive for normal good
Negative for inferior good
Cross-Price Elasticity
%ΔQuantity / %ΔPriceʳᵉˡᵃᵗᵉᵈ ᵍᵒᵒᵈ
Positive for substitutes
Negative for complements
Sources of Economic Growth
Increases in:
- Labor
- Physical Capital
- Technology
- Natural Resources
- Human Capital
Guide with Verified Answers |
Guaranteed A+
Addition Rule of Probability
ADDITION: P(A or B) = P(A) + P(B) - P(AB)
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
Sharpe Ratio
Sharpe Ratio = (E(R) - RFR) / σ
Larger ratio is better
If (Rt) is higher than RFR, then it becomes Safety First Ratio
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)
Standard Error of Sample Mean
σ / n^½
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)
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"
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
Effective Annual Yield
EAY = (1 + (i/n))^n - 1
Stated Rate = (EAY^(1/n) - 1) * n
Continuous Compounding
ln(EAY) = continuously compounded stated rate
e^(continuously compounded stated rate) = EAY
Type I Error
Incorrectly rejecting a true null hypothesis
(convicting an innocent person is Type I)
Type II Error
,Failure to reject a false null hypothesis
(failure to convict a guilty person is Type II)
Significance Level / Power of a Test
Significance Level = Probability of Type I
Power of a Test = (1 - Probability of Type I)
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
Covariance (Sample)
Covariance of random variables A and B from sample with historical data with n observations
Correlation Coefficient
COVab / σaσb
Bank Discount Yield (Discount basis)
(Discount / Face Value) * (360 / Days)
Money Market Yield
(HPY) * (360 / Days)
Bond Equivalent Yield
(HPY) * (365 / Days)
Most appropriate for comparing yields!
Technical Analysis Indicators
, Continuation:
TRIANGLE (or pennant) = Suggests a pause in the stock price movement that will be followed by
a continuation of the previous trend
Reversal:
HEAD AND SHOULDERS = Suggests a future decline in the stock price regardless of prior trend
DOUBLE BOTTOM = Increasing stock price in the future (reversal of a downtrend)
Trendlines:
SUPPORT / RESISTANCE = Range that stock price trades in based on supply/demand. Stock is
"supported" from going below a certain low price, and "resists" going above a certain high price
Price Elasticity
%ΔQuantity / %ΔPrice = (ΔQ / ΔP) * (P₀ / Q₀)
Demand is elastic if less than -1
Demand is inelastic if 0 to -1
Income Elasticity
%ΔQuantity / %ΔIncome
Positive for normal good
Negative for inferior good
Cross-Price Elasticity
%ΔQuantity / %ΔPriceʳᵉˡᵃᵗᵉᵈ ᵍᵒᵒᵈ
Positive for substitutes
Negative for complements
Sources of Economic Growth
Increases in:
- Labor
- Physical Capital
- Technology
- Natural Resources
- Human Capital
