CFA Level 1 Random Deck 1 Flashcards
those that have failed are not included in the results
Survivorship bias - hedge funds
arises if a study uses information that was not available on a test date
Look ahead bias
arises if a test is based on a certain time period
time -period bias
the formulate used to calculate a point estimate
Estimator
uses sample data to calculate the range of possible (or probable) values that an unknown paramount can take, with a given probability (1-level of significance)
confidence interval
Refers to the degree of confidence that the relevant parameter will lie in the computed interval
Level of significance
degrees of freedom
sample size minus 1 (n-1)
When the variance of a normally distributed population is not know, we use the _____ to construct confidence interval.
t-distribution
Desirable properties of an estimator
- Unbiasedness; 2. Efficiency; 3: Consistency
When is the t-value used?
Normal/non-normaul distribution with unknown variance (note if sample is small it can’t be done)
Rejecting the null hypothesis when it is actually true
Type I Error
Failing to reject the null hypothesis when it is actually false
Type II Error
The ____ represents the probability of making a Type II Error
significance level (1-level of significance)
The power of a test is the
probability of correctly rejecting the null hypothesis when it is false. Power of a test = 1 - P(Type II Error)
What is shortfall risk?
Risk that the portfolio will fall below some minimum acceptable level over some time horizon.
A parametric test has as least one of two characteristics:
Features: 1) Concerned with parameters, or defining features of a distribution 2) Definite set of assumptions
Test to see if the variance amongst two independent populations is equal (normally distributed population)
F-Test (one tail - right - rejection area)
test to see if the variance of a single normally distributed population is different
Chi-Square Test (two tail - reject null if outside interval)
Key Rate Duration
measures a bond’s sensitivity to a shift at one or more maturity segments of the yield thrive which results in a change to the yield curve shape
Modified and Effective duration mention a bond’s sensitivity to _______ shifts in the entire curve
Parallel - all rates change by the same amount in the same direction
What the only difference in the formulas used to calculate modified and effective duration?
Modified uses Change in YIELD in the Denominator; Effective uses Change in CURVE
What effect does a put option have on a bond’s duration?
reduces effective duration - most likely you’ll get your cash back sooner.
Money Duration is calculated as the _______ times the ______
annual modified duration x full price
Convexity measure the ______ order effect.
Second order effect on a bond’s percentage price change given a change in the YTM.
Duration measures the ______ order effect.
First order effect - change in the bond’s price given a change in YTM
Define Convexity
Convexity adjusts the percentage price change estimate provided by modified duration to better approximated the true relationship between a bond’s price and its yield to maturity which is a curve line (convex).
CFR
Corporate Family Rating - based on the overall creditworthiness of the issues. Typically based on the issuer’s senior unsecured debt
CCR
Corporate Credit Rating - applies to a specific financial obligation of the issuer and is based on factors such the issue’s relative seniority ranking in priority of claims and covenants.
Four C’s of Credit Analysis
- Capacity
- Collateral
- Covenants
- Character
Key components of credit risk
risk or probability of default AND loss severity in the event of default (product of the two equals the expected loss)
Arbitrage plays an important role in market efficiency
- Help to determine “correct” price; 2. Improve market efficiency (accurate pricing)
What is tenor?
Certain period of time over which a series of cash flows are exchanged in a SWAP
Swap settlement amount formula
settlement amount = (fixed - (LIBOR + Spread) x (portion of time) x (principal or notional amount) Note. The rates will be the clue as to which party is getting the payment. Lower rate receives settlement payment.
The worst possible loss for a holder of a put option is:
Easy - it’s just the price of the Put Option. They are not obligated to do anything else.
The worst possible loss for a holder of a call option is:
Easy - it’s just the price of the Call Option. They are not obligated to do anything else.
Key components of the CFA Institute Code of Ethics (6 bullets pg 6 Wiley)
act with integrity, competence, diligence, respect, place integrity of investment profession and clients above self, reasonable care, maintain and improve their professional competence
Seven Standards of Professional Conduct
- Professionalism 2. Integrity of Capital Markets 3. Duties to clients 4. Duties to Employers 5. Investment Analysis, Recommendations and Actions 6. Conflicts of interest 7. Responsibilities as a CFA Institute Member or Candidate
Standard 1: Professionalism
A. Knowledge of the Law B. Independence and Objectivity C. Misrepresentation D. Misconduct
What is “applicable law”?
law that governs the member’s or candidate’s conduct. Local Law.
Regarding compliance to laws, members should follow the -
“more strict law”, be it applicable law or the Code and Standards
Name two types of market manipulation:
Information-based AND Transaction-based
Standard 2: Integrity of Capital Markets
A. Material Nonpublic information B. Market Manipulation
Standard 3: Duties to Clients
A. Loyalty, Prudence and Care B. Fair Dealing C. Suitability D. Performance Presentation E. Preservation of Confidentiality
Standard 4: Duties to Employers
A. Loyalty B. Additional Compensation Arrangements C. Responsibilities to Supervisors
Standard 5: Investment Analysis, Recommendations, and Actions
A. Diligence and Reasonable Basis B. Communication with Clients and Prospective Clients C. Record Retention
Standard 6: Conflicts of Interest
A. Disclosure of Conflicts B. Priority of Transactions C. Referral Fees
Standard 7: Responsibilities as a CFA Institute Member or CFA Candidate
A. Conduct as members and candidates in the CFA program B. Reference to CFA Institute, the CFA designation, and the CFA program
The standard in the investment management industry is to express returns on a _________.
Time-weighted basis: - not affected by cash withdrawals or contributions to portfolio - averages holding period return over time
Measurement Scales
NOIR (Nominal, Ordinal, Interval, Ratio)
Measurement Scales: N
Nominal - weakest level of measurement; count of data but no rank
Measurement Scales: O
Ordinal - sort of data ranked according to a certain characteristic
Measurement Scales: R
Ratio - strongest level of measurement, money
Measurement Scales: R
Ratio - strongest level of measurement, money
Chebyshev’s Inequality
Method of calculating an appropriate value for the proportion of observations in a data set that lie with a given number (k) of standard deviations from the mean. 1 - (1/k2)
Coefficient of Variation
CV=Allows for the comparison of relative dispersion. Standard deviation / sample mean. Or in otherwords, if speaking about investment returns, risk per unit of total return. Scale free measure. Can be used when data sets of significantly different means and units of measurement.
s/x = CV
Sharpe Ratio
Measure excess return per unit of risk.
Mean Portfolio Return - Risk Free Return
Standard deviation of portfolio returns
Mean Standard Deviation (MAD)
average of all absolute values (AV) of deviations in a data set. Recall that the sum of deviations from the arithemtic mean equal zero. Therefore, AV are used.
Semivariance
average of squared deviations below the mean (note still used (n-1) in the denominator). Semideviation is simply the square root of the semivariance.
Describe a postively skewed distribution
skewed to the right (this means skinny side stretched to the right - long tail on the right). Bulk of data pushed to left.
Mode < Median < Mean
Described a negatively skewed distribution
skewed to the left (this means skinny side stretched to the left- long tail on the left). Bulk of data pushed to right. Mean is pulled down by the lower outliers in the skinny tail.
Mean < Median < Mode
Negative (left) Skewed distribution - sample skewness is _______
Sample skewness is negative - numerator is formula will be a negative number because the average number of devations below the mean is large than the average of deviations above the mean.
Positive (right) Skewed distribution - sample skewness is _______
Skinny tail on right. Sample skewness is positive - numerator is formula will be a positive number because the average number of devations abover the mean is larger than the average of deviations below the mean.
Kurtosis
measures the extent to which a distribution is more or less peaked than a normal distribution. A normal distribution has a kurtosis of 3.
What does the following statement mean: P (AB)
Joint probability - what is the probability of both A and B occuring?
What does the following statement mean: P (A | B)
Conditional probability - the probability of event A occuring give that event B has occured.
P( A | B) = P (AB)/P(B)
Multiplication rule for probability
P (AB) = P( A | B) x P(B)
Addition rule for probabilities
P (A or B) = P(A) + P(B) - P(AB)
Calculates the probability of at least one of A and B occuring.
Covariance
measures how a random variables varies with another random variable
Limitations of Covariance
- Difficult to compare covariance across data sets that have different scales
- difficult to interpret as it can take on extreme values
- does not tell us anything about the strength of the relationship between variabes
Describe Covariance Formula
Cov(RA,RB) = Σ Probability * (RA - E(RA)) * (RB - E(RB))
Correlation Coefficient
COVA,B/σ(RA)σ(RB)
Covariance divided by product of standard deviations of variables
When is the Combinations Formula used?
nCr is used when the order in which the items are assigns the labels in NOT important.
Example: 20 people try out for a team. 11 are chosen. How many different ways can the eleven member team be chose from the 20 aspirants?
20! / (9!)(11!)
When is the Permutations formula used?
nPr is used when the order in which the items are assigned to two groups is an important considerations.
Example: 20 people try out for a team. 11 are chosen AND must be ranked according to skill level. How many different ways can the eleven member team be chose from the 20 aspirants?
20! / (20-11)!
n! / (n - r)!
Should result is a greater number than Combinations because, like a padlock, the order of numbers matters. For example, the actual combinations of numbers I use to unlock my padlock (1,3 = 3,1) is much less than the acutal number or unique sequences that could be used to unlock the paddlock.
When would we use the Labeling formula?
When we are working with three or more groups of predetermined size and each item must be labled as a member of one of the groups.
In this scenario we need to elimate the counting of redundances.
Refer to page 203 Wiley for example.
12! / 6! x 4! x 2!
Probability estimated from data as a relative requency of occurrence is an ______.
Empirical Probability
A probability drawing on personal or subjective judgement is a ___________.
Subjective probability.
A probability based on logical analyis is an ____.
an a priori probability
The unconditional probability of an event A is denoted by __
P(A)
Unconditional probabilities are also called ____
marginal probabilities
The probability of an event A given and event B is denoted as
P(A | B)
Number of unique covariances depending on ‘n’
n (n - 1) / 2
Shortfall Risk
The probability that a portfolio’s value or return E(Rp), will fall below a particular target value or return (RT) over a given period.
Roy’s safety first criterion states….
that an optimal porfolio minimized the probablity that the actual portfolio return, Rp, will fall below the target return, RT
Define: Binomial Random Variable
defined as the number of success in n Bernoulli trials (which are trials that produce one of two outcomes). Binomial distribution is used to make probability statemtns about a crecord of successes and failures or about anything with binary (twofold) outcomes.
Binomial Distribution
P(X=x) = nCx(p)x(1-p)n-x
p = probability of success
1-p = probabilty of failure
nCx = number of possible outcomeshave x success in n trials
Variance of a Binomial Random Variable
σ2 = n x p x (1-p)
Standard Error
Amout by which our sample statistic differs from our population statistic
standard error typically = standard deviation of sample / square root of number of observations
we don’t use standard deviation of population in the numerator because we often do not know it.
Desirable Properties of Estimator:
- Unbiasedness
- Efficiency
- Consistency
t-Distribution used in the following scenarios:
- to construct confidence intervals for a normally (or approx. normal) distributed population whose variance is unknown when the sample size is small (n < 30)
- non-normally distributed population whose variance is unknown if the sample size is large (n >= 30)
When the population is normally distributed we ___.
use the z-statistic if the population variance is known
use the t-statistic if the population variance is unknown
When the population is non-normally distributed we ___.
selection of the appropriate statistic depends on the sample size and whether the population variance is known
- if population variance is known and sample size is large (n>30) we use z-statistic
- if population variance is unknown and sample size is large (n>30) we use z-statistic or t-statistic. A t-statistic will give more conservative answer
The probability (1 – α) is referred to as the confidence level while α refers to ___________.
the significance level
Normal Good
a good that is consumer in greater quantities as income increases
Inferior good
as income rises, spend less on good. income elasticity is less than zero (negative).
Profit maximization occurs:
- difference between TR and TC is greatest
- MR = MC
- MRP (marginal revenue product) equals the resource cost for each type of input
Economic profit
Economic Profit = Accounting Profit - Total Opportunity Costs
Accounting Profit
bascially financial statement net income
Accounting Profit = Economic Profit + Normal Profit
Normal Profit
is the level of accounting profit needed to just cover the implicit opportunity costs ignored in accounting costs. Cost of equity is a typical example.
In the long run, all inputs to a firm are ________
variable - they can be changed. Adjusted. You can sell an asset, leave a business line, etc. Short term is a different story.