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Quantitative Formulas for CFA Exam
59
Economics
Graduate
05/30/2011

Additional Economics Flashcards

 


 

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Term
Multinomial Formula: used for labeling problems in assigning k different labels to n members, with n1 labels of the first type, n2 labels of the second type, etc. ( note: n = n1 + n2 +…+ nk)
Definition

The total number of possibilities =

n! / (n1!n2!…nk!)

Term

Combination: Choosing r objects from n total objects when order does not matter

 

Permutation: Choosing r objects from n total objects when order does matter

 

Definition

nCr= n! / [(n-r)! x r!]


nPr = n! / (n-r)!

Term
Money Market Yield formula
Definition
MMY = HPY (360/t)
Term
Money-Weighted Rate of Return (formula / how to calc)
Definition

Set total outflows equal to inflows discounted at rate (r) appropriately for each period (per 1 goes over (1+r), per 2 goes over (1+r) sqrd, etc)

Use IRR fxn.

 

Term
Time-Weighted Rate of Return (formula/how to calculate)
Definition

For each period, do (Inflows-Outflows+DivRec)/Outflows where Outflows is appropriate cost unit for inflow. Get % for each period.

 

TWrr: [(1+HPY1)*(1+HPY2)]^(1/t) - 1

Term
Total Probability Rule
Definition

 

P(A) = P(A|B1)P(B1) + P(A|B2)P(B2) + ... + P(A|Bn)P(Bn)

 

Term

Chebyshev’s Inequality

(and what it measures)

Definition

For any distribution, the minimum perentage of observations that lie w/i k standard deviations of mean is:

1 - (1/k^2). If k=3 -- 1- (1/9) = 89%.

Term
Convert HPY to EAY
Definition
EAY = (1 + HPY)365/t − 1
Term
Convert EAY into HPY
Definition
HPY = (EAY + 1)t/365 − 1
Term
Continuous compounding
Definition

The continuously compounded rate of return = ln( S1 / S0 ) = ln(108,427 / 127,350) = –16.09%. 

Term
Z-statistic, calculating
Definition

With a large sample size (175) the z-statistic is used. The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic =

 

(sample mean – hypothesized mean) / (population standard deviation / (sample size)1/2 = (X − µ) / (σ / n1/2) = (67,000 – 58,500) / (5,200 / 1751/2) = (8,500) / (5,200 / 13.22) = 21.62.

Term
F-test
Definition
Term
Significance level of test equals:
Definition
The probability of a Type I error is equal to the significance level of the test.
Term
Power of a test
Definition
The power of a test is 1 minus the probability of a Type II error.
Term
Empirical probability
Definition
An empirical probability is established by analyzing past/historical data.
Term
The lower the alpha the ____ the confidence interval
Definition
The lower the alpha level, the wider the confidence interval.
Term
Degree of confidence
Definition
The degree of confidence is equal to one minus the alpha level, and so the wider the confidence interval, the higher the degree of confidence and the lower the alpha level. Note that the lower alpha level requires a higher reliability factor which results in the wider confidence interval. 
Term
A priori probability
Definition
An a priori probability is one based on logical analysis rather than on observation or personal judgement
Term

Calculate annual yield of T-bill on BEY basis (Given HPY)

ex. 91-day treasury has HPY of 1.5%

Definition

BEY = HPY x (365/t)

=1.5% x (365/91) = 6.02%

Term
Subjective Probability
Definition
subjective probability is the least formal method of developing probabilities and involves the use of personal judgment.
Term
Unbiased estimator
Definition
Has an expected value equal to the true value of the population parameter
Term
Consistent estimator
Definition
More accurate the greater the sample size
Term
Efficient Estimator
Definition
Has the sampling distribution that is less than that of any other unbiased estimator
Term
Positively skewed distributions (mean, median, mode)
Definition

When skewed to the right, generally:

 

Mean > Median > Mode

Term
Coefficient of Variation (higher CV implies more or less risk?)
Definition

CV = SD / Arithmetic Mean

 

More risk.

Term
Joint probability definition
Definition
The probability that 2+ events happen concurrently
Term
Standard normal distribution
Definition
Has a mean of 0 and a SD of 1
Term
90% Confidence Interval
Definition
X% +/- 1.65(s)
Term
95% Confidence Interval:
Definition
X% +/- 1.96(s/sqrt(n))
Term
99% Confidence Interval
Definition
X% +/- 2.58(s)
Term
According to central limit theorem, the sample mean for large sample sizes will be:
Definition
normally distributed regardless of the distribution of the underlying population
Term
Sampling error (definition)
Definition
The difference betwwen the observed value of a statistic and the value it is intended to estimate
Term
Simple random sample
Definition
A sample obtained in such a way that each elemt of the population has an equal probability of being selected
Term
EAR with semiannual compounding
Definition
EAR = (1 + annual rate/2)2 - 1
Term
Covariance definition
Definition
A measure of how the returns of two assets tend to move over time
Term
Correlation Coefficient
Definition
CC = Covariance / (s1s2)
Term
Cross-sectional data
Definition
Sample of observations taken at a single point in time
Term
Time-series data
Definition
Observations taken at specific and equally spaced points in time
Term
Standard Deviation of two stocks that are perfecctly positively correlated
Definition

Weighted average of the two standard deviations:

 

WA(SA) + WB(SB)

Term
Sharpe Ratio
Definition
(Mean portfolio return - Risk-Free Return) / SD
Term
Permutation Formula when order matters:
Definition
n! / (n-r)!
Term
Standard error of the sample mean (formula)
Definition
Population SD / sqrt(n)
Term
Univariate distribution
Definition
Describes a single random variable
Term
Multivariate distribution
Definition
Specifies the probabilities for a group of random variables
Term
When testing hypotheses about the population mean when the population SD is UNKNOWN, the population is normal a/o the sample is large:
Definition
tn-1 = (X - M0) / (s / sqrt(n))
Term
T-test must be used when:
Definition
Sample size is small, population is normal and the population variance is unknown
Term
Robert Mackenzie, CFA, buys 100 shares of GWN Breweries each year for four years at prices of C$10, C$12, C$15 and C$13 respectively. GWN pays a dividend of C$1.00 at the end of each year. One year after his last purchase he sells all his GWN shares at C$14. Mackenzie calculates his average cost per share as [(C$10 + C$12 + C$15 + C$13) / 4] = C$12.50. Mackenzie then uses the internal rate of return technique to calculate that his money-weighted annual rate of return is 12.9%. Has Mackenzie correctly determined his average cost per share and money-weighted rate of return?
Definition

Because Mackenzie purchased the same number of shares each year, the arithmetic mean is appropriate for calculating the average cost per share. If he had purchased shares for the same amount of money each year, the harmonic mean would be appropriate. Mackenzie is also correct in using the internal rate of return technique to calculate the money-weighted rate of return. The calculation is as follows:


Time

Purchase/Sale

Dividend

Net cash flow

0

-1,000

0

-1,000

1

-1,200

+100

-1,100

2

-1,500

+200

-1,300

3

-1,300

+300

-1,000

4

400 × 14 = +5,600

+400

+6,000

 

CF0 = −1,000; CF1 = −1,100; CF2 = −1,300; CF3 = −1,000; CF4 = 6,000; CPT → IRR = 12.9452.

Term
Covariance for historical data
Definition
cov1,2 = {Σ[(Rstock A − Mean RA)(Rstock B − Mean RB)]} / (n − 1)
Term
Mean to use when calculating average cost/share when same number of shares purchased each year
Definition
Arithmetic mean
Term
Mean to use when shares purchased for same amount of money each year
Definition

Harmonic mean

 

N

_____

 

Sum(1/Xi)

Term

P-value of a test (what it means)

 

How you decide to accept/reject null hypothesis at given significance level

Definition

P-value is smallest significance level at which null hypothesis can be rejected.

 

If test p-value < 10%, test can be rejected at 10% significance level

 

If p-value > 1%, test cannot be rejected at 1% significance level

Term
The future value of a given lump sum, calculated using continuous compounding, is:
Definition
FV = PV × ert
Term

Negative kurtosis (name) is ______ (more/less) peaked and has _______ (thinner/fatter) tails compared to normal

 

Positive excess kurtosis (name) is ______ peaked and has ______ tails than normal

Definition

Negative:

Platykurtic distribution

LESS peaked

THINNER tails

 

Positive:

Leptokurtic distribution

MORE peaked

FATTER tails

Term
Finding t-statistic
Definition

t = [(X1 - X2) - (PopMean1 - PopMean2)]

/

[(s2 / n1) + (s2/n2)]0.5

 

If not given, pooled estimate of sample variance (s2) =

 

s2 = [(n1 - 1)s21 + (n2 - 1)s22]

/

(n1 + n2 - 2)

Term
Required rate of return (nominal interest rate formula)
Definition
E(R) = (1 + RFRreal)(1 + Inflation Premium)(1+Risk Premium) - 1
Term
Harmonic mean
Definition
HM = N / Sum(1/X)
Term
Population Variance + Sample Variance
Definition

Sigma2 = [(Sum(Xi-M)2 / N]

 

s2 = [(Sum(Xi-M)2 / n-1]

Term
Standard Error
Definition
sx = s / sqrt(n)
Term
Code of ethics
Definition

The Six Components to the Code of Ethics
Members of the CFA Institute (including Chartered Financial Analyst [CFA] charterholders) and candidates for the CFA designation ("Members and Candidates") must:

  1. Act with integrity, competence, diligence, respect, and in an ethical manner with the public, clients, prospective clients, employers, employees, colleagues in the investment profession, and other participants in the global capital markets.
  2. Place the integrity of the investment profession and the interests of clients above their own personal interests.
  3. Use reasonable care and exercise independent professional judgment when conducting investment analysis, making investment recommendations, taking investment actions, and engaging in other professional activities.
  4. Practice and encourage others to practice in a professional and ethical manner that will reflect credit on themselves and the profession.
  5. Promote the integrity of, and uphold the rules governing, capital markets.
  6. Maintain and improve their professional competence and strive to maintain and improve the competence of other investment professionals. 

    Read more: http://www.investopedia.com/exam-guide/cfa-level-1/ethics-standards/code-ethics.asp#ixzz1wah44csX


Read more: http://www.investopedia.com/exam-guide/cfa-level-1/ethics-standards/code-ethics.asp#ixzz1waglg7Mu

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