# Shared Flashcard Set

## Details

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

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
 A 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
Term
 Harmonic mean
Definition
 HM = N / Sum(1/Xi )
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 EthicsMembers of the CFA Institute (including Chartered Financial Analyst [CFA] charterholders) and candidates for the CFA designation ("Members and Candidates") must: 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. Place the integrity of the investment profession and the interests of clients above their own personal interests. Use reasonable care and exercise independent professional judgment when conducting investment analysis, making investment recommendations, taking investment actions, and engaging in other professional activities. Practice and encourage others to practice in a professional and ethical manner that will reflect credit on themselves and the profession. Promote the integrity of, and uphold the rules governing, capital markets. 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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