CFA L1_0609 - Quant

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What is the formula for the mutual funds ratio used as a technical indicator?: (mutual fund cash / total fund assets)
When do you use the permutation formula nPr versus the combination formula nCr?: When order of selection matters, use the permutation formula
When is an unbiased estimator efficient: The variance of its sampling distribution is smaller than all the other unbiased estimators of the parameter you are trying to estimate.
Formula to calculate a confidence interval for a normal distribution on a population mean with a known variance: X+za/2 x (σ / √n ) WHERE x = point est., za/2 = reliability factor, and (σ / √n ) is the standard error
How do you determine the number of ways labels can be assigned?: Labeling is where there are n items of which each can receive one of k labels. The number of items that receive label "1" is n1 and the number that receive label "2" is n2, etc. Also, the following relationship holds: n1 + n2 + n3 +...+ nk = n. The number of ways labels can be assigned is: n! / (n1!) × (n2!) ×...× (nk!). On your TI financial calculator, factorial is [2nd], [x!]. Example: A portfolio consists of eight stocks. The goal is to designate four of the stocks as "long-term holds," designate three of the stocks as "short-term holds," and designate one stock a "sell." How many ways can these labels be assigned to the eight stocks? The answer is (8!) / (4! × 3! × 1!) = (40,320) / (24 × 6 × 1) = 280.
What test statistic is used when sampling from a non-normal distribution with a known variance and the sample size is large: Z-statistic
What is meant by "cross-sectional data?": Sample of observations taken at a single point in time.
Describe what a confidence interval is: In statistics, a confidence interval (CI) is an interval estimate of a population parameter. Instead of estimating the parameter by a single value, an interval likely to include the parameter is given. Thus, confidence intervals are used to indicate the reliability of an estimate. How likely the interval is to contain the parameter is determined by the confidence level or confidence coefficient. Increasing the desired confidence level will widen the confidence interval. For example, a confidence interval can be used to describe how reliable survey results are. In a poll of election voting-intentions, the result might be that 40% of respondents intend to vote for a certain party. A 95% confidence interval for the proportion in the whole population having the same intention on the survey date might be 38% to 42%. From the same survey date one may calculate a smaller 90% confidence interval for the proportion in the whole population of for instance 36% to 44%. All other things being equal, a survey result with a small CI is more reliable than a result with a large CI and one of the main things controlling this width in the case of population surveys is the size of the sample questioned. Confidence intervals and interval estimates more generally have applications across the whole range of quantitative studies.
How does a non-parametric test differ from a parametric test: Either do not consider a particular population parameter or have few assumptions about the population that is sampled.
What is the reliability factor for a 90% confidence interval?: 1.645
Definition of time-period bias: Relation does not hold over other time periods
Where can an analyst find a company's significant accounting methods and estimates: both the footnotes to the financial statements and Management's Discussion and Analysis
What do parametric tests rely on: assumptions regarding the distribution of the population and are specific to population parameters.
What are the properties of a standard normal random variable, Z?: The standard normal random variable, denoted Z, has mean equal to 0 and variance equal to 1
When is a chi squared test used: hypothesis tests concerning the variance of a normally distributed population. H0: σ2 = σ02 and HA: σ2 ≠ σ02
How is variance calculated given a standard deviation statistic?: SD^2
Standard error of the sample mean (known population): σX = σ / √n where: σX = standard error of the sample mean, σ = standard deviation of the population, n = size of the sample
What are the three desirable properties of an estimator?: The three desirable properties of an estimator are unbiasedness, efficiency, and consistency.
The Sharpe ratio and the safety first ratio differ in one of the three variables used to calculate them, which one.: Since each ratio has the standard deviation of returns in the denominator, the difference depends upon the effect on the numerator. The risk-free rate (in the Sharpe ratio) and the threshold rate (in the SF ratio) are subtracted from the expected return
What is the definition of a discrete uniform random variable: one where the probabilities are equal for all possible outcome. The discrete uniform distribution is characterized by an equal probability for each outcome. A single die roll is an often-used example of a uniform distribution. In combining two random variables, such as coin flip or die roll outcomes, the sum will not be uniformly distributed.
What test statistic is used when sampling from a normal distribution with an unknown variance and the sample size is large: t-statistic
What do quartiles, quintiles, deciles, and percentiles measure?: Quartile .25, quintiles .20, deciles .10, and .01 percentiles
Type II error: Failure to reject a hypothesis when it is actually false
Calculate Z-Score from percentile: sample mean + (z-score corresponding to % input)(standard deviation)
What happens if a return distribution has positive excess kurtosis and the analyst uses statistical models that do not account for the fatter tails?: The analyst will underestimate the likelihood of very bad or very good outcomes. The fatter the tails associated with the positive kurtosis, the higher the probabilities of very high and very low returns as compared to the normal distribution with kurtosis = 3.0
Advance-decline line: running total sum of the daily advances less the declines on the NYSE
What do "smart money" technicians look at ?: 1. Confidence index (yield on high quality bond / yield on average quality) 2. T-bill - Eurodollar spreads 3. Debit (margin) balances in brokerage accounts
Definition of confidence intervals: range of estimated values within which the actual value of the parameter will lie with a given probability of 1 - α. The term α is also called the significance level of the test. The probability 1 - α is also known as the confidence level.
What is a binomial random variable?: The binomial random variable may be defined as the number of "successes" in a given number of "trials" where the outcome can either be "success" or "failure." The probability of success is constant for each trial, and the trials are independent. A trial is like a mini-experiment and the final outcome is the number of successes in the series of n trials. Example: Assuming a binomial distribution, compute the probability of drawing three black beans from a bowl of black and white beans if the probability of selecting a black bean in any given attempt is 0.6. You will draw five beans from the bowl. This reflects a basic property of binomial outcomes. They take on whole number values that must start at zero up to the upper limit n. The set of all outcomes may look like this: (0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11)
What is the reliability factor for a 99% confidence interval?: 2.575
How is the investment advisory ratio used by technical traders?: When the investment advisory ratio (bearish opinions/total opinions) is equal to or greater than 0.60, it means that investors are bearish, and contrary-opinion technicians are bullish.
What is a money weighted return?: The money-weighted return applies the concept of internal rate of return (IRR) to investment portfolios. The money-weighted rate of return is defined as the internal rate of return on a portfolio, taking into account all cash inflows and outflows. The beginning value of the account is an inflow as are all deposits into the account. All withdrawals from the account are outflows, as is the ending value.
What is the reliability factor for a 95% confidence interval: 1.960
What are the two defining properties of a probability?: There are two defining properties of probability. 1. The probability of any event "i" is between zero and one. 2. If a set of events: E1, E2, ....En, are mutually exclusive and exhaustive, then the sum of the probabilities of those events equals one.
What is the Barron's Confidence Index (aka Confidence Index, CI) and how is it used by smart money investors?: Smart-money technicians believe that in periods of confidence about the future direction of the economy, fixed income investors try to increase yields by selling higher quality bonds and buying lower quality bonds, which tends to narrow the yield spread between lower quality and higher quality bonds. The Confidence Index is high-quality bond yields divided by average bond yields. If average bond yields increase relative to high-quality bond yields (that is, if credit spreads are widening), the Confidence Index will decrease.
Time-series data definition: Observations taken over a period of time at specific and equally spaced time intervals.
What does the TED spread measure?: The TED spread is an indicator of perceived credit risk in the general economy.[1] This is because T-bills are considered risk-free while LIBOR reflects the credit risk of lending to commercial banks. When the TED spread increases, that is a sign that lenders believe the risk of default on interbank loans (also known as counterparty risk) is increasing. Interbank lenders therefore demand a higher rate of interest, or accept lower returns on safe investments such as T-bills. When the risk of bank defaults is considered to be decreasing, the TED spread decreases.[2]
How is the OTC to NYSE volume indication used by technical traders?: Investors are considered bearish if the OTC volume is decreasing relative to NYSE volume.
How do you calculate a continuously compounded return if provided with an annual return number (calculator)?: LN(1+return) = LN(1 + 10%) = 9.53%
What is the probability density function for a true normal distribution?: From negative to positive infinity.
What test statistic is used when sampling from a normal distribution with a known variance and the sample size is small: Z-statistic
Formula to show hypothesis comparing paired differences: H0: μd = μdz, HA: μd ≠ μdz
What a continuous variable is NOT: countable
Definition of survivorship bias: Using only surviving mutual funds, hedge funds, etc.
How do the following variables affect the size (width) of a confidence interval: sample size, reliability, degrees of freedom?: Sample size, DOF decrease width; reliability factor increases (confidence interval = point estimate +/- reliability factor x standard error. Sample size increases sqrt(n) in denominator if standard error formula, same with DOF
What causes skewness?: The magnitude of positive deviations from the mean being either larger or smaller than the magnitude of negative deviations from the mean.
Calculate variance of the distribution of sample means: σ2/n, the population variance divided by the sample size.
When comparing p values to significance levels, when should we reject the null hypothesis: p-value < significance level
What are two cases where there is no known sample statistic (Z or T)?: 1. Small sample, known variance, non normal distribution 2. Small sample, unknown variance, non normal distribution
What is relative frequency?: Relative frequency is calculated by dividing the absolute frequency of each return interval by the total number of observations. Simply stated, relative frequency is the percentage of total observations falling within each interval. Cumulative relative frequency is calculated by summing the absolute or relative frequencies starting at the lowest interval and progressing through the highest. Cumulative absolute frequency or cumulative relative frequency for any given interval is the sum of the absolute or relative frequencies up to and including the given interval
What test statistic is used when sampling from a normal distribution with a known variance and the sample size is large: Z-statistic
What are the characteristics of a consistent estimator?: Provides a more accurate estimate of the parameter as the sample size increases.
What does the "safety-first" criterion focus on?: The safety-first criterion focuses on shortfall risk which is the probability that a portfolio's value or return will not fall below a given threshold level. The safety-first criterion usually dictate choosing a portfolio with the lowest probability of falling below the threshold level or return. According to the safety-first criterion, the optimal portfolio is the one that has the largest value for the SFRatio (mean − threshold) / Standard Deviation.
Does the expected value in a binomial distribution have to be a whole number?: The expected value is n × p. A simple example shows us that the expected value does not have to be a whole number: n = 5, p = 0.5, n × p = 2.5.
What are the components of required interest rate on a security: Made up of the nominal rate which is in turn made up of the real risk-free rate plus the expected inflation rate. It should also contain a liquidity premium as well as a premium related to the maturity of the security.
What are the 3 smart money indicators?: * Confidence index (yield on high-quality bond/yield on average-quality bonds) When the spread between high and low quality bond narrows, the confidence index increases, indicating a bullish market. * T-bill - Eurodollar yield spreads * Debit (margin) balances in brokerage accounts
What test statistic is used when sampling from a normal distribution with an unknown variance and the sample size is small: t-statistic
Why are time weighted returns used in the investment industry?: Time-weighted returns are not affected by the timing of cash flows. Money-weighted returns, by contrast, will be higher when funds are added at a favorable investment period or will be lower when funds are added during an unfavorable period. Thus, time-weighted returns offer a better performance measure because they are not affected by the timing of flows into and out of the account.
What test statistic is used when sampling from a non-normal distribution with an unknown variance and the sample size is large: t-statistic
Bayes formula to determine likelihood of one of two types of bonds defaulting and the bond is of type B: P(B / default) = P(default and B) / P(default), P(B) weight x default risk, P(default) = (weight A x default risk) + (weight B x default fisk), P(B / default) = P(default and B) / P(default) = 0.075 / 0.355 = 0.211
What are the reliability factors for 90 %, 95%, and 99% confidence intervals?: 1.65, 1.96, and 2.58.
Definition of sample selection bias: Selection is non-random
Description of how a test statistic is calculated: comparing the estimated parameter with the hypothesized value of the parameter ( sample statistic - hypothesized value)/standard error of the sample statistic
When comparing p values to significance levels, when should we fail to reject the null hypothesis: p-value > significance level. The p-value is the smallest level of significance at which the null hypothesis can be rejected. The smaller the p-value, the stronger the evidence against the null hypothesis and in favor of the alternative hypothesis.Consider an experiment where you've measured values in two samples, and the means are different. How sure are you that the population means are different as well? There are two possibilities: * The populations have different means. * The populations have the same mean, and the difference you observed is a coincidence of random sampling. The P value is a probability, with a value ranging from zero to one. It is the answer to this question: If the populations really have the same mean overall, what is the probability that random sampling would lead to a difference between sample means as large (or larger) than you observed?
What are the 6 indicators that contrarian technicians use?: 1. Mutual fund cash positions. 2. Investor credit balances in brokerage accounts. 3. Opinions of investment advisory services. 4. OTC vs. NYSE volume. 5. CBOE put/call ratio. 6. Stock index futures.
What are the three types of probabilities?: An empirical probability is established by analyzing past data. An a priori probability is determined using a formal reasoning and inspection process. A subjective probability is the least formal method of developing probabilities and involves the use of personal judgment.
Definition of data mining bias: Significant relationships that have occurred by chance
When is a statistical result not statistically significant: When we fail to reject the null hypothesis
What is a probability distribution?: Probabilities must be zero or positive, but a probability distribution is not necessarily normally distributed. A probability distribution describes the probabilities of all the possible outcomes for a random variable. The probabilities of all possible outcomes must sum to 1. A simple probability distribution is that for the roll of one fair die; there are six possible outcomes and each one has a probability of 1/6, so they sum to 1. The probability distribution of all the possible returns on the S&P 500 index for the next year is a more complex version of the same idea.
The advance-decline line is used to measure . . .: breadth of the market
What test statistic is used when sampling from a non-normal distribution with a known variance and the sample size is small: not available
Why is it more difficult to reject the null hypothesis with a t-distribution than a z-distribution: Thicker tails mean more observations away from the center of the distribution (i.e., more "outliers")
What is an F-Test and when is it used?: When the samples are random, independent of each other, and generated by normally distributed populations, and F-test is used. Simply divide the larger sample variance by the smaller sample variance. Use the F-table to accept reject. F-table shows one sided significance levels.
What is the expression for the confidence level of a two-tailed test: -critical value ≤ test statistic ≤ +critical value
What is the difference between how technicians and supporters of EMH view the speed at which new information is priced into securities?: Followers of the efficient market hypothesis believe prices adjust quickly to new information. Technicians believe that the reaction is slow. Followers of the efficient market hypothesis believe that the reaction is quick.
What test statistic is used when sampling from a non-normal distribution with an unknown variance and the sample size is small: not available
significance level of the test: Type I error, or rejection of a hypothesis when it is actually true
Decile calculation: (n + 1)(decile / 10)
What is sampling error: The difference between a sample statistic (the mean, variance, or standard deviation of the sample) and its corresponding population parameter (the true mean, variance or standard deviation of the population).
What is a conditional probability?: Probability of an event given that another event has occurred.
What is the formula for Bayes formula?: P((information/event)/information x P(Event)
What is the formula for the position of a percentile in an array with n entries in ascending order?: (n+1) x (y/100). Y is the percentage point at which we are dividing the distribution, and L is the location (L) of the percentile (P) in the array sorted in ascending order. Given 16 variables, the 75th percentile (3rd quartile) is (16 + 1)x75/100 = 12.75, between 12th and 13th items arranged in ascending order.
What does a binomial distribution assume about a random variable X?: That the variable is discrete
Describe the cross elasticity of complements.: The cross-elasticity for complements is negative. Think of soft drinks and pizzas. When the price of drinks increases, the quantity of pizzas sold decreases as people demand less pizza. The price and quantity change move in opposite directions. The closer the complement, the cross elasticity is large, i.e. movies and popcorn. (percentage change in quantity demanded / percentage change in price of a complement)
If we cannot determine whether a distribution is normal, how can we determine the proportion of observations that lie within k standard deviations of the mean?: We cannot assume that the distribution is normal, so we cannot rely on the z-table. We must use Chebyshev's inequality, which states that for any distribution, the proportion of observations that lie within k standard deviations of the mean is at least 1 - 1 / k2, we calculate 1 - 1 / 2.42 = 1 - 0.17361 = 0.82639, or 82.6%
Definition of a consistent estimator: One for which the accuracy of the parameter estimate increases as the sample size increases. As the sample size increases, the standard error of the sample mean falls, and the sampling distribution bunches more closely around the population mean.
What is the definition of a probability function?: A probability function specifies that a random variable takes on a specific value
power of the test: Type II, errors occur when you fail to reject a hypothesis
Definition of look-ahead bias: Basing the test at a point in time on data not available at that time
When is a statistical result statistically significant: When we reject the null hypothesis
What is a key feature of the outcomes in a binomial distribution?: Binomial distributions are either successes or failures.
Type I error: Rejection of a hypothesis when it is actually true
What is the formula for effective annual yield?: The effective annual yield (EAY) is based on a 365-day year and accounts for compound interest. EAY = (1 + holding period yield)365/t − 1. The holding period yield formula is (price received at maturity − initial price + interest payments) / (initial price) = (10,000 − 9,900 + 0) / (9,900) = 1.01%. EAY = (1.0101)^365/40 − 1 = 9.60%.
Kurtosis reading indicating fat tails: Positive values of excess kurtosis (kurtosis > 3) indicate fat tails. Positive values of kurtosis do not indicate a distribution that has fat tails.
When margin balances in brokerages accounts increase what group of technicians would be interested, and what direction would they take on the market.: Smart money, long. An increase in margin (debit) balances in brokerages accounts means investors are bullish, this would be a bullish sign to smart-money technicians.
What is the formula to calculate holding period yield: [(ending cash flows - beginning cash flows)/beginning price] x 100 *OR* [(P1-P0+D1)/P0]-1
What is an a priori probability?: An a priori probability is based on formal reasoning rather than on historical results or subjective opinion.
Formula to show an hypothesis indicating a two tailed test: H0: μ = μ0 vs. HA: μ ≠ μ0
What is the formula for calculating a test statistic?: The test statistic = (sample mean - hypothesized mean) / (sample standard deviation / (sample size1/2)) = (X − µ) / (s / n1/2) = (65,000 - 62,500) / (2,600 / 1251/2) = (2,500) / (2,600 / 11.18) = 10.75.
Sampling error of the mean calculation: sample mean − population mean = X − µ
Binomial probability formula for the probability of x success in n trials: p(x) = P(X = x) = [number of ways to choose x from n]px(1 − p)^n − x WHERE number of ways to choose x from n = n! / {(n − x)!x!}
What are some of the risks of using a normal distribution for analyzing equity returns?: 1) In most equity series, kurtosis is greater than 3 2) Underestimates extreme returns 3) Option returns are skewed, since normal distribution is symmetrical, a portfolio with many options is hard to model in a normal distribution 4) normal distribution extends beyond 0 continuously, equity returns do not
What is a continuous distribution?: A continuous random variable is one for which the number of possible outcomes is infinite, even if lower and upper bounds exist. The normal distribution is an example of a continuous distribution. Random variables measuring time, rates of return and weight will be continuous.
What is the relationship between normal and lognormal distributions?: For any random variable that is normally distributed its natural logarithm (ln) will be lognormally distributed. The opposite is also true: for any random variable that is lognormally distributed its natural logarithm (ln) will be normally distributed.
Confidence level: 1 - significance level
What is the formula to determine probability of a contrinuous distribution?: Random variable X follows a continuous uniform distribution over 12 to 28, that is a = 12, and b = 28. The probability of an outcome between 15 and 25 is: P(15 ≤ X ≤ 25) = (25 − 15) / (28 − 12) = 10 / 16 = 0.625
A permanent decrease in demand in a perfectly competitive industry will . . .: A permanent decrease in demand in a perfectly competitive industry will in the short-run cause the demand curve to shift to the left, causing prices to fall. However, in the long-run, firms will leave the industry due to economic losses. As firms leave the industry, supply decreases (i.e., the supply curve shifts left-ward) thus increasing prices back to the equilibrium where economic profit is zero.
What is an empirical probability?: An empirical probability is established by analyzing past data. For example, a basketball player has scored at least 22 points in each of the season's 18 games. Therefore, there is a high probability that he will score 22 points in tonight's game.
Correlation coefficient (SS2, R8): COV(Ri,Rj)/(sdRI,sdRJ)
What is the formula for mean average deviation?: To get the mean absolute deviation, sum the deviations around the mean (ignoring the sign), and divide by the number of observations
What would a significance level of a = 0.05 indicate: 5% chance of rejecting a true null hypothesis, also stated, this is the probability of making a Type I error
What are the defining characteristics of a normal distribution?: 1. Completed described by two parameters - its mean and variance 2. Skewness of 0 (it is symmetric) 3. Kurtosis is 3 4. Excess kurtosis is 0 5. Mean, median, and mode are all equal 6. A normal distribution is a continuous symmetric probability distribution
What is an unconditional probability?: The probability of an event without any restriction, can be thought of as a stand alone probability. "What is the prob. of this event A"
How is standard deviation calculated?: SQRT(variance)
Formula to show an hypothesis indicating a one tailed test: H0: μ ≤ μ0 vs. HA: μ > μ0
What is the formula to calculate effective annual yield: [(1+HPY)^365/t ]- 1
When is a F-distributed test statistic used: To test the equality of the variances of two normally distributed populations, based on two independent random samples H0: σ1^2 = σ2^2
What is the formula used to calculate a money market yield?: HPY × (360 / t) = 0.0190 × (360 / 110) = 0.06218 = 6.22%.
What is a time weighted return?: Time-weighted rate of return measures compound growth. It is the rate at which $1.00 compounds over a specified performance horizon. Time-weighting is the process of averaging a set of values over time. The annual time-weighted return for an investment may be computed by performing the following steps: 1. Value the portfolio immediately preceding significant additions or withdrawals. Form subperiods over the evaluation period that correspond to the dates of deposits and withdrawals. 2. Compute the holding period return (HPR) of the portfolio for each subperiod. 3. Compute the product of (1 + HPR) for each subperiod to obtain a total return for the entire measurement period [i.e., (1 + HPR1) × (1 + HPR2)× ...× (1 + HPRn)]. If the total investment period is greater than one year, you must take the geometric mean of the measurement period return to find the annual time-weighted rate of return.
What is the threshold level for the CBOE put-call index?: When the CBOE put call ratio is equal to or greater than 0.50, this suggests that investors are bearish and thus contrary-opinion technicians are bullish.
Describe the cross elasticity of substitutes.: The cross-elasticity for substitutes is positive. Think of burgers and pizzas. When the price of burgers increases, the quantity of pizzas sold increases as people demand less burgers and more pizza. Both the price and quantity change move in the same direction. (percentage change in quantity demanded / percentage change in price of a substitute)
How do you determine the standard deviation of two stocks in a portfolio?: The standard deviation of two stocks that are perfectly positively correlated is the weighted average of the standard deviations: 0.5(18.9) + 0.5(14.73) = 16.82%. This relationship is true only when the correlation is one. Otherwise, you must use the formula: SQRT(w1o1 + w2o2 + 2w1w2o1o2*corr(1,2)
Compare the shape of a t-distribution to a normal distribution.: less peaked (but symmetrical), more probability in the tails, As the degrees of freedom, df, increases, however, its shape approaches that of the normal distribution
Given a confidence level, how is a significance level calculated?: 1 - confidence level
The central limit theorem states that, for any distribution, as n gets larger . . .: the variance of the distribution of sample means is reduced, and the distribution of sample means approximates a normal distribution
What does a binomial distribution assume about the inter-dependence of trials?: That they are independent
What is the addition rule for probability?: Given events A and B, the probability that A or B occurs, or both occur, is equal to the probability that A occurs, plus the probability that B occurs, minus the probability that A and B occur. P(A or B) = P(A) + P(B) - P(AB)
What are the 7 steps in hypothesis testing?: Depending upon the author there can be as many as seven steps in hypothesis testing which are: 1. Stating the hypotheses. 2. Identifying the test statistic and its probability distribution. 3. Specifying the significance level. 4. Stating the decision rule. 5. Collecting the data and performing the calculations. 6. Making the statistical decision. 7. Making the economic or investment decision.
What is the probability of events that are 1 standard deviation and 1.65 standard deviations away from the mean?: 1 sd = 68% two tailed, 34% one tailed; 1.65 sd = 90% two-tailed, 45% one-tailed
Formula to calculate a confidence interval for a normal distribution on a population mean with an unknown variance: X+ta/2 x (σ / √n ) WHERE x = point est., ta/2 = t-reliability factor (critical t value) with n-1 degrees of freedom, and (σ / √n ) is the standard error
Stratified random sampling definition: Uses a classification system to separate the population into smaller groups based on one or more distinguishing characteristics. From each subgroup, or stratum, a random sample is taken and the results are pooled. The size of the samples from each stratum is based on the size of the stratum relative to the population.
What is the formula and definition associated with the "power of a test": probability of rejecting the null hypothesis when it is false, 1 − probability (Type II error)
How is the null hypothesis variable determined?: The alternative hypothesis is determined by the theory or the belief. The researcher specifies the null as the hypothesis that he wishes to reject (in favor of the alternative).
Standardize a random variable: (observation - population mean)/standard deviation
One of the underlying assumptions of technical analysis is that supply and demand is driven by . . .: Rational and irrational behavior during all market conditions.
Definition of point estimates: Single (sample) values used to estimate population parameters.
What do we need to look at before we imply that statistical significance implies economic significance: Transaction costs, taxes, risk
What are the steps to calculate covariance given joint probability?: 1. Calculate expected return on each stock (probability x return) 2. Determine deviations from expected return at each level for each stock 3. Multiply product of deviations at each level for each stock 4. Multiply product of combined deviations at each level against the probabilty of the condition 5. Add up the probability weighted conditions at each condition, this is covariance of joint probability
What is a discrete random variable?: One where we can list all the possible outcomes and for each possible outcome there is a measurable, positive probability
When measuring dispersion around the mean, what is the significant problem? What is the workaround this problem?: The deviations around the mean always sum to 0. A solution is to examine the mean absolute deviations around the mean; ignore the signs of the deviations around the mean.
What is the formula for calculating the probability of a continuous uniform distribution?: (F value - bottom of range)/(top of range - bottom of range) = (180 - 175)/(205 - 175) = 16.7%

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