CFA Level 1 Quantitative Methods Exam 318 Questions with Answers,100% CORRECT

CFA Level 1 Quantitative Methods Exam 318 Questions with Answers Three ways interest rates can be thought of - CORRECT ANSWER First, they can be considered required rates of return—that is, the minimum rate of retur ...

CFA Level 1 Quantitative Methods Exam 318 Questions with Answers Three ways interest rates can be thought of - CORRECT ANSWER First, they can be considered required rates of return—that is, the minimum rate of return an investor must receive in order to accept the investment. Second, interest rates can be considered discount rates. In the example above, 5.26 percent is that rate at which we discounted the $10,000 future amount to find its value today. Thus, we use the terms "interest rate" and "discount rate" almost interchangeably. Third, interest rates can be considered opportunity costs. An opportunity cost is the value that investors forgo by choosing a particular course of action. In the example, if the party who supplied $9,500 had instead decided to spend it today, he would have forgone earning 5.26 percent on the money. So we can view 5.26 percent as the opportunity cost of current consumption. How are interest rates set in the marketplace? - CORRECT ANSWER Supply and demand Interest rate formula - CORRECT ANSWER r=Real risk-free interest rate+Inflation premium +Default risk premium+Liquidity premium+Maturity premium real risk-free interest rate - CORRECT ANSWER the single-period interest rate for a completely risk-free security if no inflation were expected. In economic theory, the real risk-free rate reflects the time preferences of individuals for current versus future real consumption. Inflation Premium - CORRECT ANSWER compensates investors for expected inflation and reflects the average inflation rate expected over the maturity of the debt Nominal Risk Free Interest Rate - CORRECT ANSWER The sum of the real risk-free interest rate and the inflation premium. (T-bill). Liquidity premium - CORRECT ANSWER compensates investors for the risk of loss relative to an investment's fair value if the investment needs to be converted to cash quickly. Maturity Premium - CORRECT ANSWER compensates investors for the increased sensitivity of the market value of debt to a change in market interest rates as maturity is extended, in general (holding all else equal). Simple Interest - CORRECT ANSWER Interest rate times the principle. Is simple or compound interest more important? - CORRECT ANSWER Compound. Important consequence of present value and future value being separated in time? - CORRECT ANSWER We can add amounts of money only if they are indexed at the same point in time. EAR formula - CORRECT ANSWER EAR = (1 + Periodic interest rate)^m - 1 EAR=e^rs−1 EAR = Non EAR - CORRECT ANSWER 0.0816=(1+Periodic rate)^2−1 1.0816=(1+Periodic rate)^2 (1.0816)^1/2−1=Periodic rate (1.04)−1=Periodic rate 4%=Periodic rate calculate the continuously compounded rate corresponding to an effective annual rate of 8.33% - CORRECT ANSWER Find interest rate that solves: EAR=e^rs−1 0.0833=e^rs−1 1.0833=e^rs To solve this equation, we take the natural logarithm of both sides. (Recall that the natural log of e^rs is ln e^rs=rs .) Therefore, ln 1.0833 = rs, resulting in rs = 8 percent. We see that a stated annual rate of 8 percent with continuous compounding is equivalent to an EAR of 8.33 percent. Difference between ordinary annuity and annuity due? - CORRECT ANSWER Annuity due has first cash flow that occurs immediately while ordinary annuity has first cash flow that occurs one period from now. future value annuity factor Also need to know PV annuity for ordinary annuity and annuity due perp formula Solve for interest rate and growth rate annual compounding periods needed to reach a value calculate size of payment annuity calculate amount needed now to fund future annuity calculate lump sum annuity - CORRECT ANSWER FV=A[(1+r)^n - 1 / r] (1+r)^n = FV/PV N ln(1+r) =ln(2) N = ln(2) / ln(1+r) ln(2)/ln(1.07) = 10.24 Cash flow additivity principle - CORRECT ANSWER the idea that amounts of money indexed at the same point in time are additive Working capital management - CORRECT ANSWER Management of the company's short-term assets and short-term liabilities. Steps in computing and applying NPV Rule - CORRECT ANSWER 1) Identify all cash flows associated with the investment—all inflows and outflows.1 2) Determine the appropriate discount rate or opportunity cost, r, for the investment project.2 3) Using that discount rate, find the present value of each cash flow. (Inflows have a positive sign and increase NPV; outflows have a negative sign and decrease NPV.) 4) Sum all present values. The sum of the present values of all cash flows (inflows and outflows) is the investment's net present value. 5) Apply the NPV rule: If the investment's NPV is positive, an investor should undertake it; if the NPV is negative, the investor should not undertake it. If an investor has two candidates for investment but can only invest in one (i.e., mutually exclusive projects), the investor should choose the candidate with the higher positive NPV. What is the IRR? - CORRECT ANSWER The discount rate that makes the NPV = 0. What is necessary to recognize a compound rate of return that is equal to the IRR over the life of the investment? - CORRECT ANSWER Only if we can reinvest all interim cash flows at exactly the IRR. IRR Rule - CORRECT ANSWER uses the opportunity cost of capital as a hurdle rate, or rate that a project's IRR must exceed for the project to be accepted. Note that if the opportunity cost of capital is equal to the IRR, then the NPV is equal to 0. If the project's opportunity cost is less than the IRR, the NPV is greater than 0. IRR Formula Investment - CORRECT ANSWER CF/Investment CF/IRR What do IRR and NPV rule do when projects are independent? - CORRECT ANSWER Give same accept or reject decision. When does NPV and IRR rank projects differently? - CORRECT ANSWER When they don't have enough money to do all of them and must rank them in terms of profitability. The IRR and NPV rank differently when: 1) the size or scale of the projects differ. 2) timing of the projects' cash flows differ. What do you follow when NPV and IRR are different? - CORRECT ANSWER NPV - it represents addition to shareholder wealth, and we take the basic goal of a company to be to make shareholders money. Performance measurement - CORRECT ANSWER which involves calculating returns in a logical and consistent manner. MWR What is IRR equal to? - CORRECT ANSWER Money weighted return Example of an investment measure? - CORRECT ANSWER Time-weighted rate of return - measures the compound rate of growth of $1 initially invested in the portfolio over a stated measurement period - not affected by money withdrawal/additions. Time-weighted return steps - CORRECT ANSWER Price the portfolio immediately prior to any significant addition or withdrawal of funds. Break the overall evaluation period into subperiods based on the dates of cash inflows and outflows. Calculate the holding period return on the portfolio for each subperiod. Link or compound holding period returns to obtain an annual rate of return for the year (the time-weighted rate of return for the year). If the investment is for more than one year, take the geometric mean of the annual returns to obtain the time-weighted rate of return over that measurement period. Pure discount instrument - CORRECT ANSWER Pay less than face value (T-bill). What does a bank discount basis do? What is quoted this way? - CORRECT ANSWER It's a quoting convention that annualizes, based on a 360 day year, the discount as a percentage of face value. T-bills. Why is yield on a bank discount basis not a meaningful measure of investors' return? - CORRECT ANSWER First, the yield is based on the face value of the bond, not on its purchase price. Returns from investments should be evaluated relative to the amount that is invested. Second, the yield is annualized based on a 360-day year rather than a 365-day year. Third, the bank discount yield annualizes with simple interest, which ignores the opportunity to earn interest on interest (compound interest). Effective Annual Yield - CORRECT ANSWER The EAY takes the quantity 1 plus the holding period yield and compounds it forward to one year, then subtracts 1 to recover an annualized return that accounts for the effect of interest-on-interest. What does the money market yield do? - CORRECT ANSWER This convention makes the quoted yield on a T-bill comparable to yield quotations on interest-bearing money-market instruments that pay interest on a 360-day basis. In general, the money market yield is equal to the annualized holding period yield and bigger than bank discount yield. What is the bank discount yield based on? - CORRECT ANSWER Face value of the bill. not its price. What must discount rates be compatible with? - CORRECT ANSWER The time period. Bond equivalent yield of a yield stated on semi annual basis - CORRECT ANSWER That yield multiplied by 2. Descriptive statistics vs statistical inferenc - CORRECT ANSWER Descriptive statistics is the study of how data can be summarized effectively to describe the important aspects of large data sets. By consolidating a mass of numerical details, descriptive statistics turns data into information. Statistical inference involves making forecasts, estimates, or judgments about a larger group from the smaller group actually observed. Parameter - CORRECT ANSWER Any descriptive measure of a population characteristic. Sample statistic - CORRECT ANSWER a quantity computed from or used to describe a sample. Level of measurement hierarchy from lowest to highest - CORRECT ANSWER 1) nominal scales 2) ordinal scales 3) interval scales 4) ratio scales Nominal scales - CORRECT ANSWER Categorizes data but does not rank it Ordinal scales - CORRECT ANSWER sort data into categories that are ordered with respect to some characteristic. Can involve numbers to identify categories. Interval scales - CORRECT ANSWER provide not only ranking but also assurance that the differences between scale values are equal. As a result, scale values can be added and subtracted meaningfully. What does the zero on an interval scale represent? - CORRECT ANSWER the zero point of an interval scale does not reflect complete absence of what is being measured; it is not a true zero point or natural zero. Zero degrees Celsius corresponds to the freezing point of water, not the absence of temperature. As a consequence of the absence of a true zero point, we cannot meaningfully form ratios on interval scales. As an example, 50°C, although five times as large a number as 10°C, does not represent five times as much temperature. What kind of scale are questionnaires often treated as? - CORRECT ANSWER Interval Ratio Scales - CORRECT ANSWER represent the strongest level of measurement. They have all the characteristics of interval measurement scales as well as a true zero point as the origin. How are ratio scales different that interval scales? - CORRECT ANSWER Ratio scales have a natural zero. What type of scale are rates of return as well as money? - CORRECT ANSWER Ratio. Histogram - CORRECT ANSWER A bar chart of data that have been grouped into a frequency distribution. Frequency polygon - CORRECT ANSWER plot the midpoint of each interval on the x-axis and the absolute frequency for that interval on the y-axis; we then connect neighboring points with a straight line. Cumulative frequency distribution - CORRECT ANSWER Such a graph can plot either the cumulative absolute or cumulative relative frequency against the upper interval limit. The cumulative frequency distribution allows us to see how many or what percent of the observations lie below a certain value. How do cumulative distributions tend to look? - CORRECT ANSWER tends to flatten out when returns are extremely negative or extremely positive. The steep slope in the middle of Figure 4 reflects the fact that most of the observations lie in the neighborhood of −2 percent to 6 percent. Measures of central tendency vs measures of location - CORRECT ANSWER Measures of central tendency specifies where the data are centered while measures of location include not only measures of central tendency but also other measures that illustrate the location or distribution of data. Arithmetic Mean - CORRECT ANSWER Sum of observations divided by number of observations. What can sample mean also be called? - CORRECT ANSWER Arithmetic average. Cross-sectional data - CORRECT ANSWER characteristics of some units at a specific point in time. What will the sum of the deviations around the mean equal? - CORRECT ANSWER Zero. What is an advantage of the arithmetic mean over the median and the mode? - CORRECT ANSWER Mean uses all the information about the size and magnitude of the observations. Mean is also easy to work with mathematically. Drawback of median? - CORRECT ANSWER oes not use all the information about the size and magnitude of the observations; it focuses only on the relative position of the ranked observations. Calculating the median is also more complex More complex = less mathematically tractable than the mean. Unimodal vs bimodal vs trimodal - CORRECT ANSWER one mode vs two modes vs three modes How is mode different? - CORRECT ANSWER only measure of central tendency that can be used with nominal data. Difference between geometric and arithmetic mean? - CORRECT ANSWER Geometric mean is always less than or equal to arithmetic mean. Only equal when there is no variability in the observations. Do arithmetic and geometric means rank investments the same always? - CORRECT ANSWER No. Harmonic Mean - CORRECT ANSWER the value obtained by summing the reciprocals of the observations—terms of the form 1/Xi—then averaging that sum by dividing it by the number of observations n, and, finally, taking the reciprocal of the average. Used in cost averaging ("amount per unit"). Harmonic vs geometric vs arithmetic mean - CORRECT ANSWER Unless there is no variability, the harmonic mean is less than geometric mean, which in turn is less than arithmetic mean. Quantile - CORRECT ANSWER Most general term for a value at or below which a stated fraction of the data lies. Ly=(n+1)Y/100 whole/not whole numbers - CORRECT ANSWER When the location, Ly, is a whole number, the location corresponds to an actual observation. When Ly is not a whole number, Ly lies between the two closest integers (one above and one below). Then use linear interpolation. Linear interpolation - CORRECT ANSWER Interpolation means estimating an unknown value on the basis of two known values that surround it (lie above and below it); the term "linear" refers to a straight-line estimate. Absolute dispersion - CORRECT ANSWER the amount of variability present without comparison to any reference point or benchmark. Advantage and disadvantage of range - CORRECT ANSWER Ease of computation/ only uses two pieces of info from the distribution (so can't tell us how data is distributed). Benefit and drawback of Mean Absolute Deviation? - CORRECT ANSWER Uses all observations and thus is superior to range but difficult to manipulate mathematically compared with the variance. Variance - CORRECT ANSWER Average of the squared deviations around the mean. Mean absolute deviation vs standard deviation - CORRECT ANSWER The mean absolute deviation will always be less than or equal to the standard deviation because the standard deviation gives more weight to large deviations than to small ones (remember, the deviations are squared). Semivariance and semideviation - CORRECT ANSWER Semivariance is defined as the average squared deviation below the mean. Semideviation (sometimes called semistandard deviation) is the positive square root of semivariance. When are semivariance and variance effectively equivalent? - CORRECT ANSWER When return distributions are symmetric. Asymmetric distributions, variance vs semi variance rank prospects' risk differently - CORRECT ANSWER Semivariance (or semideviation) and target semivariance (or target semideviation) have intuitive appeal, but they are harder to work with mathematically than variance. Variance or standard deviation enters into the definition of many of the most commonly used finance risk concepts, such as the Sharpe ratio and beta. Perhaps because of these reasons, variance (or standard deviation) is much more frequently used in investment practice. Chebyshev's Inequality - CORRECT ANSWER According to Chebyshev's inequality, for any distribution with finite variance, the proportion of the observations within k standard deviations of the arithmetic mean is at least 1 − 1/k2 for all k > 1. The inequality gives the proportion of values within K standard deviations of the mean. Most quoted things from Chebysev's inequality? - CORRECT ANSWER a two-standard-deviation interval around the mean must contain at least 75 percent of the observations, and a three-standard-deviation interval around the mean must contain at least 89 percent of the observations, no matter how the data are distributed. Holds for samples + pops + continuous + discrete. Coefficient of variation - CORRECT ANSWER the ratio of the standard deviation of a set of observations to their mean value Cautions concerning Sharpe Ratio - CORRECT ANSWER 1) With negative Sharpe ratios, increasing risk results in numerically larger Sharpe ratio. Cannot assume, our of two negative sharpe ratios, that the one closer to zero is better risk-adjusted performance. 2) Conceptual limitation: Sharpe ratio considers only one aspect of risk: standard deviation of return. Standard deviation is most appropriate as a risk measure for portfolio strategies with approximately symmetric return distributions. Strategies with option elements have asymmetric returns. Characteristics of normally distributed characteristics - CORRECT ANSWER Its mean and median are equal. It is completely described by two parameters—its mean and variance. Roughly 68 percent of its observations lie between plus and minus one standard deviation from the mean; 95 percent lie between plus and minus two standard deviations; and 99 percent lie between plus and minus three standard deviations. Positively/Negatively skewed distributions - CORRECT ANSWER A return distribution with positive skew has frequent small losses and a few extreme gains. A return distribution with negative skew has frequent small gains and a few extreme losses. For the positively skewed unimodal distribution, the mode is less than the median, which is less than the mean. For the negatively skewed unimodal distribution, the mean is less than the median, which is less than the mode. Investors should be attracted by a positive skew because the mean return falls above the median. Relative to the mean return, positive skew amounts to a limited, though frequent, downside compared with a somewhat unlimited, but less frequent, upside. Skewness - CORRECT ANSWER Average cubed deviation from the mean standardized by dividing by the standard deviation cubed to make the measure free of scale. Positively skewed distribution mean vs median - CORRECT ANSWER Mean > median, then more than half of the deviations from the mean are negative and less than half are positive. In order for the sum to be positive, the losses must be small and likely, and the gains less likely but more extreme. Therefore, if skewness is positive, the average magnitude of positive deviations is larger than the average magnitude of negative deviations. Kurtosis - CORRECT ANSWER he statistical measure that tells us when a distribution is more or less peaked than a normal distribution. A distribution that is more peaked than normal is called leptokurtic (lepto from the Greek word for slender); a distribution that is less peaked than normal is called platykurtic (platy from the Greek word for broad); and a distribution identical to the normal distribution in this respect is called mesokurtic (meso from the Greek word for middle). The situation of more-frequent extremely large surprises that we described is one of leptokurtosis. What is kurtosis equal to for all normal distributions? - CORRECT ANSWER 3 For a sample of 100 from a normal distribution, what would an excess kurtosis sample be to be considered extremely large? - CORRECT ANSWER 1 or larger. geo vs arithmetic mean for past performance / forward looking. - CORRECT ANSWER Use geometric mean for past performance, arithmetic mean for making investment statements in a forward-looking context. Use arithmetic mean over one period horizon, geometric over multiple periods. Semilogarithmic graph - CORRECT ANSWER a semilogarithmic graph has an arithmetic scale on the horizontal axis for time and a logarithmic scale on the vertical axis for the value of the investment. The vertical axis values are spaced according to the differences between their logarithms. On a semilogarithmic scale, what do equal movements on the vertical axis reflect? - CORRECT ANSWER equal percentage changes, and growth at a constant compound rate plots as a straight line. A plot curving upward reflects increasing growth rates over time. The slopes of a plot at different points may be compared in order to judge relative growth rates. In terms of arithmetic and geometric means, what does uncertainty in cash flows cause? - CORRECT ANSWER Arithmetic mean to be larger than geometric mean. Event - CORRECT ANSWER Specified set of outcomes. Two defining properties of probability - CORRECT ANSWER 1) Probability of any event is a number between zero and 1. 2) Sum of probabilities of any mutually exclusive and exhaustive events equals 1. 3 approaches to estimating probabilities - CORRECT ANSWER 1) empirical probabilities: - estimate probability of an event as a relative frequency of occurrence based on historical data. - relationships must be stable through time. 2) subjective probability: - draw on personal judgment. Very important in investments. 3) Priori probability (grouped as objective probability): - based on logical analysis rather than on observation or personal judgment. Pairs arbitrage trade - CORRECT ANSWER A trade in two closely related stocks involving the short sale of one and purchase of the other. Dutch Book theorem - CORRECT ANSWER Inconsistent probabilities create profit opportunities. What is unconditional probability also called? - CORRECT ANSWER Marginal probability. Independent events - CORRECT ANSWER P(AGB)= P(A) What is the total probability rule meant for? - CORRECT ANSWER A rule for stating an unconditional probability in terms of conditional probabilities. It's also a weighted average. Expected value vs sample or historical mean - CORRECT ANSWER Sample mean also summarizes in a single number of a central value. However, the sample mean presents a central value for a particular set of observations as an equally weighted average of those observations. To summarize, the contrast is forecast versus historical, or population versus sample. What unit is variance in? - CORRECT ANSWER Squared units of X. What do covariance terms capture? - CORRECT ANSWER How the co-movements of returns affect portfolio variance. Two essential observations about covariance - CORRECT ANSWER 1) We can interpret the sign of covariance as follows: - covariance of returns is negative if, when the return on one asset is above its expected value, the return on the other asset tends to be below its expected value. (average inverse relationship between returns). - Covariance of returns is zero if returns on the assets are unrelated. - Covariance of returns is positive when the returns on both assets tend to be on the same side of their expected values at the same time. 2) The covariance of a random variable with itself is its own variance. Contribution of individual variances to portfolio variance - CORRECT ANSWER W1^2(R1) + W2^2(R2) + w3^2(R3). If returns were independent, covariances would be 0 and that would be total portfolio standard deviation. The portfolio would have less risk. Covariance terms negative = risk reduced. When are diversification benefits possible? - CORRECT ANSWER As long as returns are not perfectly positively correlated. In terms of correlation, when is the cost of not diversifying greater? - CORRECT ANSWER The smaller the correlation the bigger the cost of not diversifying. Properties of Correlation - CORRECT ANSWER 1) It's a number between 1 and -1, for two random variables, X and Y. 2) Correlation of zero = absence of any linear relationship between the variables. What do I use when I want to assign every member of a group of size n to n slots? - CORRECT ANSWER n factorial. What do I use when I want to count the number of ways to apply one of three or more labels to each member of a group? - CORRECT ANSWER Multinomial. What do I use when I want to count the number of ways I can choose r objects from n, when the order in which I list the r objects does not matter (can I give the r objects a label)? - CORRECT ANSWER Combination. What do I use when to count the number of ways I can choose r objects from a total of n, when the order in which I list the r objects is important? - CORRECT ANSWER Permutation. What do the computation/permutation/etc formulas apply to? - CORRECT ANSWER Tasks with a finite number of possible outcomes. What is the covariance of a random variable with itself? - CORRECT ANSWER Its own variance. What places the upper limit on bond price? - CORRECT ANSWER The discount rate. What assumptions does binomial distribution make? - CORRECT ANSWER Probability, P, is constant for all trials and trials are independent. When is binomial distribution symmetric? - CORRECT ANSWER When probability of success on a trial = .5 If you are paying a fair price on average with a broker, what should be the probability of a profitable trade? - CORRECT ANSWER .5 Tracking error - CORRECT ANSWER Total return on the portfolio on the portfolio (gross of fees) minus the total return on the benchmark index. Tracking risk - CORRECT ANSWER Standard deviation of tracking error. What is a general binomial random variable the sum of? - CORRECT ANSWER is the sum of n Bernoulli random variables, and so the mean of a B(n, p) random variable is np. Given that a B(1, p) variable has variance p(1 − p), the variance of a B(n, p) random variable is n times that value, or np(1 − p), assuming that all the trials (Bernoulli random variables) are independent. Possible critique of binomial model, like when looking at bond discount rates? - CORRECT ANSWER Events may share common factors, making them not independent. What is the technical range of possible outcomes of a continuous random variable? - CORRECT ANSWER Negative to positive infinity or some subset of that line. (The real line). Main uses of uniform distribution? - CORRECT ANSWER As the basis of techniques for generating random numbers, the uniform distribution plays a role in Monte Carlo simulation. As the probability distribution that describes equally likely outcomes, the uniform distribution is an appropriate probability model to represent a particular kind of uncertainty in beliefs in which all outcomes appear equally likely. What does graph of uniform continuous distribution look like? - CORRECT ANSWER Horizontal line. Continuous random variable equation thing - CORRECT ANSWER For any continuous random variable X, P(a ≤ X ≤ b) = P(a < X ≤ b) = P(a ≤ X < b) = P(a < X < b), because the probabilities at the endpoints a and b are 0. For discrete random variables, these relations of equality are not true, because probability accumulates at points. When is standard deviation not particularly useful as a risk measure? - CORRECT ANSWER for a uniform distribution, however. The probability that lies within various standard deviation bands around the mean is sensitive to different specifications of the upper and lower limits (although Chebyshev's inequality is always satisfied) Central limit theorem - CORRECT ANSWER The sum (and mean) of a large number of independent random variables is approximately normally distributed. Range of possible outcomes for normal distribution? - CORRECT ANSWER Entire real line. Defining characteristics of a normal distribution? - CORRECT ANSWER 1) Can be completely described by two parameters, it's mean and variance (or std dev). 2) Skewness of zero (it's symmetric). Kurtosis of 3 (excess kurtosis = 0). Mean, median, and mode are equal for a normal random variable. 3) Linear combination of two or more normal random variables is also normally distributed. What three parameters completely defines a multivariate normal distribution on stocks? - CORRECT ANSWER 1) the list of the mean returns on the individual securities (n means in total); 2) the list of the securities' variances of return (n variances in total); and 3) the list of all the distinct pairwise return correlations: n(n − 1)/2 distinct correlations in total. What is a distinguishing features of a multivariate normal distribution compared to univariate normal distribution? - CORRECT ANSWER The need to specify correlations. What can normal distributions be considered an approximate model for? What is it not as good at? - CORRECT ANSWER Asset returns. Asset prices: normal random variable has no lower limit, asset prices can only drop to zero. What does the distribution of options returns look like? - CORRECT ANSWER Skewed. Normal distribution probability statements - CORRECT ANSWER Approximately 50 percent of all observations fall in the interval μ ± (2/3) σ. Approximately 68 percent of all observations fall in the interval μ ± σ. Approximately 95 percent of all observations fall in the interval μ ± 2σ. (+- 1.96 Std. Dev) Approximately 99 percent of all observations fall in the interval μ ± 3σ. (+- 2.58 Std. Dev). Most used standard normal table values - CORRECT ANSWER The 90th percentile point is 1.282: P(Z ≤ 1.282) = N(1.282) = 0.90 or 90 percent, and 10 percent of values remain in the right tail. The 95th percentile point is 1.65: P(Z ≤ 1.65) = N(1.65) = 0.95 or 95 percent, and 5 percent of values remain in the right tail. Note the difference between the use of a percentile point when dealing with one tail rather than two tails. Earlier, we used 1.65 standard deviations for the 90 percent confidence interval, where 5 percent of values lie outside that interval on each of the two sides. Here we use 1.65 because we are concerned with the 5 percent of values that lie only on one side, the right tail. The 99th percentile point is 2.327: P(Z ≤ 2.327) = N(2.327) = 0.99 or 99 percent, and 1 percent of values remain in the right tail. Relations for Z tables w/o values less than zero. - CORRECT ANSWER For a non-negative number x, use N(x) from the table. Note that for the probability to the right of x, we have P(Z ≥ x) = 1.0 − N(x). For a negative number −x, N(−x) = 1.0 − N(x): Find N(x) and subtract it from 1. All the area under the normal curve to the left of x is N(x). The balance, 1.0 − N(x), is the area and probability to the right of x. By the symmetry of the normal distribution around its mean, the area and the probability to the right of x are equal to the area and the probability to the left of −x, N(−x). For the probability to the right of −x, P(Z ≥ −x) = N(x). What does mean-variance analysis say? - CORRECT ANSWER holds exactly when investors are risk averse; when they choose investments so as to maximize expected utility, or satisfaction; and when either 1) returns are normally distributed, or 2) investors have quadratic utility functions. What do safety-first rules focus on? - CORRECT ANSWER shortfall risk. When does safety-first optimal portfolio maximize the safety first ratio? - CORRECT ANSWER When returns are normally distributed. How does SFRation become Sharpe Ratio? - CORRECT ANSWER substitute the risk-free rate, RF, for the critical level RL. The portfolio with the highest Sharpe ratio is the one that minimizes the probability that portfolio return will be less than the risk-free rate (given a normality assumption). Stress testing/ scenario analysis - CORRECT ANSWER Set of techniques for estimating losses in extremely unfavourable combinations of events. Value at risk - CORRECT ANSWER A money measure of the minimum value of losses expected over a specified time period at a given level of probability. When do random variables follow lognormal distributions? - CORRECT ANSWER f its natural logarithm, ln Y, is normally distributed. The reverse is also true: If the natural logarithm of random variable Y, ln Y, is normally distributed, then Y follows a lognormal distribution. Important aspects of lognormal distribution - CORRECT ANSWER bounded below by 0 and it is skewed to the right. Good for financial asset prices. Price relative - CORRECT ANSWER S1/S0, is an ending price, S1, over a beginning price, S0; it is equal to 1 plus the holding period return on the stock from t = 0 to t = 1 What should we assume about one-period continuously compounded returns? - CORRECT ANSWER Assume that the one-period continuously compounded returns (such as r0,1) are IID random variables with mean μ and variance σ2 What is a characteristic feature of the Monte Carlo Simulation? - CORRECT ANSWER The generation of a large number of random samples from a specified probability distribution or distributions to represent the role of risk in the system. Uses for Monte Carlo - CORRECT ANSWER A) Planning. B) Develop estimates of VaR. C) Value complex securities, i.e. European options. D) Test models and tools. Asian Call Option - CORRECT ANSWER a European-style option with a value at maturity equal to the difference between the stock price at maturity and the average stock price during the life of the option, or $0, whichever is greater. For instance, if the final stock price is $34 with an average value of $31 over the life of the option, the value of the option at maturity is $3 (the greater of $34 − $31 = $3 and $0) Steps of Monte Carlo - CORRECT ANSWER 1) Specify quantities of interest in terms of underlying variables. 2) Specify a time grid. 3) Specify distributional assumptions for the risk factors that drive the underlying variables 4) Using computer program/spreadsheet, draw K random values of each risk factor. 5) Calculate the underlying variables using the random observations generated in Step 4 6) Computer the quantities of interest. 7) Go back to step 4 until a specified number of trials is completed. How many Monte Carlo trials are needed to get another digit of accuracy? - CORRECT ANSWER Factor of 100. Random number generator - CORRECT ANSWER Refers to an algorithm that produces uniformly distributed random numbers between 0 and 1. What do I need to know about converting random numbers into random observations? - CORRECT ANSWER random observations from any distribution can be generated using a uniform random variable. Draw back of historical simulation vs Monte Carlo? - CORRECT ANSWER HS does not account for risk not in the data, or what if situations. Draw back of Monte Carlo? - CORRECT ANSWER It provides only statistical estimates, not exact results. Analytical methods, where available, provide more insight into cause-and-effect relationships. However, only some types of options can be priced with analytical expressions. Simple Random Sample - CORRECT ANSWER A simple random sample is a subset of a larger population created in such a way that each element of the population has an equal probability of being selected to the subset. Systematic Sampling - CORRECT ANSWER select every kth member until we have a sample of the desired size. The sample that results from this procedure should be approximately random. Real sampling situations may require that we take an approximately random sample. Sampling error - CORRECT ANSWER Sampling error is the difference between the observed value of a statistic and the quantity it is intended to estimate. Sampling Distribution of a Statistic - CORRECT ANSWER The sampling distribution of a statistic is the distribution of all the distinct possible values that the statistic can assume when computed from samples of the same size randomly drawn from the same population. Stratified Random Sampling - CORRECT ANSWER In stratified random sampling, the population is divided into subpopulations (strata) based on one or more classification criteria. Simple random samples are then drawn from each stratum in sizes proportional to the relative size of each stratum in the population. These samples are then pooled to form a stratified random sample. Benefits of stratified random sampling? - CORRECT ANSWER In contrast to simple random sampling, stratified random sampling guarantees that population subdivisions of interest are represented in the sample. Another advantage is that estimates of parameters produced from stratified sampling have greater precision—that is, smaller variance or dispersion—than estimates obtained from simple random sampling. What is the size of the sampling error when random variables are generated by different underlying distributions? - CORRECT ANSWER Unknown. Central Limit Theorem - CORRECT ANSWER Given a population described by any probability distribution having mean μ and finite variance σ2, the sampling distribution of the sample mean X⎯⎯⎯ computed from samples of size n from this population will be approximately normal with mean μ (the population mean) and variance σ2/n (the population variance divided by n) when the sample size n is large. What does the central limit theorem allow us to do? Required sample size? - CORRECT ANSWER It allows us to make quite precise probability statements about the population (any one, as long as there is finite variance) mean by using the sample mean. Need a sample size of at least 30. What properties will distribution of sample mean always have with CL Theorem if sample size is sufficiently large? - CORRECT ANSWER The distribution of the sample mean X⎯⎯⎯ will be approximately normal. The mean of the distribution of X⎯⎯⎯ will be equal to the mean of the population from which the samples are drawn. The variance of the distribution of X⎯⎯⎯ will be equal to the variance of the population divided by the sample size. Two traditional branches of statistical inference - CORRECT ANSWER Hypothesis testing and estimation. Estimate - CORRECT ANSWER Particular value we calculate from sample observations. Estimators - CORRECT ANSWER The formulas we use to compute sample statistics. Estimator vs estimate - CORRECT ANSWER An estimator has a sampling distribution; an estimate is a fixed number pertaining to a given sample and thus has no sampling distribution. Unbiasedness - CORRECT ANSWER An unbiased estimator is one whose expected value (the mean of its sampling distribution) equals the parameter it is intended to estimate. Three desirable properties of estimators - CORRECT ANSWER Unbiasedness, efficiency, consistency. Efficiency - CORRECT ANSWER An unbiased estimator is efficient if no other unbiased estimator of the same parameter has a sampling distribution with smaller variance. Consistency - CORRECT ANSWER A consistent estimator is one for which the probability of estimates close to the value of the population parameter increases as sample size increases. (sometimes hard to find estimators that have unbiasedness in small samples, so we look at the estimator's sampling distribution in extremely large samples and consistency is among the most important of these asymptotic properties). Does increasing sample size help when the estimator is inconsistent? - CORRECT ANSWER No. Confidence Interval - CORRECT ANSWER a range for which one can assert with a given probability 1 − α, called the degree of confidence, that it will contain the parameter it is intended to estimate. Reliability factors for Confidence Intervals - CORRECT ANSWER 90%: 1.65 95%: 1.96 99%: 2.58 Approaching zero standard normal distribution vs t-distribution - CORRECT ANSWER Standard normal distribution has tails that approach zero faster, and the more the degrees of freedom increase, the more the T looks like the standard normal. What does t-value .1 say? - CORRECT ANSWER .1 chance that the probability remains in the right tail for that specified degrees of freedom. Computing reliability from samples, non normal / different sizes: differences? - CORRECT ANSWER Normal distribution with known variance: z for large and small sample size. Normal distribution with unknown variance: T for small, and either T or Z for large. Nonnormal distribution with known variance: No statistic for small sample size, z for large sample size. Nonnormal distribution with unknown variance: no statistic for small sample size, either t or z for large sample size. What makes up the reliability factor in a confidence interval? - CORRECT ANSWER Choice of T or Z and choice of confidence. Issues regarding sample size - CORRECT ANSWER Larger sample size = smaller standard error = smaller confidence interval. But, increasing size of sample may result in sampling from more than one population and the additional expenses may outweigh the value of the extra precision. Data Mining Bias - CORRECT ANSWER Overuse of the same or related data. What is an out-of-sample test? - CORRECT ANSWER Uses a sample that does not overlap the time periods of the samples on which a strategy, etc. was developed. Future results is most crucial out-of-sample test. How do you investigate presence of data mining bias? - CORRECT ANSWER Do an out-of-sample test. Intergenerational data mining - CORRECT ANSWER using information developed by previous researchers using a dataset to guide current research using the same or a related dataset. Two signs that can warn analysts about data mining - CORRECT ANSWER 1) Too much digging/too little confidence. How many variables were tested? "we noticed" "someone noted." 2) No story/no future: Absence of an explicit economic rationale for a variable or trading strategy = the no story part. If there is a good explanation, when it's publicized the market may adjust prices and remove its benefit. Sample Selection Bias - CORRECT ANSWER When data availability leads to certain assets being excluded from the analysis. Look-ahead bias - CORRECT ANSWER When information that was not available on the test date is used. Time-period bias - CORRECT ANSWER if it is based on a time period that may make the results time-period specific. A short time series is likely to give period specific results that may not reflect a longer period. A long time series may give a more accurate picture of true investment performance; its disadvantage lies in the potential for a structural change occurring during the time frame that would result in two different return distributions Two types of estimates of a parameter - CORRECT ANSWER The two types of estimates of a parameter are point estimates and interval estimates. A point estimate is a single number that we use to estimate a parameter. An interval estimate is a range of values that brackets the population parameter with some probability. Hypothesis - CORRECT ANSWER A statement about one or more populations. What is the process of hypothesis testing part of? What does this thing start with? - CORRECT ANSWER Scientific method. Scientific method starts with an observation and the formulation of a theory to explain the observation. Steps in hypothesis testing - CORRECT ANSWER Stating the hypotheses. Identifying the appropriate test statistic and its probability distribution. Specifying the significance level. Stating the decision rule. Collecting the data and calculating the test statistic. Making the statistical decision. Making the economic or investment decision. Null hypothesis - CORRECT ANSWER The null hypothesis is the hypothesis to be tested. For example, we could hypothesize that the population mean risk premium for Canadian equities is less than or equal to zero. Alternative Hypothesis - CORRECT ANSWER The alternative hypothesis is the hypothesis accepted when the null hypothesis is rejected. Our alternative hypothesis is that the population mean risk premium for Canadian equities is greater than zero. What hypothesis is used when we have a "hoped for" condition? - CORRECT ANSWER Make the alternative hypothesis the statement that this hypothesis is true. Test Statistic - CORRECT ANSWER A test statistic is a quantity, calculated based on a sample, whose value is the basis for deciding whether or not to reject the null hypothesis. Hypothesis errors - CORRECT ANSWER We reject a true null hypothesis. This is called a Type I error. We do not reject a false null hypothesis. This is called a Type II error. What is the probability of a type 1 error denoted by? - CORRECT ANSWER Alpha, aka the level of significance for the test. What is the probability of a type 2 error denoted by? - CORRECT ANSWER Beta. What is the only way to reduce both types of hypothesis testing errors? - CORRECT ANSWER Increase sample size. Difference between calculating type 1 and type 2 errors - CORRECT ANSWER Quantifying the type two error is extremely challenging so we normally only do it for type 1. Power of a test - CORRECT ANSWER Chance of correctly rejecting the null hypothesis Statistically significant - CORRECT ANSWER Reject the null hypothesis. Rejection point for the Test Statistic - CORRECT ANSWER A rejection point (critical value) for a test statistic is a value with which the computed test statistic is compared to decide whether to reject or not reject the null hypothesis. P-value - CORRECT ANSWER The smallest level of significance at which at which the null hypothesis can be rejected. How is t-distribution different from normal distribution? - CORRECT ANSWER More spread out and a higher standard deviation. Rejection points for Z test - CORRECT ANSWER Significance level of α = 0.10. H0: θ = θ0 versus Ha: θ ≠ θ0. The rejection points are z0.05 = 1.645 and −z0.05 = −1.645. Reject the null hypothesis if z > 1.645 or if z < −1.645. H0: θ ≤ θ0 versus Ha: θ > θ0. The rejection point is z0.10 = 1.28. Reject the null hypothesis if z > 1.28. H0: θ ≥ θ0 versus Ha: θ < θ0. The rejection point is −z0.10 = −1.28. Reject the null hypothesis if z < −1.28. Significance level of α = 0.05. H0: θ = θ0 versus Ha: θ ≠ θ0. The rejection points are z0.025 = 1.96 and −z0.025 = −1.96. Reject the null hypothesis if z > 1.96 or if z < −1.96. H0: θ ≤ θ0 versus Ha: θ > θ0. The rejection point is z0.05 = 1.645. Reject the null hypothesis if z > 1.645. H0: θ ≥ θ0 versus Ha: θ < θ0. The rejection point is −z0.05 = −1.645. Reject the null hypothesis if z < −1.645. Significance level of α = 0.01. H0: θ = θ0 versus Ha: θ ≠ θ0. The rejection points are z0.005 = 2.575 and −z0.005 = −2.575. Reject the null hypothesis if z > 2.575 or if z < −2.575. H0: θ ≤ θ0 versus Ha: θ > θ0. The rejection point is z0.01 = 2.33. Reject the null hypothesis if z > 2.33. H0: θ ≥ θ0 versus Ha: θ < θ0. The rejection point is −z0.01 = −2.33. Reject the null hypothesis if z < −2.33. Tests Concerning the Population Mean (Population Variance Unknown - CORRECT ANSWER Large Sample Small sample Pop Norm. T-test (Z alt) t-test Pop Not norm t-test (Z alt) Not available How is chi-square distribution different? - CORRECT ANSWER It is asymmetrical. But, it is a family of distributions like the T distribution. But it is different than T distribution because it is bounded below by zero (x^2 doesn't take on negative values). Also unlike t-test, the chi square is sensitive to violations of its assumptions (if sample is not random or does not come from a normally distributed population), inferences based on chi-square test will likely be faulty. How is chi square similar to another distribution? - CORRECT ANSWER Like chi-square, F distribution is a family of asymmetrical distributions bounded from below by zero. F-square is also not robust to violation of its assumptions. Parametric Test - CORRECT ANSWER Any test (or procedure) concerned with parameters or whose validity depends on assumptions concerning the population generating the sample. nonparametric test - CORRECT ANSWER A test that is not concerned with a parameter, or that makes minimal assumptions about the population from which a sample comes. When do we primarily use nonparametric tests? - CORRECT ANSWER in three situations: when the data we use do not meet distributional assumptions, when the data are given in ranks, or when the hypothesis we are addressing does not concern a parameter. What do we often convert original data into in nonparametric tests? - CORRECT ANSWER Ranks. - also use nonparametric tests when original data is already in ranks as parameter tests require a stronger measurement scale than ranks normally. When do we use Spearman rank correlation coefficient? - CORRECT ANSWER hen we believe that the population under consideration meaningfully departs from those assumptions (assumptions of correlation coefficient). What is Spearman rank correlation coefficient calculated on? - CORRECT ANSWER Ranks of the two variables within their respective samples. What does the statistical decision consist of? - CORRECT ANSWER Rejecting or not rejecting the null hypothesis. What does the economic decision take into consideration? - CORRECT ANSWER All economic issues pertinent to the decision. What is the T-distribution defined by? - CORRECT ANSWER A single parameter, the degree of freedom. Technical Analysis - CORRECT ANSWER A form of security analysis that uses price and volume data, which is often displayed graphically, in decision making. In what markets can technical analysis be used for securities? - CORRECT ANSWER In any freely traded market around the world. + can be used for any time frame. + technical analysis doesn't require in-depth knowledge of that instrument, the chart just needs to represent action in a freely traded market. What is the underlying logic of technical analysis? - CORRECT ANSWER Supply and demand determine prices. Changes in supply and demand cause changes in prices. Prices can be projected with charts and other technical tools. What kind of analysis do traders with short-term horizons prefer? - CORRECT ANSWER Because fundamental analysis is more time consuming than technical analysis, investors with short-term time horizons, such as traders, tend to prefer technical analysis—but not always. How do technical analysts view humans? What else do they believe? - CORRECT ANSWER irrational and emotional and that they tend to behave similarly in similar circumstances (vs fundamentalists who propose markets are rational and efficient). Market trends and patterns reflect this irrationality. Another tenet of technical analysis is that the market reflects the collective knowledge and sentiment of many varied participants and the amount of buying and selling activity in a particular security. - only those buying and selling impact price in freely traded market, and those who believe the strongest affect the price more (they trade higher amounts). A key tenet of technical analysis is that the equity market moves roughly six months ahead of inflection points in the broad economy. (Institute 310) What do technicians believe about market trends and patterns? - CORRECT ANSWER They repeat themselves and therefore, are somewhat predictable. - so technicians rely on recognizing patterns they have seen in the past. Difference in time for analysis between technicians and fundamentalists? - CORRECT ANSWER he technician is benefiting from the wide range of knowledge of market participants and the collective conclusion of market participants about a security. In contrast, the fundamental analyst must wait for the release of financial statements to conduct financial statement analysis, so a time lag occurs between the market's activities and the analyst's conclusions. Where is technical analysis widely used? - CORRECT ANSWER assets, such as a bushel of wheat, gallon of crude oil, or ounce of silver, do not have underlying financial statements or an income stream, so valuation models cannot be used to derive their fundamental intrinsic values. For these assets, technical analysis is the only form of analysis possible. So, whereas fundamental analysis is widely used in the analysis of fixed-income and equity securities, technical analysis is widely used in the analysis of commodities, currencies, and futures. What is a technician's analysis derived solely from? - CORRECT ANSWER Price and volume data. - assumes all the factors looked at by fundamentalists are reflected in the price of the stock through its trading activities. What's a key distinction between technical and fundamental analysis? - CORRECT ANSWER the technician has more concrete data, primarily price and volume data, to work with. The financial statements analyzed by fundamental analysts are not objective data. When do both types of analysis become subjective? - CORRECT ANSWER When the data become subject to analysis, however, both types of analysis become subjective because judgment is exercised when a technician analyzes a price chart and when a fundamental analyst analyzes an income statement. Technical/fundamental "will"/"should" trade - CORRECT ANSWER Technicians seek to project the level at which something will trade, while fundamentalists seek to predict where it should trade. Why may deviations between correct fundamental conclusion and intrinsic value persist? - CORRECT ANSWER It takes buying activity to raise or lower prices in freely traded markets. Drawback of technical analysis? - CORRECT ANSWER - Technicians are limited to studying market movements and do not use other predictive analytical methods, such as interviewing the customers of a subject company, to determine future demand for a company's products. Technicians study market trends and are mainly concerned with a security's price trend: Is the security trading up, down, or sideways? Trends are driven by collective investor psychology, however, and can change without warning. Additionally, it can take some time for a trend to become evident. Thus, technicians may make wrong calls and have to change their opinions. Technicians are better at identifying market moves after the moves are already under way. - Moreover, trends and patterns must be in place for some time before they are recognizable, so a key shortcoming of technical analysis is that it can be late in identifying changes in trends or patterns. This shortcoming mirrors a key shortcoming of fundamental analysis in that securities often overshoot fundamental fair values in an uptrend and undershoot fundamental fair values in a downtrend. Is fundamental or technical analysis newer? - CORRECT ANSWER Fundamental, as reliable fundamental data is a relatively new phenomenon. Situations where technical analysis is limited? - CORRECT ANSWER - In markets that are subject to large outside manipulation, the application of technical analysis is limited. - Technical analysis is also limited in illiquid markets, where even modestly sized trades can have an inordinate impact on prices. - Another example of when technical analysis may give an incorrect reading is in the case of a company that has declared bankruptcy and announced that its shares will have zero value in a restructuring. A positive technical trend may appear in such cases as investors who hold short positions buy shares to close out their positions. What's a good example of when technical analysis was superior to fundamental? - CORRECT ANSWER the case of securities fraud, such as occurred at Enron Corporation and WorldCom. These companies were issuing fraudulent financial statements, but many fundamental analysts continued to hold favorable views of the companies' equity securities even as the share prices declined. Simultaneously, a small group of investors came to the opposite view and expressed this view through high-volume sales of the securities. The result was clearly negative chart patterns that could then be discerned by technical analysis. Line Chart - CORRECT ANSWER In technical analysis, a plot of price data, typically closing prices, with a line connecting the points. The vertical axis (y-axis) reflects price level, and the horizontal axis (x-axis) is time. Bar Chart - CORRECT ANSWER A price chart with four bits of data for each time interval—the high, low, opening, and closing prices. A vertical line connects the high and low. A cross-hatch left indicates the opening price and a cross-hatch right indicates the close. - customarily constructed from daily data. Candlestick Chart - CORRECT ANSWER provides four prices per data point entry: the opening and closing prices and the high and low prices during the period. A vertical line represents the range through which the security price traveled during the time period. The line is known as the wick or shadow. The body of the candle is shaded if the opening price was higher than the closing price, and the body is clear if the opening price was lower than the closing price. Advantage of candlestick chart over bar chart? - CORRECT ANSWER price moves are much more visible in the candlestick chart, which allows faster analysis. The bar chart indicates market volatility only by the height of each bar, but in candlestick charts, the difference between opening and closing prices and their relationship to the highs and lows of the day are clearly apparent. Doji - CORRECT ANSWER positive and negative (price) actions of traders cancelled each other out. When can a dog signal something - CORRECT ANSWER If a doji occurs at the end of a long uptrend or downtrend, it signals that the trend will probably reverse. Point and Figure Chart - CORRECT ANSWER A technical analysis chart that is constructed with columns of X's alternating with columns of O's such that the horizontal axis represents only the number of changes in price without reference to time or volume. The vertical axis measures discrete increments of price. The first box to be filled in is to the right and below the highest X in the prior column. The technician then fills in an O to bring the column down to the price level at the close. Info point and figure chart gives - CORRECT ANSWER they have a clear focus on entry and exit levels but no focus on holding periods. What do you need to determine to construct a point and figure chart? - CORRECT ANSWER both the box size and the reversal size - ox size refers to the change in price represented by the height of each box (boxes are generally square, but the width has no meaning). In Exhibit 6, the box size is HK$1. The reversal size is used to determine when to create a new column. Most common reversal size is 3 and box size is 1. Why are point and figure charts especially handy? - CORRECT ANSWER are particularly useful for making trading decisions because they clearly illustrate price levels that may signal the end of a decline or advance. They also clearly show price levels at which a security may frequently trade. Linear scale - CORRECT ANSWER A scale in which equal distances correspond to equal absolute amounts. Also called arithmetic scale. Logarithmic Scale - CORRECT ANSWER A scale in which equal distances represent equal proportional changes in the underlying quantity. When is linear and when is logarithmic scale appropriate? - CORRECT ANSWER A logarithmic scale is appropriate when the data move through a range of values representing several orders of magnitude (e.g., from 10 to 10,000); a linear scale is better suited for narrower ranges (e.g., prices from $35 to $50). What does stock traded volume assess? - CORRECT ANSWER Conviction of buyers and sellers in determining a security's price. Relative Strength Analysis - CORRECT ANSWER A comparison of the performance of one asset with the performance of another asset or a benchmark based on changes in the ratio of the securities' respective prices over time. - asset under analysis = numerator, benchmark is denominator. Rising line = beating benchmark. What is trend analysis based on? - CORRECT ANSWER Market participants act similarly for extended periods of time. What does an uptrend contain? - CORRECT ANSWER An uptrend for a security is when the price goes to higher highs and higher lows. Retracement - CORRECT ANSWER Reversal in the movement of a security's price. What signals uptrend is over? - CORRECT ANSWER Major breakdowns in price, however, when the price drops through and below the trendline by a significant amount (many technicians use 5-10 percent below the trendline) indicate that the uptrend is over and may signal a further decline in the price. The longer the security price stays below the trendline, the more meaningful the breakdown is considered to be. How do you draw a down trend? - CORRECT ANSWER a technician draws a line connecting the highs of the price chart. Major breakouts above the downtrend line (e.g., 5-10 percent) indicate that the downtrend is over and a rise in the security's price may occur. And as with an uptrend, the longer the security price stays above the trendline, the more meaningful the breakout is considered to be. Uptrends vs downtrends and combining fundamental/technical. - CORRECT ANSWER From a purely technical standpoint, the reason is irrelevant. The downtrend is assumed to continue until contrary technical evidence appears. Combining fundamental analysis with technical analysis in such a case, however, might reveal a security that has attractive fundamentals but a currently negative technical position. In uptrends, however, a security with an attractive technical position but unattractive fundamentals is rare because most buying activity is driven by traders who expect the security price to increase in the future. The rare exception is covering short positions after a sizable decline in the share price. Support - CORRECT ANSWER a low price range in which buying activity is sufficient to stop the decline in price. Resistance - CORRECT ANSWER a price range in which selling is sufficient to stop the rise in price. Change in Polarity Principle - CORRECT ANSWER A tenet of technical analysis that once a support level is breached, it becomes a resistance level. The same holds true for resistance levels; once breached, they become support levels. Why do chart patterns have predictive value? - CORRECT ANSWER they are graphic representations of human trading activity and human behavior is frequently repeated, especially trading activity that is driven by fear (in market sell-offs) or hope and greed. Two types of chart patterns - CORRECT ANSWER 1) Reversal Patterns: - A type of pattern used in technical analysis to predict the end of a trend and a change in direction of the security's price. 2) Continuation Patterns: - A type of pattern used in technical analysis to predict the resumption of a market trend that was in place prior to the formation of a pattern. Need clear trend in place prior to pattern, for pattern to have predictive value. Head and Shoulders Pattern what does each part of the pattern show? - CORRECT ANSWER In technical analysis, a reversal pattern that is formed in three parts: a left shoulder, head, and right shoulder; used to predict a change from an uptrend to a downtrend. Left shoulder: This part appears to show a strong rally, with the slope of the rally being greater than the prior uptrend, on strong volume. The rally then reverses back to the price level where it started, forming an inverted V pattern, but on lower volume. Head: The head is a more pronounced version of the left shoulder. A rally following the first shoulder takes the security to a higher high than the left shoulder by a significant enough margin to be clearly evident on the price chart. Volume is typically lower in this rally, however, than in the one that formed the first, upward side of the left shoulder. This second rally also fails, with price falling back to the same level at which the left shoulder began and ended. This price level is called the neckline. This price level also will be below the uptrend line formed by connecting the low prices in the uptrend preceding the beginning of the head and shoulders pattern. This head pattern is the first signal that the rally may be coming to an end and that a reversal may be starting. Right shoulder: The right shoulder is a mirror image (or close to a mirror image) of the left shoulder but on lower volume, signifying less buying enthusiasm. The price rallies up to roughly the same level as the first shoulder, but the rally reverses at a lower high price than the rally that formed the head. Volume is an important characteristic in interpreting this pattern. What must prior trend be for head and shoulders pattern? - CORRECT ANSWER Uptrend. Divergence - CORRECT ANSWER In technical analysis, a term that describes the case when an indicator moves differently from the security being analyzed. What is the expectation after head and shoulders have formed? - CORRECT ANSWER the expectation is that the share price will decline down through the neckline price Inverse head and shoulders - CORRECT ANSWER Left shoulder: This shoulder appears to show a strong decline, with the slope of the decline greater than the prior downtrend, on strong volume. The rally then reverses back to the price level where it started, forming a V pattern, but on lower volume. Head: The head is a more pronounced version of the left shoulder. Another decline follows but on diminishing volume, which takes the price to a lower low than the prior shoulder by a significant enough margin that it is clearly evident on the price chart. This second decline also reverses, with price rising to the same level at which the left shoulder began and ended. This price level, the neckline, will also be above the downtrend line formed by connecting the high prices in the downtrend preceding the beginning of the inverse head and shoulders pattern. This pattern is the first signal that the decline may be coming to an end and that a reversal may be near. Right shoulder: The right shoulder is roughly a mirror image of the left shoulder but on lower volume, signifying less selling enthusiasm. The price declines down to roughly the same level as the first shoulder, but the rally reverses at a higher low price than the rally that formed the head. Price targets with head and shoulder pattern Price target for inverse head and shoulders? - CORRECT ANSWER The stronger and more pronounced the rally was, the stronger and more pronounced the reversal is likely to be. Similarly, once the neckline is breached, the security is expected to decline by the same amount as the change in price from the neckline to the top of the head. If the preceding rally started at a price higher than the neckline, however, the correction is unlikely to bring the price lower than the price level at the start of the rally. Head and shoulders = bearish = short. Price Target head and shoulder: Neckline - (Head - Neckline) Price target inverse head and shoulder: Neckline + (Neckline - Head) Double Top Price Target? - CORRECT ANSWER In technical analysis, a reversal pattern that is formed when an uptrend reverses twice at roughly the same high price level; used to predict a change from an uptrend to a downtrend. - volume is normally smaller on second one, signalling diminishing demand. - The longer the time is between the two tops and the deeper the sell-off is after the first top, the more significant the pattern is considered to be Price target: price is expected to decline below the low of the valley between the two tops by at least the distance from the valley low to the high of the double tops. Double Bottom Price target? - CORRECT ANSWER In technical analysis, a reversal pattern that is formed when the price reaches a low, rebounds, and then sells off back to the first low level; used to predict a change from a downtrend to an uptrend. Price Target: the price is expected to appreciate above the peak between the two bottoms by at least the distance from the valley lows to the peak. Triple Top - CORRECT ANSWER In technical analysis, a reversal pattern that is formed when the price forms three peaks at roughly the same price level; used to predict a change from an uptrend to a downtrend. Triple Bottom - CORRECT ANSWER In technical analysis, a reversal pattern that is formed when the price forms three troughs at roughly the same price level; used to predict a change from a downtrend to an uptrend. Challenge/criticism of double+triple top + technical in general? - CORRECT ANSWER Analyst can't know which pattern will emerge until after the fact. Continuation Pattern - CORRECT ANSWER A type of pattern used in technical analysis to predict the resumption of a market trend that was in place prior to the formation of a pattern. - indicates change in ownership from one investor to another. What type of pattern are triangle patterns? What types of triangle patterns are there? - CORRECT ANSWER Continuation Patterns. symmetrical triangles, ascending triangles, and descending triangles. A triangle pattern forms as the range between high and low prices narrows, visually forming a triangle. a trendline connects the highs and a trendline connects the lows. As the distance between the highs and lows narrows, the trendlines meet, forming a triangle. In a daily price chart, a triangle pattern usually forms over a period of several weeks. What are the trend lines like in an ascending triangle and what does that - CORRECT ANSWER the trendline connecting the high prices is horizontal and the trendline connecting the low prices forms an uptrend. What this pattern means is that market participants are selling the stock at the same price level over a period of time, putting a halt to rallies at the same price point, but that buyers are getting more and more bullish and stepping in at increasingly higher prices to halt sell-offs instead of waiting for further price declines. An ascending triangle typically forms in an uptrend. The fact that the rally continues beyond the triangle may be a bullish signal; it means that another set of investors is presumably willing to buy at an even higher price because their analysis suggests the intrinsic value of the security is higher. Alternatively, the fundamental facts themselves may have changed; that is, the security's fundamental value may be increasing over time. Descending triangle trend lines - CORRECT ANSWER the low prices form a horizontal trendline and the high prices form a series of lower and lower highs. Typically, a descending triangle will form in a downtrend. At some point in the sell-offs, buyers appear with enough demand to halt sell-offs each time they occur, at around the same price. Again, this phenomenon may be the result of fundamental analysts believing that the security has reached a price where it represents a significant discount to its intrinsic value and these analysts step in and buy. As the triangle forms, each rally ceases at a lower and lower high price point, suggesting the selling demand is exerting greater price influence than buying demand. Symmetrical triangle trend lines - CORRECT ANSWER the trendline formed by the highs angles down and the trendline formed by the lows angles up, both at roughly the same angle, forming a symmetrical pattern. What this triangle indicates is that buyers are becoming more bullish while, simultaneously, sellers are becoming more bearish, so they are moving toward a point of consensus. Because the sellers are often dominated by long investors exiting positions (as opposed to short sellers creating new short positions), the pressure to sell diminishes once the sellers have sold the security. Thus, the pattern ends in the same direction as the trend that preceded it, either uptrend or downtrend. What is the measuring implication and how do you derive it? What happens when pattern is broken? - CORRECT ANSWER The term "measuring implication" refers to the height of a triangle. The measuring implication is derived by calculating the difference in price from the two trendlines at the start of the triangle. Once the pattern is broken and the price breaks through one of the trendlines that form the triangle, the analyst expects the price to move by at least the amount of the breakthrough above or below the trendline. Typically, price breaks out of a triangle pattern between halfway and three-quarters of the way through the pattern. The longer the triangle pattern persists, the more volatile and sustained the subsequent price movement is likely to be. Rectangle Pattern - CORRECT ANSWER A rectangle pattern is a continuation pattern formed by two parallel trendlines, one formed by connecting the high prices during the pattern, and the other formed by the lows. The support level in a bullish rectangle is ... because ... - CORRECT ANSWER natural because the long-term trend in the market is bullish. The resistance line may simply represent investors taking profits. Conversely, in a bearish rectangle, the support level may represent investors buying the security. Again, the technician is not concerned with why a pattern has formed, only with the likely next price movement once the price breaks out of the pattern. What are flags and pennants considered to be? - CORRECT ANSWER minor continuation patterns because they form over short periods of time. (week, daily price charts). Flags - CORRECT ANSWER A technical analysis continuation pattern formed by parallel trendlines, typically over a short period. A flag is formed by parallel trendlines, in the same way that most countries' flags are rectangular and create a parallelogram. Typically, the trendlines slope in a direction opposite to the trend up to that time; for example, in an uptrend, they slope down. Pennants - CORRECT ANSWER A technical analysis continuation pattern formed by trendlines that converge to form a triangle, typically over a short period. A pennant formation is similar except that the trendlines converge to form a triangle, similar to the pennants of many sports teams or pennants flown on ships. Key difference between triangle and pennant - CORRECT ANSWER pennant is a short-term formation whereas a triangle is a long-term formation. Pennant Pricing - CORRECT ANSWER a downtrend begins at point A, which is $104. At point B, which is $70, a pennant begins to form. The distance from point A to point B is $34. The pennant ends at point C, which is $76. The price target is $76 minus $34, which is $42, the line labeled D. Technical indicator - CORRECT ANSWER any measure based on price, market sentiment, or funds flow that can be used to predict changes in price. These indicators often have a supply-and-demand underpinning; that is, they measure how potential changes in supply and demand might affect a security's price. Price-based indicator - CORRECT ANSWER Price-based indicators somehow incorporate information contained in the current and past history of market prices. Indicators of this type range from simple (e.g., a moving average) to complex (e.g., a stochastic oscillator). Exponential moving average vs simple moving average - CORRECT ANSWER Technicians commonly use a simple moving average, which weights each price equally in the calculation of the average price. Some technicians prefer to use an exponential moving average (also called an exponentially smoothed moving average), which gives the greatest weight to recent prices while giving exponentially less weight to older prices. What can the a moving average line serve as? - CORRECT ANSWER Resistance (65 day Moving Average). Golden vs dead Cross - CORRECT ANSWER hen a short-term moving average crosses from underneath a longer-term average, this movement is considered bullish and is termed a golden cross. Conversely, when a short-term moving average crosses from above a longer-term moving average, this movement is considered bearish and is called a dead cross. Bollinger Bonds - CORRECT ANSWER price-based technical analysis indicator consisting of a moving average plus a higher line representing the moving average plus a set number of standard deviations from average price (for the same number of periods as used to calculate the moving average) and a lower line that is a moving average minus the same number of standard deviations. Type of investment strategy coming from Bollinger Bonds - CORRECT ANSWER A common use is as a contrarian strategy, in which the investor sells when a security price reaches the upper band and buys when it reaches the lower band. This strategy assumes that the security price will stay within the bands. This type of strategy is likely to lead to a large number of trades, but it also limits risk because the trader can quickly exit unprofitable trades. In the event of a sharp price move and a change in trend, however, a contrarian strategy based on Bollinger Bands would be unprofitable. long-term investors might actually buy on a significant breakout above the upper boundary band because a major breakout would imply a change in trend likely to persist for some time. The long-term investor would sell on a significant breakout below the lower band. In this strategy, significance would be defined as breaking above or below the band by a certain percentage Momentum Oscilators - CORRECT ANSWER A graphical representation of market sentiment that is constructed from price data and calculated so that it oscillates either between a high and a low or around some number. These extremes can be viewed as graphic representations of market sentiment when selling or buying activity is more aggressive than historically typical. Convergence - CORRECT ANSWER The tendency for differences in output per capita across countries to diminish over time; in technical analysis, a term that describes the case when an indicator moves in the same manner as the security being analyzed. Divergence - CORRECT ANSWER In technical analysis, a term that describes the case when an indicator moves differently from the security being analyzed. It is considered to be an early warning of weakness, an indication that the uptrend may soon end. Overbought vs oversold - CORRECT ANSWER too bullish vs too bearish Uses of osiclators - CORRECT ANSWER First, oscillators can be used to determine the strength of a trend. Extreme overbought levels are warning signals for uptrends, and extreme oversold levels are warning signals for downtrends. Second, when oscillators reach historically high or low levels, they may be signaling a pending trend reversal. For oscillators that move above and below 0, crossing the 0 level signals a change in the direction of the trend. For oscillators that move above and below 100, crossing the 100 level signals a change in the direction of the trend. Third, in a non-trending market, oscillators can be used for short-term trading decisions—that is, to sell at overbought levels and to buy at oversold levels. R.o.C. Oscillator combining with trend means? - CORRECT ANSWER When the ROC oscillator crosses zero in the same direction as the direction of the trend, this movement is considered a buy or sell signal. For example, if the ROC oscillator crosses into positive territory during an uptrend, it is a buy signal. If it enters into negative territory during a downtrend, it is considered a sell signal. The technician will ignore crossovers in opposition to the trend because the technician must always first take into account the general trend when using oscillators. Relative Strength Index - CORRECT ANSWER A technical analysis momentum oscillator that compares a security's gains with its losses over a set period. - usually 14 days. moving-average convergence/divergence oscillator - CORRECT ANSWER MACD is the difference between a short-term and a long-term moving average of the security's price. The MACD is constructed by calculating two lines, the MACD line and the signal line: MACD line: difference between two exponentially smoothed moving averages, generally 12 and 26 days. Signal line: exponentially smoothed average of MACD line, generally 9 days. The indicator oscillates around zero and has no upper or lower limit. Rather than using a set overbought-oversold range for MACD, the analyst compares the current level with the historical performance of the oscillator for a particular security to determine when a security is out of its normal sentiment range. Types of Sentiment Indicators - CORRECT ANSWER 1) Opinion Polls 2) Calculated Statistical Indices - Put/Call ratio (volume of put options divided by volume of call options). Usually above one, higher values = bearish. - CBOE Volatility Index - measure of near-term market volatility - Rises when people are fearful of market decline and bid up price of puts, increasing VIX level. - Margin Debt - investors have a history of buying near market tops and selling at the bottom. When the market is rising and indices reach new highs, investors are motivated to buy more equities in the hope of participating in the market rally. Eventually, the margin traders use all of their available credit, so their buying power (and, therefore, demand) decreases, which fuels a price decline. Falling prices may trigger margin calls and forced selling, thereby driving prices even lower. - Short interest ratio = Short interest/Average daily trading volume. Short ratio considered both contrarian and to show market sentiment. Flow of Funds Indicators - CORRECT ANSWER Arms (AKA TRIN) Index Margin debt (margin loans may increase the purchases of stocks and declining margin balances may force the selling of stocks). Mutual Fund Cash position (When the mutual fund cash position is low, fund managers have already bought, and the effects of their purchases are already reflected in security prices. When the cash position is high, however, that money represents buying power that will move prices higher when the money is used to add positions to the portfolio. The mutual fund cash position is another example of a contrarian indicator). New Equity Issuance: The new equity issuance indicator suggests that as the number of initial public offerings (IPOs) increases, the upward price trend may be about to turn down. Secondary Offerings: Although secondary offerings do not increase the supply of shares, because existing shares are sold by insiders to the general public, they do increase the supply available for trading or the float. Kondratieff Wave - CORRECT ANSWER 54 year cycle by Kond. Where is 18 year cycle most often discussed? - CORRECT ANSWER Real estate markets Decennial Pattern - CORRECT ANSWER the pattern of average stock market returns (based on the DJIA) broken down on the basis of the last digit in the year. Years ending with a 0 have had the worst performance, and years ending with a 5 have been by far the best. Presidential Cycle - CORRECT ANSWER Election year = 4. Year 3 does best. Election years also good. Others bad. Problems with cycles - CORRECT ANSWER The primary problem is the small sample size. Only 56 presidential elections have been held in the United States, and only 4 completed Kondratieff cycles have occurred in US history. Another problem is that even with the small number of cycles, the data do not always fit the cycle theory, and when they do, that fit may not be obvious. Elliot Wave Theory - CORRECT ANSWER the market moves in regular, repeated waves or cycles. a pattern of five waves moving up in a bull market in the following pattern: 1 = up, 2 = down, 3 = up, 4 = down and 5 = up. He called this wave the "impulse wave." The impulse wave was followed by a corrective wave with three components: a = down, b = up and c = down. When the market is a bear market, as defined in Dow Theory—that is, with both of Dow's major indices in bear markets—the downward movements are impulse waves and are broken into five waves with upward corrections broken into three subwaves. Longest wave = "grand super cycle" and takes place over several centuries. Important aspect of Elliot's work? - CORRECT ANSWER Discover Fibonacci sequence: A sequence of numbers starting with 0 and 1, and then each subsequent number in the sequence is the sum of the two preceding numbers. In Elliott Wave Theory, it is believed that market waves follow patterns that are the ratios of the numbers in the Fibonacci sequence. He was more interested in the ratios of the numbers: - size of subsequent wave was generally a Fibo ratio. - He also noticed that the ratio of a Fibonacci sequence number to its preceding number is important: 2/1 = 2, 3/2 = 1.5, 5/3 = 1.6667, 8/5 = 1.600, 13/8 = 1.6250 These ratios converge around 1.618. In mathematics, 1.618 is called the "golden ratio," and it can be found throughout nature. Steps of each wave (theory) in bull market? - CORRECT ANSWER Wave 1 starts as a basing pattern and displays an increase in price, volume, and breadth.10 Wave 1 consists of five smaller waves. Wave 2 moves down, retracing much of the gain in Wave 1 but not all of it. Common percentage retracements are Fibonacci ratios, such as 50 percent or 62 percent. Wave 2 never erases all of the gains from Wave 1. Wave 2 consists of three smaller waves. Wave 3 moves above the high of the first wave and has strong breadth, volume, and price movement. Most of the price movement in an uptrend typically occurs in Wave 3. Wave 3 consists of five smaller waves. Wave 3 often moves prices 1.68 times higher than the length of Wave 1, which is a Fibonacci ratio. Wave 4 is, again, a correction, and the ratio of the change in price during this wave to the price change during the third wave is also generally a Fibonacci ratio. Wave 4 commonly reverses 38 percent of the gain in Wave 3. Wave 5 is also an up wave. Generally, the price movement in Wave 5 is not as great as that in Wave 3. The exception to the rule is that Wave 5 may become extended, as when euphoria overtakes the market. Wave 5 consists of five smaller waves. After Wave 5 is completed, the market traces out a series of three corrective waves, labeled a, b and c in Exhibit 34. Wave a is a down wave in a bull market; Wave a itself breaks down into three waves. Wave b is an upward movement and breaks down into five waves. Wave b is a false rally and is often called a "bull trap." Wave c is the final corrective wave. In a bull market, it does not move below the start of the prior Wave 1 pattern. Wave c breaks down into three subwaves. Description of each of the waves in bear market? - CORRECT ANSWER in bear markets, the impulse waves are labeled A through E and the corrective waves are labeled 1, 2, and 3. Waves in the direction of the trend consist of five subwaves, and counter-waves consist of three subwaves. How do price movements in Wave move? - CORRECT ANSWER Positive price movements generally take prices up by some Fibonacci ratio of prior highs (e.g., 1.5 or 1.62), and price declines generally reverse prices by a Fibonacci ratio (e.g., 0.50 or 0.667). Intermarket Analysis - CORRECT ANSWER A field within technical analysis that combines analysis of major categories of securities—namely, equities, bonds, currencies, and commodities—to identify market trends and possible inflections in a trend. Examples of Intermarket relationships? - CORRECT ANSWER Stock prices are affected by bond prices. High bond prices are a positive for stock prices since this means low interest rates. Lower interest rates benefit companies with lower borrowing costs and lead to higher equity valuations in the calculation of intrinsic value using discounted cash flow analysis in fundamental analysis. Thus rising bond prices are a positive for stock prices, and declining bond prices are a bearish indicator. Bond prices impact commodity prices. Bond prices move inversely to interest rates. Interest rates move in proportion to expectations to future prices of commodities or inflation. So declining bond prices are a signal of possible rising commodity prices. Currencies impact commodity prices. Most commodity trading is denominated in US dollars and so prices are commonly quoted in US dollars. As a result, a strong dollar results in lower commodity prices and vice versa.