Quantitative Methods Flashcards
Compound Interest
Interest on interest. Growth in the value of the investment from period to period reflects not only interest earned on the original principal amount, but also on the interest earned on the previous period’s interest earnings
Future Value
Projecting the cash flows forward, on the basis of an appropriate compound interest rate (compounding). Amount a current deposit will grow over time when placed in an account paying compound interest
FV = PV(1+1/Y)^N
Present Value
Brings the cash flows from an investment back to the beginning of an investment’s life based on the appropriate compound interest rate (discounting). Today’s value of of cash that is to be received some point in the future. Amount of money that must be invested today, at a given rate of return over a period of time, in order to end up with a specified FV
Equilibrium Interest Rates
Required rate of return for a particular investment
Market Rate of Return
Return that investors and savers require to get them to willingly lend their funds
Discount Rates
Interest rates. If you can borrow at 10%, discount payments to be made in the future at that rate in order to get equivalent value in dollars
Opportunity Cost of Current Consumption
Earning an additional interest in excess of the interest rate is the opportunity foregone when current consumption is chosen rather than saving (postponing consumption)
Real Risk Free Rate
Theoretical rate on a single-period loan that has no expectation of inflation in it. An investor’s increase in purchasing power after adjusting for inflation
Risk Free Rates
T-bills: since expected inflation in future periods is not zero
Nominal Risk Free Rates
Contain an inflation premium: nominal risk free rate = real risk free rate + expected inflation rate
Default Risk
Risk that a borrower will not make the promised payments in a timely manner
Liquidity Risk
Risk of receiving less than fair value for an investment if it must be sold for cash quickly
Maturity Risk
Prices of longer term bonds are more volatile than those of shorter term bonds (more maturity risk)
Required Interest Rate
= nominal risk free rate + default risk premium + liquidity premium + maturity risk premium
Effective Annual Rate (EAR)
Rate of interest actually realize as a result of compounding. Annual rate of return actually being earned after adjustments have been made for different compounding periods
(1 + periodic rate)^m - 1 where periodic rate = stated annual rate/m and m = number of compounding periods
Future Value Factor
(1+I/Y)^N represents compounding rate on an investment
Annuity
Stream of equal cash flows that occurs at equal intervals over a given period
Ordinary Annuity
Cash flows that occur at the end of each compounding period
Annuity Due
Payments or receipts occur at the beginning of each period
Perpetuity
Pays a fixed amount of money at set intervals over an infinite period of time (preferred stock)
PV of a Perpetuity
Fixed periodic cash flow divided by the appropriate periodic rate of return
Cash Flow Additivity Principle
Present value of any stream of cash flows equals the sum of the present values of the cash flows
Net Present Value
Present value of expected cash inflows associated with the project less the present value of the project’s expected cash outflows, discounted at the appropriate cost of capital
Internal Rate of Return
Rate of return that equates the PV of an investment’s expected benefits with the PV of its costs. Discount rate for which the NPV of an investment is zero
NPV Decision Rule
If a project has positive NPV, the amount goes to the firm’s shareholders. When two projects with positive NPV are mutually exclusive, choose the one with the higher positive NPV
IRR Decision Rule
Accept projects with an IRR greater than the firm’s required rate of return
Holding Period Return
The percentage change in the value of an investment over the period it is held
Total Return
Assets with cash flows such as dividend or interest payments, added to interim cash flows, have total return
Money Weighted Return
Internal rate of return on a portfolio, taking into account all cash inflows and outflows.
Time Weighted Rate of Return
Measures compound growth. Rate at which $1 compounds over a specified performance horizon. Averaging a set of values over time
Bank Discount Yield
Quotes for T-bills, based on the face value of the instrument instead of the purchase price. Not representative of return earned by an investor
Holding Period Yield
Total return an investor earns between the purchase date and the sale or maturity date. Actual return an investor will receive if the money market instrument is held until maturity
Effective Annual Yield
Annualized value, based on 365 day year, that accounts for compound interest. Annualized HPY on basis of 365 day year that incorporates annual compounding
Money Market Yield
Annualized holding period yield, assuming a 360 day year. Makes quote yield on the t-bill comparable to yield quotes for interest bearing money market instruments
Bond Equivalent Yield
2 x the semiannual discount rate
Descriptive Statistics
Summarize important characteristics of large data sets
Inferential Statistics
Procedures used to make forecasts, estimates, or judgments about a large set of data based on the statistical characteristics of a smaller set
Population
Set of all possible members of a stated group
Sample
Subset of the population of interest. Can be used to describe the population as a whole (N)
Nominal Scales
Level of measurement that contains the least information. Observations classified or counted with no particular order (n)
Ordinal Scales
Every observation is assigned to one of several categories. Then the categories are ordered with respect to a specified characteristic
Interval Scale
Provide relative ranking, plus the assurance that differences between scale values are equal. A measurement of zero does not necessarily indicate the total absence of what we are measuring
Ratio Scales
Most refined level. Provide ranking and equal differences between scale values, and they have a true zero point as the origin
Parameter
Measure used to describe a characteristic of a population
Sample Statistic
Used to measure a characteristic of a sample
Frequency Distribution
Tabular presentation of statistical data that aids the analysis of large data sets. Summarize statistical data by assigning it to specified groups or intervals
Interval
Class. The set of values that an observation may take on
Absolute Frequency
Actual number of observations that fall within a given interval
Modal Interval
In frequency distribution, the interval with the greatest frequency
Relative Frequency
Divide the absolute frequency of each return interval by the total number of observations (percentage of total observations falling within each interval)
Cumulative Absolute Frequency
Sum of the absolute frequencies starting at the lowest interval and progressing through the highest. Sum of the absolute frequencies up to and including the given interval
Cumulative Relative Frequency
Sum of the relative frequencies starting at the lowest interval and progressing through the highest. Sum of the relative frequencies up to and including the given interval
Histogram
Graphical presentation of the absolute frequency distribution. Bar chart of continuous data that has been classified into a frequency distribution (chosen intervals on horizontal axis, absolute frequencies on vertical)
Frequency Polygon
The midpoint of each interval is plotted on the horizontal axis, and the absolute frequency for that interval is plotted on the vertical axis. Each point is connected with a straight line
Measures of Central Tendency
Identify the center, or average, of a data set (typical or expected value)
Population Mean
All the observed values in the population are summed and divided by the number of observations in the population
Sample Mean
Sum of all the values in a sample of a population, divided by the number of observations in the sample. Used to make inferences about the population mean
Arithmetic Means
Sum of the observation values divided by the number of observations. All interval and ratio data sets have one, all data values are considered and included, a data set only has one, sum of deviations from the mean is zero
Weighted Mean
Different observations may have a disproportionate influence on the mean
Median
Midpoint of a data set when the data is arranged in ascending or descending order. Not affected by extreme values
Mode
Value that occurs the most frequently in a data set. May have more than one or none (unimodial, bimodial, trimodial)
Geometric Mean
Often used when calculating investment returns over multiple periods or when measuring compound growth rates. Only has a solution if product under radical is positive. Always less than or equal to arithmetic mean (can only be equal when observations are all equal)
Harmonic Mean
Average cost per shares purchased over time (will be less than geometric mean)
Quantile
Measures of location. Value at or below which a stated proportion of the data in a distribution lies (quartile = quarters, quintile = fifths, decile = tenths, percentile = hundredths)
Dispersion
Variability around the central tendency
Range
Distance between the largest and smallest value in the data set
Mean Absolute Deviation (MAD)
Average of the absolute values of the deviations of the individual observations from the arithmetic mean)
Population Variance
Average of the squared deviations from the mean
Biased Estimator
Systematically underestimating the population parameter, specifically for small samples (that’s why n-1 is used)
Chebyshev’s Inequality
For any set of observations, whether sample or population data and regardless of shape of distribution, the percentage of observations that lie within k standard deviations of the mean is at least 1 - 1/k^2 for all k > 1 (minimum percentage of any distribution that lies within a given standard deviation)
Relative Dispersion
The amount of variability in a distribution relative to a reference point or benchmark
Coefficient of Variation
Measures the amount of dispersion in a distribution relative to the distribution’s mean. Can make a direct comparison of dispersion across different sets of data (measure risk per unit of expected return)
Sharpe Ratio
Measures excess return per unit of risk (reward to variability ratio)
Symmetrical Distribution
Shaped identically on both sides of the mean, intervals of losses and gains will exhibit the same frequency (mean, median and mode are equal)
Skewness
Extent to which a distribution is not symmetrical (outliers in a data set)
Outliers
Observations with extraordinarily large values, either positive or negative
Positively Skewed
Many outliers in the upper region, or right tail
(mode < media < mean) - mean is most affected by outliers
Negatively Skewed
Disproportionately large amount of outliers that fall within its lower (left) tail
(mean < median < mode)
Kurtosis
Measure of the degree to which a distribution is more or less “peaked” than a normal distribution
Leptokurtic
More peaked than a normal distribution (more returns clustered around the mean and more returns with large deviations from the mean –> fatter tails). Greater percentage of small deviations from the mean and extremely large deviations from the mean (greater likelihood of increased risk)
Platykurtic
Less peaked (flatter) than a normal distribution
Mesokurtic
Same kurtosis as a normal distribution
Excess Kurtosis
Either more or less kurtosis than the normal distribution (normal kurtosis is 3, excess is 0)
Sample Skewness
Sum of the cubed deviations from the mean divided by the cubed standard deviation and by the number of observations
Random Variable
Uncertain quantity/number
Outcome
Observed value of a random variable
Event
Single outcome or set of outcomes
Mutually Exclusive
Events that cannot both happen at the same time
Exhaustive Events
Include all possible outcomes
Empirical Probability
Established by analyzing past data (objective)
A priori Probability
Determined using a formal reasoning and inspection process (objective)
Subjective Probability
Least formal method of developing probabilities, involves use of personal judgment
Unconditional Probability
Marginal probability. Probability of an event regardless of the past or future occurrence of other events
Conditional Probability
Occurrence of one event affects the probability of the occurrence of another event. Key word is “given”.
P(A | B). Also called likelihood
Joint Probability
Probability that both events will occur
Independent Events
Events for which the occurrence of one has no influence on the occurrence of the others
Total Probability
Relationship between unconditional and conditional probabilities of mutually exclusive and exhaustive events
Expected Value
Weighted average of the possible outcomes for the variable
Covariance
Measure of how two assets move together . Expected value of the product of the deviations of the two random variables from their respective expected values
Correlation
Covariance of two random variables divided by the product of their standard deviations. Strength of the linear relationship between two random variables
Bayes’ Rule
Update a given set of prior probabilities for a given event in response to the arrival of new information
Labeling
Situation where there are n items that can receive one of k different labels
Combination Formula
Binomial, formula for labeling when K = 2
Permutation
Specific ordering of a group of objects
Probability Distribution
Probabilities of all possible outcomes for a random variable (must sum to 1)
Discrete Random Variable
The number of possible outcomes can be counted, and for each possible outcome, there is a measurable and positive probability (eg. number of days it will rain in a given month)
Probability Function
Specifies the probability that a random variable is equal to a specific value p(x)
Continuous Random Variable
The number of possible outcomes is infinite, even if lower and upper bounds exist (eg. actual amount of daily rainfall)
Discrete Distribution
p(x) = 0 when x cannot occur, pr p(x) > 0 when if it can
Continuous Distribution
p(x) = 0 even though x can occur. X is between two positive values only when x1 and x2 are actual numbers
Cumulative Distribution Function
Defines the probability that a random variable X takes on a value equal to or less than a specific value (sum, or cumulative value, of the probabilities for the outcomes up to and including a specified outcome)
Discrete Uniform Random Variable
The probabilities for all possible outcomes for a discrete random variable are equal
Binomial Random Variable
Number of successes in a given number of trials, whereby the outcome can be either success or failure. Probability of success, p , is constant for each trial, and trials are independent
Bernoulli Random Variable
Binomial random variable for which the number of trials is 1
Binomial Tree
All possible combinations of up moves and down moves over a number of successive periods
Node
All possible values along a binomial tree
Continuous Uniform Distribution
Range spans between lower limit a and upper limit b (parameters of distribution). Outcomes can only be between a and b
Normal Distribution
Completely described by its mean and variance (X is normally distributed with mean mu and variance sigma squared). Symmetric about its mean (skew = 0) and kurtosis is normal (3), Tails get very thin but do not reach zero
Univariate Distributions
Distribution of a single random variable
Multivariate Distribution
Specifies the probabilities associated with a group of random variables and is meaningful only when the behavior of each random variable in the group is in some way dependent upon the behavior of the others
Confidence Interval
Range of values around the expected outcome within which we expect the actual outcome to be some specified percentage of the time. (68% within one standard deviation of the mean, 95% within two for normal distribution)
Standard Normal Distribution
Normal distribution that has been standardized so that it has a mean of zero and a standard deviation of 1
Z-value
Number of standard deviations a given observation is from the population mean
Standardization
Process of converting an observed value for a random variable to its z value
Z-table
Contains values generated using the cumulative density function for a standard normal distribution. Values in the table are the probabilities of observing a z-value that is less than a given value
Shortfall Risk
Probability that a portfolio value or return will fall below a particular value or return over a given time period
Roy’s Safety First Criterion
Optimal portfolio minimizes the probability that the return of the portfolio falls below some minimum acceptable level (threshold level)
Lognormal Distribution
e^x, where x is normally distributed. Skewed to the right, bounded from below by zero (modeling asset prices that never take negative values)
Price Relatives
End of period price of the asset divided by the beginning price
Continuous Compounding
Use for shorter and shorter compounding periods (the limit of discrete compounding)
Monte Carlo Simulation
Repeated generation of one or more risk factors that affect security values, in order to generate a distribution of security values. Specify parameters of the probability distribution, computer generates random values used to draw conclusions about mean and variance (valuation, simulate p&l, VaR)
Limitations: no better than the assumptions, statistical not analytical
Historical Simulation
Based on actual changes in value or actual changes in risk factors over some prior period. Set of all changes in relevant risk factors over some prior period. Uses actual distribution of risk factors, but past changes may not be indicative of future changes. Not good with “what if” scenarios
Simple Random Sampling
Method of selecting a sample where each item or person in the population being studied has the same likelihood of being included in the sample
Systematic Sampling
Selecting every nth number from a population
Sample Error
Difference between a sample statistic (mean, variance or standard deviation) and its corresponding population parameter
Sampling Distribution
From the sample statistic. A probability distribution of all possible sample statistics computed from a set of equal-size samples that were randomly drawn from the same population (probability distribution if a statistic from many samples)
Stratified Random Sampling
Uses a classification system to separate the population into smaller groups based on one or more distinguishing characteristics
Stratum
Each subgroup of a stratified random sampling. Random sample is taken from each and results are pooled
Time Series Data
Observations taken over a period of time at specific and equally spaced time intervals
Cross-sectional Data
Sample of observations taken at a single point in time
Longitudinal Data
Observations over time of multiple characteristics of the same entity
Panel Data
Observations over time of the same characteristic for multiple entities
Central Limit Theorem
For simple random samples of size n from a population with mean mu and finite variance sigma squared, the sampling distribution of the sample mean x bar approaches a normal probability distribution with mean mu and variance sigma squared divided by n
Standard Error of the Sample Mean
Standard deviation of the distribution of the sample means
Unbiased Estimator
One for which the expected value of the estimator is equal to the parameter you are trying to estimate (sample mean is unbiased estimator of population mean bc expected value of mean is equal)
Efficient Estimator
Variance of its sampling distribution is smaller than all the other unbiased estimators of the parameter you are using
Consistent Estimator
Accuracy of the parameter estimate increases as the sample size increases (standard error falls, bunches more closely around population mean)
Point Estimates
Single sample values used to estimate population parameters (calculated using the estimator)
T-distribution
Bell shaped probability distribution that is symmetrical about its mean. Appropriate to use when constructing confidence intervals based on small samples (n<=30) with populations with unknown variance and normal distribution. Flatter, more area under the tails
Degrees of Freedom
Number of sample observations minus one (define t-distributions). Given the mean, only n - 1 observations can be unique
Confidence Interval
Estimates result in a range if values within which the actual value of a parameter will lie, given the probability of 1 minus alpha
Level of Significance
Alpha in a confidence interval
Degree of Confidence
1 minus alpha in a confidence interval
Probabilistic Perspective
Repeatedly taking samples, constructing confidence intervals for each sample’s mean, finding that X% of the resulting confidence intervals include the population mean
Practical Perspective
Being X% confident that the population mean score is between two numbers for things in this population
Data Mining
Analysts repeatedly use the same database to search for patterns or trading rules until one that “works” is discovered
Data Mining Bias
Results where the statistical significance of the pattern is overestimated because the results were found through data mining (lack of any economic theory, too many variables tested)
Sample Selection Bias
Occurs when some data is systematically excluded from the analysis, usually because of lack of availability (nonrandom)
Survivorship Bias
Databases only include funds currently in existence, not funds that have ceased to exist. The funds that are dropped from the sample have lower returns, so the surviving sample is biased toward better funds (not random), will overestimate returns
Look-ahead Bias
A study tests a relationship using sample data that was not available on the test date (estimating future values)
Time-period Bias
If the time period over which the data is gathered is either too short or too long. Might reflect phenomena specific to that time period, or fundamental economic relationships might have changed
Hypothesis Testing
Statistical assessment of a statement or idea regarding a population. Testing the validity of a statement at a given significance level
Null Hypothesis
The hypothesis researchers want to reject. It is what’s actually tested and is the basis for selection of test statistics (always includes equal to condition)
Alternative Hypothesis
What is concluded if there is sufficient evidence to reject the null hypothesis (what you are trying to assess)
One-tailed Test
One-sided alternative hypothesis (test if something is greater than zero). Level of significance is the amount under the one tail (confidence interval is 100 - 2*significance)
Two-tailed Test
Two-sided alternative hypothesis (test if return is anything other than zero). Allow for deviations on both sides of the hypothesized value (zero). Level of significance is divided by 2 to find amount under each tail (confidence interval is 100 - significance)
Critical Values
Rejection points in a two-tailed test. Reject H0 if test statistic > upper critical value or test statistic < lower critical value.
One tailed: Reject H0 if test stat > upper tail or test stat < lower tail
Decision Rule
Rejection Rule. Two-tailed test at Z = 0.05, reject if test stat < -1.96 or test stat > 1.96
Test Statistic
Calculated by comparing the point estimate of the population parameter with the hypothesized value of the parameter. Difference between the sample statistic and hypothesized value, scaled standard error of sample stat
Type I Error
Rejection of the null hypothesis when it is actually true (False Negative)
Type II Error
Failure to reject the null hypothesis when it is false (False Positive)
Significance Level
Probability of making a Type I error (designated by alpha). Probability of rejecting a null hypothesis when it’s true
Power of a Test
Probability of correctly rejecting the null hypothesis when it’s false (1 - probability of Type II Error)
Statistical vs Economic Significance
Transaction costs, taxes, additional risk could make a strategy that seems statistically significant economically unattractive
P-value
Probability of obtaining a test statistic that would lead to a rejection of the null hypothesis, assuming the null hypothesis is true. Smallest level of significance for which the null hypothesis can be rejected
One Tailed: probability that lies above the computed test statistic for upper tailed tests, or below test for lower tailed
Two Tailed: probability that lies above the positive value of the computed test statistic plus the probability that lies below the negative value of the test statistic
T-test
Population variance is unknown, sample is large (n >= 30), sample is small (n < 30) but the distribution of the population is normal
Z-test
Population is normally distributed with known variance. Compared to the critical z-value corresponding to the significance of the test
Pooled Variance (Difference in Means)
Used with the t-test for testing the hypothesis that the means of two normally distributed are equal, when the variances of the populations are unknown but assumed to be equal
Equality of Population Means
T-test when populations are normally distributed and have variances that are unknown and assumed to be unequal, use the sample variance for both populations
Paired Comparisons Test (Mean Differences)
Test of whether the average difference between monthly returns is significantly different from zero, based on the standard error of the differences in monthly returns. Sample is normally distributed. When sample is dependent
Chi Square Test
Hypothesis tests concerning the variance of a normally distributed population (true population variance vs hypothesized variance). Values cannot be negative
F-test
Hypotheses concerned with the equality of the variances of two populations. Normally distributed, independent. Only consider the critical value in the right tail. Right skewed, bounded by zero on the left
Parametric Tests
Rely on assumptions regarding the distribution of the population and are specific to population parameters (z-test)
Nonparametric Tests
Do not consider a particular population parameter or have few assumptions about the population that is sampled. Used when there is a concern about quantities other than the parameters of a distribution or when the assumptions pf parametric tests can’t be supported (when you can’t use t-test or z-test, data is ordinal or ranked)
Spearman Rank Correlation Test
Used when the data are not normally distributed. Large positive value indicates high rank in one year means high rank in second year and vice versa
Technical Analysis
Study of collective market sentiment, as expressed in buying and selling assets. Prices are determined by the interaction of supply and demand, market price is supply and demand at any instant. Price and volume reflect collective behavior of buyers and sellers (both rational and irrational). Investor behavior is reflected in trends and patterns that tend to repeat and can be identified to forecast price
Fundamental Analysis
Attempts to determine the intrinsic value of an asset. Uses financial statements
Line Charts
Show closing prices for each period as a continuous line
Bar Charts
Add high and low prices for each trading period and often include opening prices. Closing price bar or dash on right of line
Candlestick Charts
Same data as bar charts, display a box bounded by the opening and closing prices. Clear if closing price higher than opening price, filled if closing price lower than opening
Point and Figure Charts
Identify changes in direction of price movements. Price on vertical, horizontal is number if changes in direction. Box size is price increment, reversal size is change of direction (three times the box size). X’s increase in box size, O;s decrease (fill in opposite directions in adjacent columns)
Volume Charts
Displayed below price charts (each period’s volume is a vertical line)
Relative Strength Analysis
Calculate the ratio of an asset’s closing prices to benchmark values (index, comp asset). Draw a line chart of the ratios. Increasing (positive) is outperforming, Decreasing (negative strength) underperforming
Uptrend
Prices reaching higher highs and retracing higher lows (demand increasing relative supply)
Downtrend
Prices declining lower lows and retracing to lower highs (supply is increasing relative to demand –> selling pressure)
Trendline
Uptrend: line traces increasing lows
Downtrend: connects decreasing highs
Breakout/Breakdown
Price crosses trendline by a significant amount (out from downtrend, down from an uptrend)
Support Level
Buying is expected to emerge to prevent further price decreases
Resistance Level
Selling is expected to emerge to prevent further price increases
Change in Polarity
Breached resistance levels become support levels and breached support levels become resistance levels
Reversal Patterns
Occur when a trend approaches a range of prices but fails to continue beyond that range
Head and Shoulders Pattern
Demand has been driving upward and is fading, especially if each of the highs in the pattern occurs on declining volume. Size can be used to predict price (difference in price between the head and the neckline –> high minus support level). Ensuing downturn price is then neckline - size –> Double Top, Triple Top
Reversal patterns are Inverse Head and Shoulders, double bottom, triple bottom
Continuation Patterns
Suggest a pause in a trend rather than a reversal
Triangles
Form when prices reach lower highs and higher lows over a period of time. Trendlines converge when they are projected forward. Buying and selling pressure have become roughly equal temporarily (pennants appear on short term price charts)
Rectangles
Form when trading temporarily forms a range between a support level and a resistance level (flags appear on short term price charts)
Moving Average Lines
Smooth the fluctuations in a price chart. Mean of the last n closing prices (larger value of n, smoother the moving average line). Can be viewed as support or resistance levels
Uptrend: price is higher than moving average
Downtrend: price is lower than moving average
Golden Cross
Short-term average crosses above the long-term average, indicator of an emerging uptrend (buy signal)
Dead Cross
Short-term average crosses below long-term average, indicator of an emerging downtrend (sell seignal)
Bollinger Bands
Based on the standard deviation of closing prices over the last n periods. Draw high and low bands a chosen number of deviations (2) above and below the n-period moving average. Move away from each other when volatility increases
Overbought
Prices at or above upper Bollinger band (too high, likely to decrease in the near term)
Oversold
Prices at or below lower Bollinger band (too low, likely to increase in the near term)
Contrarian Strategy
Buy when most traders are selling, sell when most traders are buying. Believe in overbought and oversold markets because most investors buy and sell at wrong times
Oscillators
Based on the market prices but scaled so that they oscillate around a given value, or between two values. Extreme highs and lows indicate overbought and oversold
Convergence
Oscillator shows the same pattern as prices (both reaching higher highs). Indicates price trend is likely to continue
Divergence
Oscillator shows a different pattern than prices (failing to reach higher high). Indicates potential change in price trend
Rate of Change Oscillator
Momentum, 100 times the difference between the latest closing price and the closing price n periods earlier. Oscillates around zero. Buy when it changes from negative to positive and vice versa. Ratio of current prices to past prices oscillates around 100
Relative Strength Index
Based on the ratio of total price increases to total price decreases over a selected number of periods. Oscillate between 0 and 100 (>70 is high –> overbought, <30 low –> oversold)
Moving Average Convergence/Divergence (MACD)
Drawn using exponentially smoothed moving averages, which place greater weight on more recent observations. MACD line is difference between moving averages of the price, signal line is moving average of MACD line. Oscillate around 0, not bounded. MACD crosses above signal line is buy signal, MACD line crosses below signal lines is sell signal
Stochastic Oscillator
Calculated from the latest closing price and highest and lowest prices reached in a recent period. Sustainable uptrend has prices close nearer to recent high. Sustainable downtrend has prices close nearer to recent low. Bounded by 0 and 100
%K line: difference between latest price and recent low as percentage of difference between recent high and low
%D line: 3 period average of the K line
Sentiment Indicators
Used to discern the views of potential buyers and sellers (bullish vs. bearish)
Put/Call Ratio
Put options increase in value when price of asset decreases, call options increase in value when price of asset increases. Volume reflects activity by investors with negative and positive outlooks. Increases in put/call are negative outlook, decreases positive. Contrarian indicator. Extremely high ratio is bearish and could mean oversold, extremely low is bullish and could mean overbought
Volatility Index (VIX)
Measures the volatility of options on S&P 500 stock index. High levels suggest fears of decline in market. Contrarian indicator
Margin Debt
Increases in margin debt outstanding suggest aggressive buying by bullish margin investors. As they reach their margin limit, ability to continue buying decrease, which can cause price declines. As price decreases, securities must be sold to meet margin calls, driving prices lower. Increasing margin debit indicates increasing market prices, and vice versa
Short Interest Ratio
Increases in shares sold short indicate strong negative sentiment. Number of shares investors have borrowed or sold short. Short interest divided by average daily trading volume. High ratio could mean investors expect price to decrease, could imply future buying demand when short sellers must return borrowed shares
Arms Index or Short Term trading Index (TRINS)
Measure of funds flowing into advancing and declining stocks. Value close to 1 suggests funds are flowing about evenly to advancing and declining stocks. Values greater than 1 suggest majority of volume is in declining stocks, less than 1 volume is in advancing stocks
Mutual Fund Cash Position
Ratio of mutual funds’ cash to total assets. In uptrends, managers want to invest cash quickly. During downtrends, fund cash balances increase overall fund returns. Cash positions increase when market is falling, decrease when market is rising. Contrarian indicator (accumulating cash indicates future buying power)
New Equity Issuance and Secondary Offerings
IPO’s and sales of additional shares by issuer add to the supply of stocks. New shares issued when market is high, increases in issuance coincide with market peaks
Cycle Theory
Study of processes that occur in cycles. 4 year presidential cycles, decennial patterns
Kondratieff Wave
54 year cycles
Elliott Wave Theory
Based on a belief that financial market prices can be described by an interconnected set of cycles.
Subminuette: cycle of a few minutes
Grand Supercycle: centuries long cycle
Waves
Prevailing Uptrend: upward moves in price consist of 5 waves, downward moves occur in 3 waves
Prevailing Downtrend: downward moves have 5 waves, upward moves have 3 waves
Fibonacci Ratios
Sizes of the waves in Elliott wave patterns, help with estimating price targets. Ratios of consecutive fibonacci numbers converge to 0.618 and 1.618 as the numbers get larger
Intermarket Analysis
Analysis of the interrelationships among the market values of major asset classes. Relative strength ratios determine outperforming asset classes. Apply relative strength analysis to identify assets within each class outperforming others
