Quantitative Methods Flashcards
Quantitative Methods
Interest Rates
Three ways to interpret interest rates
- Required rate of return
- Discount rate
- Opportunity cost
Quantitative Methods
Interest Rates
3 components of interest rates
- Risk free rate
- Inflation
- Default risk
Quantitative Methods
Interest Rates
Periodic interest rate
Simple rate of interest over a single compounding period
e.g. interest rate of 1.5% per quarter
Quantitative Methods
Interest Rates
Stated annual interest rate
= quoted interest rate
Annual rate ignoring compounding e.g. 4 * quarterly interest rate
Quantitative Methods
Interest Rates
Effective annual rate (EAR)
Annual interest rate taking into account compounding
Quantitative Methods
What is an “annuity due”?
Annuity with first payment at T0 (so last payment at T(n-1)
Formula: FV of annuity
IRR Problems
1 - Reinvestment Problem
2 - Scale Problem
3 - Timing Problem
IRR Problem 1
Reinvestment Problem
Assumes that all cash flows can be reinvested immediately at the IRR rate.
IRR Problem
2 Scale Problem
IRR ignores the scale of the return unlike NPV which would prioritise larger cash returns with the same IRR.
IRR Problem 3
Timing Problem
In the case where two projects have differing cash flow profiles (big cash flows early or late) IRR comparison is not useful.
Definition: Holding Period Return (HPR)
aka Total Return
This is the total return over a given period, including capital and distributions.
Dollar Weighted Rate of Return
Basically the IRR of an investment, taking amount and timing of cash flows into account.
So investing more cash when portfolio value is low leads to positive return, even if portfolio performance over the whole period is unchanged.
Thus a measure of what you earned from investing in the portfolio over the period, not a measure of the performance of the portfolio itself.
Time Weighted Rate of Return
The compound growth rate of $1 invested in the portfolio over the period. Ignores timing of cash flows (ie purchase/sale of portfolio) so is appropriate for measuring portfolio performance.
Simply calculate the return for each period (divs and share price movement) and then annualise.
Money Market Instruments
Bank Discount Yield
Definition and formula
This is the basis on which money market instruments are quoted.
Discount = FV - price you pay
t = Time to maturity
Money Market Instruments
4 money market interest rates
- Holding Period Yield (HPY): simple periodic rate, just discount/FV or (FV-PV)/PV
- Bank Discount Yield: Odd simple annualised rate used for money market, (discount/FV) * (360/t)
- Money Market yield (rm): Simple annualised yield, 360 basis, =HPY * 360 / t
- Effective Annual Yield: Proper compound annual yield, = (1+HPY)365/t - 1
Money Market Instruments
Bank Discount Yield
Issues with them
- Based on the FV instead of purchase price, return should be measured off purchase price
- Annualised of 360 days instead of 365
- Annualised with simple interest, ignores value of compounding
Money Market Instruments
Holding Period Yield
Total return earned if held to maturity (not annualised).
Money Market Instruments
Effective Annual Yield
The annualised HPY based on 365 day year, annualised.
Money Market Instruments
Money Market Yield
aka?
definition
calculation from BDY
a.k.a. CD equivalent yield
Annualised HPY using simple interest on 360 day basis. (HPY = holding period yield).
rmm = HPY * 360 / t
From BDY:
Bonds
Bond Equivalent Yield
Bond yields (in the US) typically quoted semi-annually. This method just doubles it (ignoring compound interest) to get an annualised yield.
So DON’T compare an annual yield bond to the BEY of a semi-annual yield bond.
Statistics
Definition of Parameter
A characteristic (value) of a population (not of a sample), denoted by greek letter.
For example the mean.
In investments, examples inlcude mean return and standard deviation of returns.
Statistics
Definition of a Statistic
An estimate of a parameter of a population, taken from a sample of that population.
Statistics
Definition of Inferential Statistics methods
Required qualities of the sample
Inferential Statistical Methods are used to draw conclusions about a large group based on a sample taken.
Require the sample to be either random or representative in different cases.
Statistics
Measurement
Definition of Nominal Scale
Assigning items to groups or categories, such as race or sex, qualitative rather than quantitative.
No ordering or ranking implied, but can allocate numbers to the groups (eg, 1 - value funds, 2 - growth funds).
Statistics
Measurement
Definition of Ordinal Scale
Allocated to each item a ranking for a certain characteristic (eg scale of 1 to 10 between worst and best performing manager).
There is an ordering implied but the scale is arbitrary and distances between the ranks not necessarily consistent.
Statistics
Measurement
Definition of Interval Scale
Items in population given a ranking for a certain characteristic, where an order is implied and the distance between each rank is standardised. Such that the difference between 0 and 10 is the same as 20 to 30.
However no zero point is defined therefore doubling from 10 to 20 is not the same as doubling from 20 to 40.
Statistics
Measurement
Definition of Ratio Scale
Ranking of items within a population on a given parameter, which has an ordering, where difference between each ranking is standardised and there is a defined zero point. So the effect of doubling from 10 to 20 is the same as from 20 to 40.
e.g. temperature on the Kelvin scale (NOT farenheit since the zero point in farenheit is arbitrary)
Statistics
Measurement
Order of Strength of the Scales
N - Nominal
O - Ordinal
I - Interval
R - Ratio
Statistics
Frequency Distributions
Definition of Absolute Frequency
Number of actual observations in a given interval.
Statistics
Frequency Distributions
Definition of Relative Frequency
The result from dividing the absolute frequency of a return interval by the total number of observations.
Statistics
Frequency Distributions
Definition of Cumulative Absolute Frequency
and
Cumulative Relative Frequency
Result of cumulating the results form absolute and relative frequency as you move from one interval to the next.
Statistics
Measures of Central Tendency
Definition of Geometric Mean
3 characteristics
See formula.
- Used when calculating returns over multiple periods
- Exists only if all values are greater than zero
- Always less than arithmetic mean unless numbers are all the same (in which case they’re the same)
Statistics
Measures of Central Tendency
Definition of Harmonic Mean
Special cases with 2 or 3 numbers
Special cases also given:
H(x1,x2) = 2x1x2 / (x1 + x2)
H(x1,x2,x3) = 3x1x2x3 / (x1x2 + x2x3 + x1x3)
Statistics
Median - ‘iles
Examples
Inter-quartile range
- There are 3 quartiles, 4 quintiles, 9 deciles and 99 percentiles in a data set
- They split the population into 4, 5, 10 and 100 groups
- Q1 is the first or lowest quartile, Q3 the highest
- Distance from Q1 to Q3 is the inter-quartile range
Statistics
Deviation
Range
Difference between the lowest and higest values in a population of numbers.
Statistics
Deviation
Mean Absolute Deviation
Take the absolute difference between each value and the mean, then take the average of those results.
Statistics
Deviation
Variance (for a population)
This is the average squared deviation of each value from the mean.
Statistics
Deviation
Variance (for a sample)
Same as population, average of squares of difference between values and the sample mean.
Dividing by n results in a baised estimator of population variance, using n - 1 gives an unbaised estimator.
Statistics
Deviation
Standard Deviation
1sd and 2sd bands
Simply the square root of the variance.
Normal distn - 68% within 1 sd, 95% within 2 sd.
Standard Deviation not directly comparable between different data sets since means are different sizes (not a relative measure).
Statistics
Deviation
Coefficient of Variation
A relative dispersion measure, so allows comparison between different data sets.
Simply divide standard deviation by the mean.
a.k.a. Relative Standard Deviation
Statistics
Chebyshev’s Theorem
For any sample/population, the proportion of observations within c standard deviations of the mean is at least 1 - 1/c2.
Works on sample and population, discrete or continuous data.
Allows us to measure minimum amount of dispersion from the standard deviation.
Statistics
Sharpe Measure
rp = mean return of portfolio
rf = risk free mean return
σp = standard deviation of portfolio
a.k.a. reward to variability ratio
Measures the reward to volatility trade-off and recognises the existence of a risk-free return.
Statistics
Skewness
Definition
Value for normal distn
The degree of asymmetry of a data set.
Normal distribution has zero skewness.
Positively Skewed Distribution means a long tail to the right (a few big wins, lots of small losses). Also say skewed to the right.
Statistics
Skewness
Where are mean, median and mode when skew is positive?
Mode: The peak of the distribution.
Mean: Pulled towards the long tail (extreme values).
Median: In-between.
Statistics
Skewness
Formula
Conditions for calculation to be valid
Valid when N is large.
Zero for normal distribution.
Statistics
Kurtosis
Definition
Measure of how much a distribution is stretched out to the tails or peaked around the mean, regardless of skew.
Normal distribution has a neutral kurtosis.
Statistics
Kurtosis
Words for types of kurtosis
- Platykurtic: Low peak, more returns with large deviations from the mean.
- Leptokurtic: Tall peak, few returns with large deviations from the mean.
- Mesokurtic: Same kurtosis as normal distribution.
Statistics
Kurtosis
Formula
Formula is for excess kurtosis.
Normal distribution has kurtosis of 3 and excess kurtosis of 0.
Probability
Empirical Probability
A probability based on frequency of occurence in a set of historical data.
Probability
Priori Probability
A probability based on logical analysis rather than historical observation (eg 50% chance of heads on coin toss).
Probability 3
Subjective Probability
A probability based on subjective judgement (eg John thinks there is a 60% chance of a merger occuring). Priori and Empirical probabilities by contrast are considered to be objective.
Probability
Marginal Probability
Another name for unconditional probability, i.e. just the probability that an event will occur, NOT conditional on any other events having occured.
Probability
Independence of two events
Multiplication Rule
Means P(A) = P(A|B) or vice versa.
In this case P(AB) = P(A) * P(B) which is the multiplication rule.
Probability
Total Probability Rule
P(A) = P(A|S1) + P(A|S2) + … + P(A|Sn)
Where S1 to Sn are mutually exclusive and exhaustive.
P(A) = P(A|S) + P(A|Sc)
Probability
Variance of a Random Variable
σ2(X) = E{ [X - E(X)]2 }
Probability
Standard Deviation of a Random Variable
The positive square root of variance.
Probability
Covariance
Calculation
Cov( Ri, Rj ) = E[( Ri - E( Ri ) ) * ( Rj - E( Rj ) )]
Note, covariance of a random variable with itself is:
Cov( Ri, Ri ) = E[( Ri - E( Ri ) )2]
i.e. it’s own variance
Probability
Correlation
Calculation for correlation between two returns
Divide covariance by the standard deviation of each random variable.
Probability
Expected return of portfolio
Expected variance of 2 member portfolio
(given means/variances of constituents)
Expected return is weighted average of individual returns.
Expected variance via formula below:
σ2(Rp) = w12σ2(R1) + w22σ2(R2) + 2w1w2Cov(R1,R2)
Probability
Bayes Formula
From total probablity rule:
P(X) = P(X|S) P(S) + P(X|Sc) P(Sc)
which gives us Bayes formula:
P(X|S) = P(X) * [P(S|X)/P(S)]
or
P(X|S) = [P(X)/P(S)] * P(S|X)
Probability
Combinations
Does order matter?
Formula
In Combinations order does NOT matter:
nCr = n! / (n-r)r!
Probability
Permutations
Does order matter?
Formula
For Permutations order DOES matter:
nPr = n! / (n-r)!
Distributions
Continuous Uniform Distribution
Describe
Probability density function
Cumulative density function
Mean
Variance
Equal probability (straight line) within a given range.
f(x) = 1/(b-a) for a<=x<=b
F(x) = (x-a) / (b-a) for a<=x<=b
µ(x) = (a+b)/2
σ2(x) = (b-a)2 / 12
Distributions
Bernoulli Trial
An experiment with two possible outcomes (i.e. single experiment in a binomial distribution)
Distributions
Binomial Random Variable
Definition and Formula
Mean
Variance
Binomial Random Variable B(n,p) is the number of successes in n bernoulli trials where probability of success in an individual trial is p.
Probability of r succeses in n trials is:
p(r) = nCr * pr * (1-p)n-r
µ(B(n,p)) = np
σ2(B(n,p)) = np*(1-p)
Distributions
Normal Distribution Confidence Intervals
90% conf. interval (5% either side)
95% conf. interval
99% conf. interval
Expressed as multiples of standard deviation
90% x-bar - 1.645σ to x-bar + 1.645σ
95% x-bar - 1.96σ to x-bar + 1.96σ
99% x-bar - 2.58σ to x-bar + 2.58σ
Distributions
Normal Distributions
Using z-tables
Z table is based on a normal distribution with mean 0 and standard deviation 1.
Z-value is therefore the number of standard deviations from the mean (z = (x - µ)/σ).
For a given potential outcome convert using the mean and SD of that test to a z value to find the probability of outcome being above/below that potential outcome.
Distributions
Multivariate Distributions
Definition
Distribution of a group of random variables, in this case several normally distributed variables e.g. the distribution of a portfolio of normally distributed stock returns.
Dependent on means and standard deviations of individual stocks plus the correlation matrix.
Distributions
Safety First
Define Shortfall risk
Roy’s Safety First Criterion
SF Ratio
Shortfall is risk that portfolio falls below an acceptable value.
Saftey First criterion is to choose a portfolio with the lowest possible probability of falling below this value.
For normal distribution this equates to maximising the SF-Ratio: SF Ratio = (E(RP) - RL) / σP
Where RP is portfolio return, RL is minimum return.
Distributions
Lognormal Distribution
Definition
A random variable Y follows a lognormal distribution if it’s natural logarithm lnY is normally distributed.
So it’s lognormal if its log is normal.
Distributions
Continuously compounded rate of return
Formula
Denoted by rt,t+1 (cont. comp. rate of return between t and t+1):
rt,t+1 = ln(St+1/St) = ln(1+Rt,t+1)
Gives a more reasonable average return as:
[(1.2/1 - 1) + (1/1.2 - 1)] / 2 = 2.5%
[ln(1.2/1) + ln(1/1.2)] / 2 = 0%
Sampling
Biased Sample
A sample that has been taken using a biased method, resulting in a sample with different characteristics than the population.
Note that a sample with different characteristics than the population as a result of randomness in a fair sample, is NOT a biased sample.
Sampling
Sample Distribution
For a given sample size, and sample statistic (e.g. the sample mean), the sample distribution is the distribution of outcomes of that statistic across an infinite number of samples.
Alternatively it’s the relative frequency of outcomes of the statistic for every possible sample of the population, of the given sample size.
Sampling
Stratified Random Sampling
Split the population up into sub-populations based on given characteristics, then select a sub-sample from each with size based on relative size of the sub-population. Put the sub-samples together to get a sample of the population.
This ensures proportional representation across the characteristics used to split the population.
Sampling
Cross-Sectional Data
As opposed to time-series data, cross-sectional data consists of observations at a single point in time, such as the closing prices of 20 different stocks at close on a given date.
Sampling
Central Limit Theorem
Given a distribution with mean µ and variance σ2, the sampling distribution of the mean x-bar approaches a normal distribution with mean µ and variance σ2/N as the sample size (N) increases.
With N > 29 it is normal EVEN IF underlying distribution is not normal.
This allows us to construct confidence intervals on the population mean from sample data using normal distn., regardless of whether the population is normally distributed!
Sampling
Standard Error (of the sample mean)
The standard error of a statistic is the standard deviation of the sampling distribution of that statistic.
σm = σ / sqrt(N)
Where σm is the standard error of the mean, σ is the standard deviation of the population and N is the sample size.
This DOES NOT require the pop distn to be normal.
Estimate using sample standard deviation (s) if population standard deviation (σ) is not known.
Sampling
Estimators
Desireable characteristics
Unbaisedness: The estimators expected value (mean of its sampling distn) equals the parameter it is meant to estimate.
Efficiency: Estimator is efficient if no other unbaised estimator of the parameter value has a lower standard error.
Consistency: Means the standard error of the unbaised estimator approaches zero as sample size increases.
Sampling
Point Estimate
Estimator
The single estimate of an unknown population parameter calculated as a sample mean is called the point estimate of the mean.
The formula used to calculate it is called the estimator.
Sampling
Confidence Intervals
eg 95% confidence interval for pop mean is 20 to 40
What is the degree of confidence?
What is the level of significance?
Degree of confidence is 95%
Level of significance is 5%
20 and 40 are the lower and higher confidence limits
There is a 95% probability that the population mean lies between 20 and 40
Sampling
T-distributions
When to use T-distribution instead of Z-distribution to build confidence intervals from sample
Degrees of freedom
requirements
If the variance is not known use t-distribution instead of z-distribution for confidence intervals (with t table based on N-1 degrees of freedom, where N is the sample size).
If the population is not normal make sure you have sample size of 30+.
If the sample size is very high using the z distn is usually ok.
Sampling
Data-snooping bias
Bias as a result of using somebody else’s results of empirical (historic data) analysis to guide your own analysis over essentially the same historical data.
Can be avoided by carrying out analysis on new data, although this is difficult in investment analysis because the set of historical data is limited.
Sampling
Data-mining bias
Bias created as a result of finding forecasting models through extensive searches of databases to find patterns.
Highly likely when there is no economic justification for the pattern.
Can be avoided by testing models on a different set of data.
Sampling
Survivorship Bias
Caused when analysis is carried out on a data set that has excluded (e.g.) stocks that have gone bankrupt. The data has an upward bias since it excludes a section of the population which performed very poorly.
Sampling
Look-ahead bias
Definition and usual direction of bias
Bias caused based on the assumption that fundamental information was available at a point in time when it isn’t.
For example assuming that people know their earnings data in January for January, when they might not find out till March.
Usually results in upwards bias.
Sampling
Time period bias
Where a conclusion drawn relates only to a particular time period which may make that conclusion time-specific.
Usually a problem if the time period is too short (eg covers only an economic upswing).
Also a problem if the time period is too long since fundamental economic structure may have changed.
Hypothesis Testing
Null Hypothesis
Designated H0 this is the hypothesis regarding the population (eg mean monthly income is $5000) which you desire to test.
It is either rejected or failed to be rejected, never accepted.
Hypothesis Testing
Alternate Hypothesis
Designated H1, this is the statement which is accepted if the sample data provides sufficient evidence that H0 is false.
Hypothesis Testing
Test Statistic
A test statistic is a number calculated from the sample whose value (relative to its probability distn) provides statistical evidence against the null hypothesis.
Typically of the form:
test statistic =
(sample statistic - H0 parameter value) / Standard error of sample statistic
Hypothesis Testing
Level of Significance
Chosen in testing, this is the probability that a null hypothesis which is true is rejected.
Designated by greek letter alpha.
Hypothesis Testing
Decision Rule
Critical Value
Critical Region
The decision rule is the statement of the conditions under which H0 is rejected or not.
The critical value (2 of them if two-sided) is the dividing point past which H0 will be rejected.
The critical region is the area where if the test stat falls in it, we REJECT H0.
Hypothesis Testing
Test Statistic for the mean
Note: With n=1 the sample distribution of the mean is just the distribution of the population, so the below simplifies to the z value.
This usually follows the normal distn (central limit theorem) therefore:
Hypothesis Testing
Errors (type I and II)
Define
Relation to alpha and ß
Type one error is the when H0 is true but is rejected.
Type two error is when H0 is false but is not rejected.
Type one is more serious and is controlled via the level of significance (alpha), which is the probability of a type one error. Reducing alpha to reduce the risk of a type one error increases the risk of a type two error (probability designated as ß).
Can only reduce both alpha and ß by increasing sample size.
Hypothesis
Power
The probability of correctly rejecting a false null hypothesis (1-ß). If the power of an experiment is low there is a high chance of an inconclusive result.
Assumes that H0 is false.
Hypothesis Testing
P-value testing
Instead of stating a decision rule, calculate the test statistic and the calculate the probability of getting a value more extreme than that (one or two-sided) assuming H0 is correct.
This probability can be compared to alpha value to decide whether to reject H0, but also provides extra information about how strong the rejection is.
Hypothesis Testing
2-independent population testing
Test statistic for differences between 2 means
Requirements
Below formula is the test statistic for the hypothesis that the difference between two population means is a given number (or zero, ie that they are the same).
Degrees of freedom are n1 + n2 - 2 if population variances are assumed to be the same.
Requires normal distribution
Hypothesis Testing
Paired Comparisons
Description
requirements
Used on differences between related data (eg before and after data, results for twins).
H0 : µd = µd0
Where µd is the difference between the means and µd0 is some fixed value (typically zero).
Requires Normal distribution
Hypothesis Testing
Paired Comparisons
Test Statistic
degrees of freedom
d-bar is the sample mean of differences
Standard error for the sample mean of differences:
sd-bar is sd/sqrt(n)
Standard deviation of the differences:
sd = sqrt( Σ(di - d-bar)2 / (n-1) )
n-1 degrees of freedom
Note: This is basically just normal distn.
Hypothesis Tesing
Difference between independent and paired testing
Subject is the testing of the differences between two means. Treatment depends on whether the two populations are related.
If the population is the same (eg before or after) or is some way dependent then it is paired testing.
If populations are different (typically also sample sizes will be different) it is independent.
Hypothesis Testing
Single Population Variance Testing
What is the test statistic (name and formula)
requirements
Chi-squared statistic.
s2 is the sample variance
σ02 is the hypothesised value for σ2
Population MUST be random AND normally distributed
n-1 degrees of freedom (similar to t-distn)
Hypothesis Testing
Single Population Variance Testing
Chi-squared distn. shape
Hypothesis Testing
Differences between variances
Relevant Distribution
Test Statistic
requirements
Fischer distribution (F-distribution)
F = S12 / S22
Convention states larger sample variance goes on top.
Requires both populations to be normally distributed.
Note that degrees of freedom are excluded since n1-1 in both denominator and numerator.
Hypothesis Testing
Differences between variances
F-distribution useage
F-distn tables inputs
H0
requirements
F-distribution tables denoted by F(n1 - 1, n2 - 2) where n1 and n2 are sample sizes of numerator and denominator.
F-distribution is one-directional, H0 is that σ12 <= σ22 because we chose 1 & 2 such that s12 > s22. We then test whether the ratio is high enough to reject H0.
For two-sided tests (H0: σ12 = σ22) need to halve alpha.
As with chi-squared, distn MUST be random AND normal.
Hypothesis Testing
Non-parametric testing
This is testing of something other than a parameter of the population (such as mean or variance).
Parametric tests are preferred where relevant, but may not be due to the distribution of the data, nature of the data (eg ordinal/ranked data) or where no parameter is involved (eg testing whether data is indeed random).
Technical Analysis
Technical vs Fundamental Analysis Philosophy
Do they believe supply and demand control prices?
Both agree that supply and demand control prices, however technical analysts believe this information feeds into prices gradually over a period of time and trends can be taken advantage of.
Technical Analysis
Point and Figure Chart
Xs represent upwards price trends and Os represent donwards trends.
X axis not linear in time, dependent on price movements. Chart switches between X’s and O’s when trend deemed to have shifted.
Technical Analysis
Trend lines
Drawn above or below the price line?
For upwards trends draw an upwards pointing support line below the low points.
For a downwards trend draw a downwards trending resistance line joining the peaks.
Technical Analysis
Change in Polarity
Definition
When a price breaks through a resistance line that same price level then becomes a support (or vice versa), referred to as a change in polarity.
Technical Analysis
Head and Shoulders Pattern
Reversal or continuation?
Volume indicators
Target price
Head and shoulders is a reversal pattern (as is inverse HaS).
Look for higher volume on the left shoulder rally than the head rally, increases in volume on the sell-offs.
Target price = neckline - (head peak - neckline)
Technical Analysis
Double/Triple top/bottom pattern
Description
Reversal or Continuation
Double (or triple) top/bottom is a reversal pattern characterised by the price hitting a support/resistance level twice and failing to break it.
Technical Analysis
Triangle Patterns
Three different types
Reversal or Continuation
Traingles are continuation patterns, either ascending (supported by ascending trend line, top is a flat resistance line), descending (descending resistance line with stock bouncing off a flat support line) and symmetrical (both support ascending and resistance descending).
The original pattern is expected to assert itself (ie the horizontal line for asc/desc is only temporary).
Technical Analysis
Rectangle Pattern
Description
Continuation or reversal
Horizontal support and resistance lines, ie rangebound. Can stay in the range for a while, but usually expect the trend before the pattern was established to eventually continue.
Technical Analysis
Flag
Pennant
Short-term continuation patterns representing a consolidation for a short time.
A flag has parallel support and resistance lines in a different direction to the larger trend.
A pennant is a symmetrical triangle (ascending support, descending resistance) with a typically neutral overall slope.
Technical Analysis
Golden Cross
Definition
What is the opposite called?
When a short-term moving average breaks out above a longer-term moving average this is considered a bullish signal.
The opposite is a dead cross.
Technical Analysis
Momentum or Rate of Change (ROC) Oscillator
Definition
Measure the percentage price change over a given period (eg charts the % price change over the last 20 days).
Technical Analysis
Relative Strength Index (RSI)
Definition
Interpretation of the figure
Compares the average price change during advancing periods to average price change during declining periods.
RSI = 100 - 100/(1 + RS)
Where RS = average gain / average loss
RSI is a range of zero to 100 where above 70 considered overbought and below 30 considered oversold.
Technical Analysis
Stochastic Oscillator
This is simply the level of the close expressed as a percentage between the lowest low and highest high in its current range (so at 50% it’s in the middle of its established range).
Technical Analysis
Moving Average Convergence Divergence (MACD)
Simply the difference between a short and long term moving average, so when they converge the value is zero, and as the moving averages diverge the MACD becomes negative or positive.
Technical Analysis
Arms index or TRIN
Indicator that measures the extent to which money is moving into or out of rising or declining stocks.
Ratio of 1 means market is in balance.
Ratio > 1 means more money is moving into declining stocks.
Ratio < 1 means more money moving into advancing stocks.
Technical Analysis
Kondratieff Waves
Sinusoidal like waves which the world economy follows on a periodicity of 40 to 60 years.
Technical Analysis
Elliot Wave Theory
Description
Numbers of waves
Fibonnaci connection
States that the market isn’t random but moves in cycles.
Says the market moves in five waves of the prevaling trend (impulse waves) and three corrective waves which counter the trend.
The waves count is a Fibonnaci sequence.
Technical Analysis
Intermarket Analysis
Simply the practice of looking at several related markets at the same time to determine patterns (eg US bond market and US equity market).
Holding Period Return
HPR = 1 + HPY
Kurtosis
Which has fatter tails, leptokurtic or platykurtic?
Leptokurtic distributions have FAT tails.
Platykurtic distributions have more observations far away (so tails stretch further away) but observations in the tails less bunched together, so they look LONG and THIN.
How do you answer questions about confidence on ranges if distribution isn’t known (i.e. not necessarily a normal distribution)?
Use Chebyshev’s equation to get confidence intervals based on # standard deviations for any distribution.
US Treasury Convention
Price of 134:09 means?
134 9/32
Aggregate Demand
Which of these 2 factors has an impact on price elasticity of demand for a product?
Changes in consumer price expectations
Amount of time since the price change
Amount of time since price change (along with % of income spent on the product and closeness of substitutes) impacts elasticity of demand.
Changes in price expectations shifts the aggregate demand curve to the left or right, but doesn’t impact elasticity of demand.
Backfill Bias
Backfill bias is when a new item is added to an index and performance from before the date of its addition is included in the index.
