annuity due BGN

• Net Present Value
  • for investment decision making in Corporate Finance

• Internal Rate of Return
  • set NPV = 0
  • IRR -> CPT

• Perpetuity
  • payment for infinite time period
  • where PV = Present Value of the Perpetuity, A = the Amount of the periodic payment, and r = yield , discount rate or interest rate.

• Risk Free Rate

Discounted Cash Flow

• Holding Period Return
  • true yield
  • (ending value + dividend)/beginning value - 1

• Bank discount yield
  • percent discount form face value

• Effective annual yield
  • for n compounding periods per year:
    

• • for infinite time period:
    

• Weighted average

• Geometric mean

• Harmonic mean

• measurement scales(NOIR) - Nominal(no context; weakest), Ordinal(accoding to characteristics), Interval(special meaning to difference to numberical values), Ratio(scale amounts; strongest)

• Correlation: degree of linear dependence between the variables
  • 1 in the case of an increasing linear relationship,
  • ?1 in the case of a decreasing linear relationship,
  • some value in between in all other cases
  • the closer the coefficient is to either ?1 or 1, the stronger the correlation between the variables.

• Bayes formula

• Permutation: order matters nPr = n! / (n-r)!
• Combination: order does not matter nCr = n! / r! (n-r)!

• Mean Absolute Deviation

• Standard deviation

• Chebyshev’s inequality : no more than 1/k2 of the values are more than k standard deviations away from the mean.

• Sharpe ratio: measure of the excess return (or Risk Premium) per unit of risk in an investment asset

• Roy's Safety-First criterion

P(Ra < Rm) = [E(R_P)-R_L]/σ_P

• Skewness
  • measure of the asymmetry
  • Positive skew: mode < median < mean
  • negative skew: mode > median > mean

• Kurtosis
  • measure of the "peakedness"; can be either leptokurtic or platykurtic

Probability Concepts

• Probability distribution: of all possible outcomes for a random variable
  • discrete distribution: finite number of possible outcomes
  • continuous distribution: infinite number of possible outcomes
  • Probability function p(x): probability that a discrete random variable will take on the value x
  • Probability density function f(x): probability a continuous random variable will take on a value within a range
  • Cumulative distribution function F(x): probability a random variable will be less than or equal to a given value
  • Binomial random variable: probability of exactly x successes in n trials

• Confidence interval: a range of values around an expected outcome within which we expect the actual outcome to occur some specified percent of the time
  • 90% confidence interval = Χ ± 1.65σ
  • 95% confidence interval = Χ ± 1.95σ
  • 99% confidence interval = Χ ± 2.58σ

• Degrees of freedom
  • sufficiently high df is approximately normal
  • higher degrees of freedom, thiner tails

• Standard normal distribution: μ=0 σ=1
  • z-value standardization

 
where  
plug-in z-value to get F(z) from z-table

• Covariance

• Coefficient of Variation

C_V = σ / μ

• Monte Carlo Simulation: to estimate distribution of derivatives prices or of Net Present Values

• Continuous compounding = ln(1+HPR)

• Sampling: to make inferences about the parameters of a population
  • time-series data- gathered from each time periods
  • cross-sectional data- data from a single time period

• Stratified sampling: random picks within subgroups

• Central limit theorem
  • sample mean for large sample sizes will be distributed normally
  • as sample size increases, becomes more accurate in respect to population data
  • holds for n > 30

• Test statistic: difference between population sample and hypothesized value

• Z-test

• Standard error

• Student's t-test
• used when sample size is small or variance unknown

• Chi square test

used when H0: σ² = σ₀<super>2</super>

• Confidence interval (level of significance:probability of rejecting true H₀)
  • 68% of observations fall in ±1σ
  • 95% of observations fall in ±1.96σ
  • 99% of observations fall in ±3σ

• Types of Bias
  • data-mining~ : repeatedly doing tests on same data sample
  • sample selection~ : sample not really random
  • survivorship~ : sampling only surviving firms
  • look-ahead~ : using information not available at the time to construct sample
  • time-period~ : relationship exists only during the time period of sample data

Hypothesis Testing

• H₀: hypothesis set up to be nullified or refuted in order to support an alternate hypothesis.
• H₁: alternative hypothesis
• Type I error(Significance level): rejecting a null hypothesis when it is actually true; decreases as confidence interval(tradeoff) increases
• Type II error(1 - Power of test): failing to reject a null hypothesis when the alternative hypothesis is the true; increases as confidence interval increases

• Volatility estimation
  • unbiased~ : has an expected value equal to the true value of the population parameter
  • consistent~ : more accurate the greater the sample size
  • efficient~ : has the sampling distribution that is less than that of any other unbiased estimator

• Statistical significance omits transaction costs, taxes, risk factor from economical significance

Technical Analysis

• Assumptions
  • stock values determined by supply & demand
  • S&D driven by both rational & irrational behavior
  • security prices move in trends
  • changes observed in market price behavior

• Fundamental analysts -> look for changes in stock values; stock prices adjust quickly to new information
• Technical analysts -> look directly for signals & indicators of changes in S&D; stock prices move in trends that can persist for long periods
  • + quick&easy, psychological reasons
  • - subjective judgement required for interpretation, no evidence in price trends, value neutralized

• Technical indicators
  • Contrarian~ : do opposite of what majority are doing
  • Smart money~ : mimic investors known for investment success