Financial Math – Basic

Time value of money (CFA Level I Suggested Reading)

  • How to calculate the future value (FV) and present value (PV) of: a single sum of money; a regular annuity and an annuity due; a series of uneven cash flows; a perpetuity
  • How to calculate an unknown variable, given the other relevant variables, in: single-sum problems; annuity problems; and perpetuity problems
  • The equivalence between present value and discounted future value
  • How to solve time value of money problems when compounding periods are other than annual
  • The difference between the stated annual interest rate and the effective annual rate
  • How to calculate the effective annual rate, given the stated annual interest rate and the frequency of compounding

DCF Applications (CFA Level I Suggested Reading)

  • Net present value and internal rate of return of a capital investment project
  • The decision rule for making investment decisions under the net present value and internal rate of return methods
  • Problems associated with the internal rate of return method
  • Money-weighted versus time-weighted rates of return
  • The bank discount yield, holding period yield, effective annual yield, and money market yield for a US Treasury bill
  • Conversion between holding period yields, money market yields, and equivalent annual yields
  • Calculation of bond equivalent yield

Investment Statistics (CFA Level I Suggested Reading)

  • Parameters and the different types of measurement scales
  • Frequency distributions
  • A holding period return
  • The use of intervals to summarize data
  • Calculating relative frequencies, given a frequency distribution
  • The properties of data presented as a histogram or a frequency polygon
  • Measures of central tendency: the population mean, sample mean, arithmetic mean, geometric mean, weighted mean, median, and mode
  • The differences between arithmetic and geometric means
  • Quartiles, quintiles, deciles, and percentiles
  • Portfolio return as a weighted mean, weighted average or mean, a range and mean absolute deviation, and a sample and a population variance and standard deviation
  • Items falling within a specified number of standard deviations of the mean, using

Chebyshev's inequality
  • Coefficient of variation and the Sharpe measure of risk-adjusted performance
  • The relative locations of the mean, median, and mode for a nonsymmetrical distribution
  • Measures of skewness and kurtosis
  • Why a semi-logarithmic scale is often used for return performance graphs

Probability concepts (CFA Level I Suggested Reading)

  • The investment consequences of probabilities that are inconsistent and the difference between unconditional and conditional probabilities
  • Dependent and independent events
  • How to calculate: a joint probability of two events; a joint probability of any number of independent events; an unconditional probability using the total probability rule; expected value, variance, and standard deviation; Covariance and correlation and the relationship among covariance, standard deviation, and correlation
  • The expected return and the variance for return on a portfolio and covariance given a joint probability function
  • Updated probability, using Bayes' formula
  • How a specified number of tasks can be performed using the multiplication rule of counting
  • Solving counting problems using the factorial, combination, and permutation notations
  • The difference between problems for which different counting methods are appropriate
  • The number of ways to choose r objects from a total of n objects, when the order in which the r objects is listed does or does not matter

Probability distributions (CFA Level I Suggested Reading)

  • Discrete and continuous random variables
  • The range of possible outcomes of a specified random variable
  • Key properties of a probability function and a cumulative distribution function
  • Calculating probabilities for a random variable, given a cumulative distribution function
  • How to calculate: probabilities given a discrete uniform probability distribution; probabilities given a binomial probability distribution; and the expected value and variance of a binomial random variable
  • Using binomial trees to describe stock price movement and calculate the expected terminal stock price
  • Continuous distribution, normal and standard normal distributions
  • Confidence intervals for a normally distributed random variable
  • The difference between univariate and multivariate distributions
  • Shortfall risk and Roy's safety-first criterion
  • Lognormal and normal distributions and the difference between discretely and continuously compounded rates of return
  • The major applications and limitations of Monte Carlo simulation and historical simulation

Sampling and estimation (CFA Level I Suggested Reading)

  • Simple random sampling, sampling error, a sampling distribution and the difference between simple random and stratified random sampling; and between time-series and cross-sectional data
  • Central limit theorem and the standard error of the sample mean
  • Point estimate and confidence interval estimate of a population parameter
  • A confidence interval for a population mean, given a normal distribution with either known or unknown population variance
  • The properties of Student's t-distribution
  • The issues surrounding selection of the appropriate sample size, as well as data-snooping/data-mining bias, sample selection bias, survivorship bias, look-ahead bias, and time-period bias

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