Quantitative Methods
What you must know
Core blocks: time value of money (PV/FV, annuities, NPV vs IRR, money-weighted vs time-weighted return); descriptive statistics (arithmetic, geometric and harmonic means, median, range, mean absolute deviation, variance, standard deviation, coefficient of variation, skewness, kurtosis); probability (addition and multiplication rules, conditional probability, Bayes, expected value, covariance, correlation); sampling and estimation (central limit theorem, standard error, confidence intervals, hypothesis testing with Type I and Type II errors and p-values); and regression (slope interpretation, R-squared, t-tests, assumptions).
Traps
(1) Pick the right mean: arithmetic for a one-period expected return, geometric for compound multi-period growth, harmonic for average cost per share with fixed dollar purchases. (2) Sample variance divides by n-1; population variance by N. (3) NPV and IRR can rank mutually exclusive projects differently - trust NPV; IRR can be undefined with multiple sign changes. (4) A p-value is not the probability the null is true; it is the smallest significance level at which the null is rejected. (5) Type I error probability equals the significance level. (6) Scalar transformations change covariance but not correlation.
Worked example
Invest $1,000 at the start of each of two years at prices of $25 and $40. Shares bought: 40 + 25 = 65, so average cost = $2,000/65 = $30.77. The harmonic mean is 2/(1/25 + 1/40) = $30.77, matching the true average cost, while the arithmetic mean of $32.50 overstates it.