Quantitative Methods
Quantitative Methods supplies the toolkit the rest of the exam leans on: time value of money, descriptive statistics, probability distributions, sampling and hypothesis testing, and simple linear regression. Items are short and computational, so precision about conventions earns more than breadth of reading.
Time value of money
- NPV sums discounted cash flows; accept a project when NPV is positive.
- IRR is the discount rate that sets NPV to zero. It can produce multiple answers with non-conventional cash flows and ignores project scale when ranking.
- Effective annual rate = (1 + stated rate/m)^m - 1; use it whenever compounding frequency differs between alternatives.
Statistics and inference
- The geometric mean is at or below the arithmetic mean and measures compound growth; the arithmetic mean is the right input for a one-period expected return.
- Coefficient of variation = standard deviation / mean, and is unitless, so it compares risk across differently priced assets.
- Standard error of the sample mean = s / square root of n; the central limit theorem makes the sample mean approximately normal for large n regardless of the population distribution.
- Test statistic = (sample statistic - hypothesised value) / standard error. A Type I error rejects a true null; the p-value is the smallest significance level at which the null is rejected.
Worked example
A sample of 16 observations has mean 52 and sample standard deviation 8. Test H0: mu = 50 against a two-sided alternative at the 5% level. Standard error = 8 / sqrt(16) = 2. t = (52 - 50) / 2 = 1.00 with 15 degrees of freedom. The two-tailed 5% critical value is about 2.131, so |t| = 1.00 does not reach it: fail to reject H0. Note that a one-tailed test at 5% would use roughly 1.753 and still fail to reject, but the threshold changes, which is exactly where candidates slip.
Traps that cost marks
- Using n rather than n-1 for the sample standard deviation in a test statistic.
- Confusing money-weighted return (an IRR, sensitive to cash-flow timing) with time-weighted return (which judges the manager).
- Reading R-squared as proof of causality, or as the slope of the regression.
- Confusing correlation with slope: correlation is scale-free and bounded by -1 and +1.