Quantitative Methods and Financial Modeling
Domain 3 - Quantitative Methods and Financial Modeling
This domain tests time value of money, descriptive statistics, probability, sampling, hypothesis testing, and regression. Modeling questions often ask you to interpret a coefficient or decide whether a result is statistically significant, not merely to compute a number.
Core rules
- Time value: PV = FV / (1 + r)^n. For annuities, use the annuity factor; for perpetuities, PV = cash flow / r. Match the rate and period conventions.
- Hypothesis testing: State the null and alternative, choose the significance level, compute the test statistic, and compare it with the critical value or p-value.
- Regression: The slope measures the expected change in the dependent variable for a one-unit change in the independent variable, holding other regressors constant. The t-statistic tests whether a coefficient differs from zero.
- R-squared: The proportion of variation in the dependent variable explained by the model; it does not prove causation.
- Model risk: Heteroskedasticity, serial correlation, multicollinearity, and data snooping can invalidate inference.
Worked example
A sample of 36 observations has a mean of 52 and a sample standard deviation of 12. Test whether the population mean differs from 50 at the 5% level. The standard error is 12 / sqrt(36) = 2. The t-statistic is (52 - 50) / 2 = 1.00 with 35 degrees of freedom. The two-tailed 5% critical value is about 2.03. Because 1.00 is less than 2.03, fail to reject the null. The p-value is roughly 0.32, so the evidence is not statistically significant at 5%. Note that the economic size of the difference may still matter; statistical insignificance is not the same as no effect.
Traps that cost marks
- Using a one-tailed critical value for a two-tailed test.
- Confusing the standard deviation of the sample with the standard error of the mean.
- Interpreting R-squared as proof that one variable causes another.
- Ignoring heteroskedasticity when reading standard errors.
- Mixing arithmetic and geometric returns when evaluating past performance.