Standard error
The dispersion of an estimate rather than of the data. It shrinks with the square root of the sample, so precision gets expensive quickly.
Where you will meet it
Standard error appears in 11 learning outcomes on the CFA syllabus. A few of them:
- Explain what a confidence interval around a population mean tells you
“A confidence interval for a population mean is the sample mean plus or minus a reliability factor times the standard error, where the standard error is the sample standard deviation divided by the square root of n.”
- Work out what debt costs a firm after tax
“Using the historical coupon is the standard error: it describes what the company agreed to in the past, not what capital costs now.”
- Set up tests of whether a multiple regression's coefficients, taken two or more at a time, are jointly significant and explain what the outcome of such joint tests tells you
“A single coefficient is tested with t = (estimate − hypothesised value) ÷ standard error, with n − k − 1 degrees of freedom, and the hypothesised value need not be zero.”
- Explain resampling techniques, the bootstrap among them
“The bootstrap draws samples of the same size with replacement, computes the statistic each time and uses the spread of those values as the standard error.”
Practise it
Practise standard error until it is automatic: questions that explain every wrong option.
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