CAIA resources

Alternative investments and portfolio applications

• Payables turnover using a purchases base

  Use the payables turnover using a purchases base relationship with explicit definitions.

  Formulas

• Quick ratio with explicit asset components

  Read the quick ratio with explicit asset components formula, variables and scope.

  Formulas

• Receivables turnover with a stated sales base

  Use the receivables turnover with a stated sales base relationship with explicit definitions.

  Formulas

• Return on equity with a stated average

  Use the return on equity with a stated average relationship with explicit definitions.

  Formulas

• Single-sum present and future value

  Use the single-sum present and future value relationship with its timing and rate conditions.

  Formulas

• Three-factor DuPont identity

  Use the three-factor dupont identity relationship with explicit definitions.

  Formulas

• Total asset turnover with an average base

  Use the total asset turnover with an average base relationship with explicit definitions.

  Formulas

• Simple and effective annualization of discount costs

  Use the simple and effective annualization of discount costs relationship with explicit definitions.

  Formulas

• Period cost of forgoing an invoice discount

  Use the period cost of forgoing an invoice discount relationship with explicit definitions.

  Formulas

• Preparing paired returns for a tracking error calculation

  Check date alignment, return conventions and missing observations before entering two series.

  Tool guides

• Bonferroni thresholds and the family error bound

  Divide a family error budget across valid individual tests.

  Formulas

• Assuming independence in every multiple-test screen

  Inspect the product step rather than treating 1 − (1 − alpha)^m as universal.

  Common mistakes

• Family-wise error and false discovery rate

  Identify whether a method controls any error or an expected fraction among rejections.

  Concepts

• False-rejection counts and family error risk

  Read two different summaries of a fictional ten-test experiment.

  Worked examples

• Halving every two-sided p-value

  Check the statistic sign and the planned alternative before using a tail shortcut.

  Common mistakes

• Mean confidence intervals and prediction intervals

  Distinguish estimating the population mean from predicting a new observation.

  Comparisons

• Reconciling a mean interval with a two-sided test

  Use the same model and uncertainty inputs in both calculations.

  Worked examples

• A mean test with known population standard deviation

  Reconstruct the standard error, standardized statistic and two-sided decision.

  Worked examples

• Error probability across independent tests

  Use the complement calculation with its independence and true-null assumptions.

  Formulas

• P-values and the null model

  Read the conditioning statement before interpreting a small probability.

  Concepts

• A one-sided test with an opposite-sign statistic

  Use the planned tail when the estimate points away from the alternative.

  Worked examples

• Treating a p-value as the probability of the null

  Repair the reversal from a model-conditional tail area to a hypothesis probability.

  Common mistakes

• Practice: tails, uncertainty and error budgets

  Check test direction, independent-mean precision and family corrections with explained answers.

  Practice

• Sample size and mean-estimation precision

  Calculate the sample-size change needed to halve standard error under a fixed-variance model.

  Worked examples
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  Statistical test research log

  Download a structured CSV for hypotheses, selection, uncertainty and family treatment.

  Templates

• Sample standard deviation versus standard error

  Explain which variation each statistic describes before comparing magnitudes.

  Concepts

• Standard error of an independent mean

  Distinguish uncertainty of a mean from variability of individual observations.

  Formulas

• Statistical significance and effect size

  Read magnitude and uncertainty before assigning practical meaning to a threshold crossing.

  Concepts

• Normal-test p-values by direction

  Calculate upper, lower and two-sided tails for a standard-normal statistic.

  Formulas

• Designing and reporting a hypothesis test

  Connect the research question, null model, test direction and reported result.

  Lessons

• Ordinary annuity and annuity-due timing

  Place equal payments at the correct dates before applying the value factor.

  Lessons

• Balance-sheet assets, liabilities and equity

  Read the accounting equation and distinguish recognised balances from a complete business valuation.

  Lessons

• Cash conversion cycle and its flow bases

  Match inventory, receivables and payables with the flows and period length used to calculate their days.

  Lessons

• Reading a common-size balance sheet

  Scale statement items by total assets while preserving accounting and measurement context.

  Lessons

• Discounting cash flows with consistent time periods

  Match cash-flow timing, rate conventions and time-zero signs.

  Lessons

• Reconciling DuPont analysis to return on equity

  Use consistent period and average-balance inputs to reconstruct the direct return ratio.

  Lessons

• Economic order quantity and the ordering-holding trade-off

  Inspect the deterministic cost objective before using the square-root order quantity.

  Lessons

• Liquidity ratios and the quality of current assets

  Compare defined numerators while retaining timing, collectability and financing context.

  Lessons

• Nominal and effective interest rates

  Compare quoted annual rates only after identifying the compounding convention.

  Lessons

• Screening constraints and the feasible portfolio set

  Separate portfolio eligibility constraints from return estimates and realised performance.

  Lessons