CFA resources

Investment analysis, valuation and portfolio management

• 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

• Bond prices and yields: understanding the inverse relationship

  Learn why a fixed-rate bond’s price changes when the market yield changes.

  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

• Default probability and credit loss severity

  Separate the likelihood of default from the loss conditional on default.

  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

• Designing engagement objectives and escalation decisions

  Build an objective, evidence trail and conditional next action for an issuer dialogue.

  Lessons

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

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

  Lessons

• Specifying an exclusion rule that can be checked

  Define the activity, metric, threshold, data source and treatment of missing information.

  Lessons

• Liquidity ratios and the quality of current assets

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

  Lessons

• Checking probabilities and a complete scenario partition

  Check individual bounds, overlaps and the sum across mutually exclusive exhaustive scenarios.

  Lessons

• Checking a two-stage probability tree

  Check each conditional split, path product and terminal probability.

  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

• Early-payment discounts and the additional credit period

  Separate invoice timing, the discount amount and the cost of financing a discounted payment.

  Lessons

• Choosing a common date for cash-flow values

  Move differently dated cash flows to the same date before adding their values.

  Lessons

• Basis points, percentage points and decimal yield changes

  Avoid a hundredfold error when entering yield changes in formulas.

  Common mistakes

• Why a cash-cycle reduction does not specify cash released

  Use each changed component’s own flow base instead of multiplying all days by COGS.

  Common mistakes

• Mixing average and ending assets in DuPont analysis

  Check that the asset amount cancels between turnover and the equity multiplier.

  Common mistakes

• Why dividing an effective annual rate by twelve changes the model

  Use the annual growth factor to obtain an equivalent monthly rate.

  Common mistakes

• Material nonpublic information during an engagement meeting

  Identify the information-handling issue before making a trading recommendation.

  Common mistakes

• A rising goodwill percentage does not identify its cause

  Separate changes in the numerator from changes in the asset denominator.

  Common mistakes

• Recognising a solution versus solving independently

  Check what you can produce before viewing the worked answer.

  Common mistakes

• Why P(A given B) differs from P(B given A)

  Recover the joint probability, then divide by the probability of the new condition.

  Common mistakes

• Variance in percentage units and decimal-return units

  Account for the squared scale factor when converting variance.

  Common mistakes

• Restarting finance exam study after a break

  Use a short diagnostic to distinguish forgotten material from unfinished material.

  Study plans

• Building a finance exam retake plan

  Separate knowledge gaps, execution errors and time pressure before choosing new work.

  Study plans

• A study plan for variable work shifts

  Assign tasks to flexible block types when the same weekday is not always available.

  Study plans