FRM resources

Market, credit, liquidity and operational risk

• What defines a simple random sample?

  Inspect the probabilities of complete samples as well as individual-unit chances.

  Concepts

• Stratified and cluster selection

  Compare what is selected from each group before deciding which design is being described.

  Comparisons
• 

  Stratum allocation and estimation sheet

  Download a CSV that separates population shares from sampled counts.

  Templates

• Stratified sampling and population weights

  Separate subgroup sample allocation from the shares used in the population estimate.

  Lessons

• Population-weighted stratum mean

  Combine stratum sample means using defined population-unit shares.

  Formulas

• Systematic sampling: random start and list order

  Inspect the interval, start rule and ordering before treating a sample as random.

  Concepts

• Treating thirty observations as a normality guarantee

  Read the theorem conditions and actual approximation quality.

  Common mistakes

• Building a sampling-design work sample

  Show how a research question becomes a frame, selection plan and defensible estimate.

  Careers
• 

  Formula recall and conditions worksheet

  Download a sheet for variables, units, boundary checks and independent attempts.

  Templates
• 

  Mock-exam error log and review worksheet

  Download an editable CSV and turn practice errors into specific review actions.

  Templates
• 

  Operating-ratio definition log

  Download a worksheet for flow bases, averages, proxies and interpretation.

  Templates
• 

  Retake review and triage worksheet

  Download a structured record for evidence, corrections and fresh tasks.

  Templates
• 

  Exclusion-screen review worksheet

  Download an editable CSV for thresholds, missing values and screening decisions.

  Templates
• 

  Weekly study-block worksheet

  Download an editable plan that records tasks, outputs and actual time.

  Templates
• 

  Finance work-sample outline

  Download an editable outline for a question, inputs, method and limitations.

  Templates
• 

  Equal-payment annuity value calculator

  Compare end-period and beginning-period payment patterns at defined dates.

  Tools
• 

  Bayes probability update calculator

  Combine a prior with evidence probabilities under an event and its complement.

  Tools
• 

  Bond price calculator

  Price a regular fixed-rate bond and inspect its cash-flow sensitivity.

  Tools
• 

  Duration and convexity calculator

  Compare duration estimates with the exact repricing of a regular bond.

  Tools
• 

  Cash conversion cycle calculator

  Compute inventory, receivable and payable days with explicit period flows.

  Tools
• 

  DuPont analysis calculator

  Reconcile three and five factors with direct return on equity.

  Tools
• 

  Expected credit loss calculator

  Explore the simple PD × LGD × EAD loss model.

  Tools
• 

  Effective annual rate calculator

  Convert a nominal annual quotation and inspect its periodic rate.

  Tools
• 

  Economic order quantity calculator

  Inspect the deterministic ordering and holding cost trade-off.

  Tools
• 

  Liquidity ratios calculator

  Calculate current, quick and cash ratios from explicit current-asset components.

  Tools
• 

  Net present value calculator

  Discount an initial payment and equally spaced future cash flows.

  Tools
• 

  Odds and probability calculator

  Convert odds for a risk event into event and complement probabilities.

  Tools
• 

  Scenario expected return and risk calculator

  Calculate expected return, variance and standard deviation from explicit scenario probabilities.

  Tools
• 

  Single-sum present and future value calculator

  Move one amount backward or forward over a stated count of equal periods.

  Tools
• 

  Study-hours planner

  Calculate an average weekly and daily workload from your own study target.

  Tools
• 

  Tracking error calculator

  Calculate sample tracking error from paired portfolio and benchmark returns.

  Tools
• 

  Trade-credit discount cost calculator

  Compare an invoice discount, two annualization conventions and a stated funding model.

  Tools

• Pricing a three-year annual-coupon bond payment by payment

  Work through every discounted coupon and principal payment.

  Worked examples

• Decomposing an uneven stream into an annuity and an extra payment

  Check cash-flow additivity using two representations of the same dated stream.

  Worked examples

• Building and reconciling a common-size balance sheet

  Divide each selected amount by the same asset base without counting subtotals twice.

  Worked examples

• Updating a control-weakness probability after an exception flag

  Calculate both flag branches before interpreting the posterior.

  Worked examples

• Converting covariance into correlation with consistent units

  Normalize a covariance of −18 using standard deviations of 6% and 5%.

  Worked examples

• Why paying current debt can raise the current ratio and lower the cash ratio

  Trace both numerator and denominator changes in a stated cash repayment.

  Worked examples

• Calculating a cash cycle with separate flow bases

  Reconstruct each days measure before combining the result.

  Worked examples

• How the debt definition changes a leverage ratio

  Compare interest-bearing debt with total liabilities using the same equity base.

  Worked examples