Sensitivity analysis tests how changes in key assumptions affect a financial result. In forensic accounting, it shows which inputs drive a loss estimate or valuation and where the conclusion may change. HM Treasury’s Green Book uses the same approach in public spending appraisal, including tests of the values at which an option stops representing value for money.
What happens if the loss period is shorter than claimed, recovery is higher than assumed, or the counterfactual business would have performed less strongly? A single figure rarely answers those questions. A properly structured analysis shows which assumptions drive the result, how far they can move, and the precise threshold at which the conclusion changes.
For UK business owners, finance directors, solicitors, insurers and individuals, that distinction matters. Sensitivity analysis can test a damages calculation, valuation, business-interruption claim, fraud loss, investment decision or tax outcome without presenting an uncertain estimate as fact. It also gives opposing experts, insurers and courts a transparent way to examine the reasoning behind a conclusion.
Table of Contents
- What Sensitivity Analysis Actually Does
- Why Single Estimates Fail in Disputes
- Comparing One-Way, Multi-Way, Scenario and Tornado Methods
- Worked Example Showing Switching Values in a Fraud Claim
- How to Present a Reproducible Sensitivity Schedule
- When to Engage a Forensic Accountant for Sensitivity Analysis
What Sensitivity Analysis Actually Does
Sensitivity analysis changes selected assumptions and measures the effect on a financial outcome. The outcome might be a quantified claim, net present value, benefit-cost ratio, gross margin, cash balance or covenant headroom. The purpose isn't to predict the future perfectly. It's to establish whether the answer remains defensible when plausible inputs change.
For public spending appraisal, HM Treasury's Green Book guidance on sensitivity analysis defines the method as testing how changes in assumptions such as costs, benefits or demand affect an appraisal's results and value-for-money conclusion. It also requires switching values, meaning the movement in a critical assumption that would cause an option to stop representing value for money.
That switching value is more useful than a vague instruction to consider optimistic and pessimistic cases. It answers a sharper question: what exact change would alter the decision?
The practical sequence
A defensible analysis normally follows this order:
- Define the conclusion. Identify the number or decision being tested, such as the claimed loss or valuation.
- Identify material assumptions. Separate revenue, volume, price, duration, remediation cost, recovery, discount rate and other drivers.
- Assess the evidence. Record the management accounts, contracts, budgets, invoices, sales records and other material supporting each input.
- Vary the assumptions transparently. Run one-way tests, linked scenarios or both, depending on the dispute.
- Record the threshold. State where the conclusion changes and why that threshold matters.
A forecast describes an expected outcome. A stress test examines an adverse condition. Sensitivity analysis goes further by showing how the output responds to defined changes and whether the central conclusion survives them. The related discipline of counterfactual analysis is often relevant where the question is what would have happened without the alleged breach, fraud or interruption.
Practical rule: A range without an explanation of its assumptions is not a robust analysis. It's only a collection of numbers.
Open video: testing assumptions with sensitivity analysis
Video by Eperoto AB.
Why Single Estimates Fail in Disputes
A single estimate can look precise while concealing several unresolved questions. Was the alleged revenue achievable? Did the interruption cause the whole claimed margin loss? Were recoveries available? Did the business continue trading under the same conditions? If the model fixes each answer without testing alternatives, the final figure may reflect the assumptions more than the evidence.
HM Treasury's current Green Book states that assumptions susceptible to change should be stress-tested because sensitivity analysis forms an important part of value-for-money assessment. The same logic applies in expert accounting. An analyst should identify variables that are both uncertain and outcome-determinative, vary them systematically, and show the effect on the conclusion.
Two different forms of uncertainty
Forensic work must distinguish parameter uncertainty from evidence uncertainty.
Parameter uncertainty concerns the value of an input. For example, the amount of diverted stock may be uncertain within a plausible range. Evidence uncertainty concerns whether the records capture the full population at all. A model can test the stock value carefully yet remain blind to missing transactions, incomplete detection or disputed causation.
Behavioural uncertainty is a further issue. A management team may say that a control would have prevented a recurrence, but the evidence may not establish whether staff would have applied it consistently. These uncertainties shouldn't be hidden inside a neat base case.
The Office for National Statistics estimated 4.2 million fraud incidents in England and Wales in the year ending March 2025, with around 3 million involving financial loss, while the Home Office estimated the economic and social cost of fraud against businesses in England and Wales at £5.2 billion for the year ending March 2024. That cost includes prevention and response, as well as consequences; it is not simply money stolen. Those figures provide context for the scale of exposure, but they don't determine an individual claim. A forensic model still needs matter-specific evidence, including detection gaps, recoveries, insurance exclusions and the timing of discovery. The ONS figures are reported in its fraud and computer misuse analysis.
A useful comparison is the Ministry of Justice Justice Data Lab report concerning HMPPS CFO. The headline analysis used a six-month waiting period for reoffences to be convicted. The sensitivity analysis extended that period to 12 months, allowing an additional six months for court outcomes to be recorded. The change didn't produce a statistically significant increase in the headline analysis, so the published one-year proven reoffending definition wasn't changed. The April 2024 Justice Data Lab report demonstrates the key discipline: test a plausible alternative specification, assess the result against a stated decision rule, and explain why the original conclusion remains or changes.
For lawyers and insurers, that record is more useful than an unexplained range. It shows what moved, why it moved, what happened to the output and which rule determined the conclusion. Research on the difference between expected return and a guaranteed outcome also offers useful background when readers need to distinguish an estimate from a promise, as explained in Artul.ai's research on earnings signals.
Comparing One-Way, Multi-Way, Scenario and Tornado Methods
The right method depends on the question. A one-way test is usually best for attribution. A multi-way test is better where variables interact. Scenario analysis communicates a coherent business condition, while a tornado diagram helps decide which evidence deserves attention first.
| Method | Purpose | Complexity | Typical Use Case |
|---|---|---|---|
| One-way sensitivity | Isolate the effect of one input while holding others constant | Low | Testing whether duration, price or volume drives a loss |
| Multi-way sensitivity | Examine more than one uncertain input and their interaction | Moderate to high | Valuation, fraud exposure or business interruption with linked drivers |
| Scenario analysis | Model a defined set of assumptions that occur together | Moderate | Closure, supply disruption, technology transition or restructuring |
| Tornado analysis | Rank inputs by their effect on the selected output | Moderate | Prioritising evidence collection and expert examination |
One-way testing
One-way analysis changes a single variable while other assumptions remain fixed. It answers questions such as, “How does the claim change if the interruption period changes?” That makes it valuable when the purpose is attribution, especially in contractual loss modelling or a disputed loss period.
Its limitation is equally important. Real events rarely change one variable in isolation. A longer interruption may reduce revenue, increase remediation costs and alter the recovery available from insurers. One-way testing can reveal the effect of each variable, but it shouldn't be presented as a complete representation of a connected event.
Multi-way analysis
Multi-way analysis changes several inputs, either independently or through linked combinations. It can address a fraud claim where larger undetected losses are associated with a longer discovery period, or a valuation where revenue growth, margin and discount assumptions move together.
This method requires restraint. Adding every conceivable uncertainty makes a model difficult to audit and can obscure the material drivers. The strongest schedules identify the variables that have a defensible evidential basis and explain the relationships between them.
Scenario analysis
Scenario analysis describes a coherent state of affairs rather than an isolated input movement. A downside scenario might combine weaker demand, delayed recovery and higher remediation costs because those conditions could arise from the same underlying event. A scenario should be traceable to evidence, not labelled “worst case” merely because it produces the lowest answer.
For technology and climate-related claims, linked scenarios can be more informative than isolated tests. The analysis may need to combine energy costs, supply disruption, staff availability, cyber incidents, regulatory change, margins, working capital, discount rates and insurance limits. It should distinguish a reversible short-term disruption from a permanent change in demand or asset value.
Tornado rankings and switching values
A tornado diagram ranks inputs by their effect on the selected output. It helps a solicitor decide which documents to request, an insurer decide which assumption requires validation, or a board decide where controls need attention. The chart is only as credible as the ranges and relationships behind it.
Switching values provide the decision threshold. Ofgem's RIIO-ED2 cost-benefit analysis guidance recommends testing the preferred option and identifying the value at which it ceases to be viable or another option becomes preferable. In a claim, that could be the interruption duration, recovery rate, revenue decline or cost escalation required to change the quantum conclusion.
Worked Example Showing Switching Values in a Fraud Claim
The following is a hypothetical example, not a client result. It illustrates how a fraud analysis can move beyond a base, downside and upside range.
A wholesale business alleges that an employee diverted stock and caused a consequential margin loss. The initial claim uses management records, stock reconciliations, sales information and bank evidence. The central model assumes that the identified diversion represents the full loss, that recoveries are limited, and that the affected sales would otherwise have generated the claimed margin.
The analyst should not just publish a single figure. The model can test:
- Diverted stock value, using only transactions supported by reliable records.
- Recovery rate, including amounts recovered or capable of recovery.
- Discovery timing, because a longer period may allow further losses but may also weaken the evidence.
- Counterfactual sales, testing whether the business could have sold the stock at the assumed price and margin.
The key output might be the modelled financial loss, after recoveries and avoided costs. Whether that amount is legally recoverable requires separate consideration of the facts and applicable terms. The switching value is the assumption at which the net claim falls below the material threshold relevant to the negotiation or expert opinion. No threshold should be invented. It must be defined by the engagement, the pleadings, the policy wording or the decision being made.
A transparent schedule
| Test | Assumption changed | Effect to report |
|---|---|---|
| One-way | Recovery increases | Net claim decreases by the documented recovery effect |
| One-way | Discovery date moves | Additional alleged loss is tested against contemporaneous records |
| Multi-way | Higher diversion and longer discovery period | Correlated exposure and evidence risk are examined together |
| Switching value | Recovery or supported loss reaches the decision threshold | The report identifies where the conclusion changes |
If the evidence suggests a relationship between the duration of an alleged fraud and its size, the model should test that relationship. Treating linked assumptions as independent could overstate confidence. The analyst should document the relationship, test alternatives and distinguish what the records establish from what the model assumes.
The analysis should preserve the source documents, reconciliation logic, excluded transactions and reasons for selecting each range. It should also state what isn't captured, such as unidentified losses, disputed causation or an insurance exclusion. That limitation may be more important than another decimal place in the calculation.
The result is a report that says not only what the claim could be, but which factual finding would change it. That supports negotiation because parties can focus on the evidence that sits closest to the switching value.
How to Present a Reproducible Sensitivity Schedule
A sensitivity schedule should allow another professional to reproduce the result. It isn't enough to list “low”, “central” and “high” figures without explaining the evidence, timing, formula and decision rule behind each case.
The Green Book and Ofgem guidance illustrate sensitivity testing in public appraisal and electricity-network investment. They do not set a general court-reporting standard. For a financial dispute, a useful schedule should show the assumption, its evidence, the change tested and the effect on the result. Any expert report must also meet the procedural requirements applicable to that instruction.
What the working papers should contain
- Scope and purpose: State whether the analysis tests quantum, causation, viability, valuation or a tax consequence.
- Assumptions register: Record each input, its source, its date, its owner and whether it is evidenced, estimated or disputed.
- Sensitivity schedule: Show the changed input and the resulting output, without hiding material exclusions.
- Switching values: Identify the exact threshold that changes the conclusion.
- Correlation notes: Explain which assumptions move together and why.
- Limitations: Separate missing evidence from ordinary estimation uncertainty.
- Version control: Preserve the model, source records and calculation date.
A chart can assist communication, but the underlying table must remain available. A tornado ranking should state the output being measured and the ranges used. A scenario chart should explain why the variables move together. Without those details, visual clarity can create a misleading impression of certainty.
The report should also distinguish reversible disruption from permanent change. A short-term interruption may affect timing and working capital, while a permanent demand reduction may affect asset value and the counterfactual itself. Those are different analytical propositions and should not be combined merely to produce a more dramatic downside.
A formal expert witness report for court should explain the expert's instructions, qualifications, methodology, sources, assumptions, conclusions and limitations. Sensitivity analysis supports that structure, but it doesn't replace the need for independent judgement or compliance with the relevant procedural requirements.
When to Engage a Forensic Accountant for Sensitivity Analysis
Sensitivity analysis is appropriate when a decision depends on uncertain financial inputs and the consequences of getting them wrong are material. Common triggers include a disputed loss period, unexplained stock movement, a business-interruption claim, a valuation challenge, an investment decision, a closure scenario or a forecast that another party treats as certain.
Early engagement helps preserve the evidence behind the assumptions. Useful records may include:
- Management accounts, budgets and board papers.
- General ledgers, tax computations and filed returns.
- Contracts, invoices, pricing records and sales-pipeline data.
- Stock reconciliations, payroll records and bank statements.
- Insurance policies, claims correspondence and recovery evidence.
- Documents establishing cessation dates, asset disposals or operational changes.
For Corporation Tax, a company may claim to carry a trading loss back against profits of the preceding 12 months, subject to statutory conditions. HMRC states that current-period profits must be used first, and a claim should generally be made within two years of the end of the accounting period in which the loss arose. The relevant HMRC guidance on company trading losses should be checked against the company's facts.
Terminal trading losses follow a different mechanism. Eligible trading losses arising in the final 12 months of a trade may be carried back against profits in the three years ending immediately before the period when the loss arose, using the most recent years first. The same-trade and apportionment rules need to be checked. HMRC explains those rules in its guidance on terminal trading losses. A modest change to the assumed cessation date can therefore alter the eligible periods and tax effect.
Engagement scope should state the question to be answered, records required, confidentiality arrangements, reporting format and independence considerations. Cost depends on complexity, records, urgency, expert requirements and the number of scenarios, so a clear scope is preferable to a superficial fixed conclusion. Lighthouse's litigation support services can be relevant where sensitivity analysis forms part of a wider quantification or expert accounting assignment.
If a Corporation Tax claim or election has no more specific statutory time limit, the normal deadline is four years from the end of the relevant accounting period, but HMRC identifies specific rules for some reliefs and loss claims. The HMRC guidance on claims and elections should be used before treating a tax effect as available.
Lighthouse Consultants can assess the assumptions behind a fraud, litigation, insurance or valuation calculation, build a reproducible sensitivity schedule and identify the switching values relevant to your question. Book a free consultation to discuss the records, scope and next steps, or call +44 20 7871 0485.
