Introduction
An integrated stress test is useful only if its different views of the same scenario reconcile. A catastrophe loss may reduce capital when recognized but be paid in cash over several weeks. A market shock may reduce asset values and also trigger collateral calls. A credit impairment may reduce capital without requiring immediate cash. Treating every stressed loss as an immediate cash outflow, or treating every cash outflow as a new loss, can materially distort the result.
This worked case brings together catastrophe, operational, credit, and market shocks. It calculates net stressed loss, projects liquidity over time, measures capital adequacy, and then applies a specified package of management actions. All amounts are hypothetical and stated in millions of dollars.
Worked Example: Integrating Four Risk Shocks
A hypothetical insurer starts with eligible own funds of $240 million and a capital requirement of $180 million. A specified enterprise stress produces the loss estimates below. The catastrophe estimate is gross of $35 million of modeled recoveries. A separate $10 million feedback estimate captures an incremental loss from interactions between risks; it has been calibrated not to duplicate any of the four category losses. The stressed capital requirement is estimated to rise by $20 million.
Worked Example: Integrating Four Risk Shocks
Method. First reconcile each risk category to a net loss, then sum the category losses and the separately identified feedback amount. Use the resulting total to bridge own funds and compare them with the stressed requirement. The common mistake to avoid is adding the gross catastrophe loss to the net catastrophe loss, or counting the feedback amount twice.
Step 1: Calculate the net catastrophe loss. The gross catastrophe loss is $120 million and modeled recoveries are $35 million:
The net catastrophe loss is $85 million. The other modeled losses are $18 million operational, $12 million credit, and $25 million market. The incremental cross-risk feedback loss is $10 million.
Step 2: Aggregate the losses.
The total net stressed loss is $150 million. This sum is appropriate here because the scenario supplies component loss estimates on a consistent basis and explicitly states that the feedback amount is incremental and non-duplicative. If component estimates were already inclusive of interactions, adding a separate feedback amount would overstate the result.
Step 3: Bridge to stressed own funds. Assume the full $150 million loss reduces eligible own funds over the measurement horizon, with no tax benefit or other capital movement:
The stressed capital requirement is $180 million plus the specified $20 million increase, or $200 million. The coverage ratio and shortfall are therefore:
The insurer has $90 million of stressed own funds against a $200 million requirement, a $110 million shortfall. As a check, the own-funds bridge removes exactly the $150 million aggregate loss from the $240 million opening balance.
Loss Is Not the Same as Cash Flow
The capital calculation above is an end-of-horizon view. A liquidity projection needs dated cash flows. For this scenario, assume the insurer begins with $100 million of liquid resources. By day 7 it pays $70 million of catastrophe claims, $8 million of operational costs, and $18 million of collateral calls; it also pays a planned $10 million distribution and receives $20 million of catastrophe recoveries. By day 30 it pays a further $50 million of catastrophe claims, receives the remaining $15 million of recoveries, and pays another $4 million collateral call. A committed $20 million facility is available by day 30.
The $120 million of catastrophe claims paid across the two dates matches the gross catastrophe loss in this simplified case. The $35 million of recoveries also matches the amount deducted in the capital loss estimate. The $18 million operational loss is not all paid by day 30: only $8 million is a cash outflow in this horizon. The $12 million credit impairment is noncash within the horizon. The market loss reduces capital, while the collateral calls are liquidity outflows; the calls are not added as a second market loss.
Before drawing the facility, the day-30 projection shows a $25 million cash deficit. Drawing the entire $20 million facility leaves a $5 million funding gap. A facility is not automatically equivalent to cash: it helps only to the extent that it is available when needed, and here its full amount does not cover the projected deficit.
Worked Example: Finding the Liquidity Need by Date
A different hypothetical insurer has $32 million of opening liquid resources and a committed $7 million facility. Its projected cash flows are: day 1, claim payments of $14 million, collateral calls of $6 million, and recoveries of $8 million; day 2, further payments of $13 million and recoveries of $3 million; day 3, payments of $16 million and recoveries of $2 million. The facility can be drawn on day 3.
Worked Example: Finding the Liquidity Need by Date
Method. Roll the cash balance forward in date order, then compare the lowest pre-facility balance with the facility limit. The common mistake is to net all horizon inflows and outflows without checking when the cash is available.
Day 1: Starting from $32 million, subtract the $14 million claim payment and $6 million collateral call, then add the $8 million recovery:
Day 2:
Day 3 before the facility:
The peak funding need is $4 million on day 3. Drawing $4 million from the $7 million facility brings the cash balance to zero and leaves $3 million undrawn. The day-3 deficit is covered, but the resulting zero balance provides no additional cash buffer. The check is that the facility draw equals the pre-facility deficit and does not exceed the available $7 million.
Worked Example: Recalculating Capital After Management Actions
Return to the integrated case, where stressed own funds are $90 million, the stressed requirement is $200 million, and the day-30 cash balance before the facility is negative $25 million. Assume management implements three actions before day 30: retain the planned $10 million distribution, raise $35 million of equity with no further issuance cost, and implement a hedge that costs $4 million in own funds and cash but reduces the stressed capital requirement by $18 million. Assume these actions are feasible, timely, and not already reflected in the original stress results.
Worked Example: Recalculating Capital After Management Actions
Method. Apply each action to the balance or requirement it changes, then recalculate the ratio and liquidity separately. The common mistake is to treat the hedge's capital relief as an increase in own funds, or to omit its $4 million cost.
Step 1: Recalculate own funds. Retaining the distribution preserves $10 million; the equity raise adds $35 million; the hedge cost reduces own funds by $4 million:
Post-action own funds are $131 million.
Step 2: Recalculate the requirement and adequacy. The hedge reduces the $200 million requirement by $18 million:
The post-action coverage ratio and shortfall are:
The package improves capital adequacy, but a $51 million shortfall remains. The hedge changes the requirement, not own funds; its stated cost is separately deducted from own funds.
Step 3: Recalculate liquidity. Before actions, day-30 cash is negative $25 million. Retaining the distribution avoids a $10 million outflow, the equity raise adds $35 million of cash, and the hedge costs $4 million:
Day-30 cash after actions is $16 million, so no facility draw is required. The $20 million facility remains available, giving $36 million of cash plus undrawn committed capacity. This is not a $36 million cash balance: only $16 million is cash on hand.
Why the Reconciliation Matters
The integrated calculation is a sequence of linked but distinct tests. Its basic capital bridge follows from the balance-sheet identity: if eligible own funds start at \(O_0\), recognized losses reduce them by \(L\), and management actions change them by \(A\), then post-stress own funds are \(O_0-L+A\). Comparing this amount with the post-stress requirement \(K_1\) gives the coverage ratio. If own funds are below the requirement, the shortfall is the difference:
The liquidity projection instead follows cash conservation: each dated balance equals the prior balance plus cash inflows, minus cash outflows, plus any facility draw. This explains why aggregating the total cash flows without their dates can be misleading. A recovery received after a large claim payment may not prevent an interim funding gap.
The scenario's estimates and assumptions determine whether these calculations are suitable. In the main case, losses are stated on a consistent measurement basis, the feedback estimate is incremental, and the requirement increase is supplied as a scenario result. If the input estimates instead overlap, use different horizons, or include the same management action already, the simple addition or bridge shown here does not apply without adjustment.
- Keep gross and net amounts distinct. Deduct the stated recoveries from the gross catastrophe loss once.
- Keep loss and liquidity schedules distinct. Do not count collateral calls as a new market loss when the capital shock already captures the market loss.
- Use the correct capital denominator. The stressed ratio uses the stressed requirement, not the opening requirement.
- Test action timing and feasibility. A planned equity raise or recovery should not improve a date-specific liquidity balance unless it is available by that date.
Check Your Understanding
For each hypothetical case, calculate the requested quantity and check that loss, capital, and cash items are not mixed.
- A stress includes a gross catastrophe loss of $64 million and modeled recoveries of $19 million, plus operational, market, and incremental feedback losses of $7 million, $11 million, and $3 million. Find total net stressed loss. (Answer: $66 million.)
- An insurer starts with $48 million of liquid resources. On day 1 it pays $22 million and $5 million and receives $9 million. On day 2 it pays $18 million and receives $4 million. Find the day-2 pre-facility balance and the total liquidity including an undrawn $12 million committed line. (Answer: $16 million pre-facility; $28 million including the undrawn line.)
- Opening own funds are $125 million. A stress reduces them by $42 million. The opening capital requirement is $90 million and the stress increases it by $8 million. Find the stressed coverage ratio and capital shortfall. (Answer: \(83/98=84.69\%\); $15 million shortfall.)
- Stressed own funds are $83 million and the requirement is $98 million. Actions retain a $6 million distribution, raise $10 million net equity, incur a $3 million cost, and reduce the requirement by $12 million. Find post-action own funds, requirement, coverage ratio, and surplus or shortfall. (Answer: $96 million; $86 million; \(111.63\%\); $10 million surplus.)
- Before actions, day-30 cash is negative $14 million. By that date an action retains a $5 million distribution, raises $12 million net equity, and pays a $2 million hedge cost. A $10 million facility is available. Find post-action cash and the amount of facility drawn to avoid a negative balance. (Answer: $1 million cash; no facility draw required.)