Allocating Group Diversification Benefit Between Two Subsidiaries

The arithmetic source. Standalone capital is calibrated to a 1-in-200 loss for each entity in isolation. Group capital is calibrated to a 1-in-200 loss for the joint distribution. The two differ because the severe outcomes for life and general insurance do not perfectly coincide: mortality or longevity stress and a catastrophe loss have limited tail dependence. The ₹1,600 crore is the difference between adding quantiles and taking the quantile of the sum - a mathematical property of the joint distribution, not a cash asset.

What determines whether it can be relied on.

• Tail dependence, not average correlation. The benefit is generated in the ordinary part of the distribution. If both entities are exposed to the same shock - a common reinsurer, a sovereign event, a shared banking counterparty, a pandemic that raises mortality and disrupts general insurance claims at once - the tails move together and the benefit shrinks. The model should be tested with a copula that allows tail dependence, and the diversification credit re-measured under it.
• Fungibility. A benefit only helps if capital can move to where the loss lands. Ring-fencing, local minimum solvency margins and regulatory approval requirements for dividends mean the ₹500 crore transferable figure, not ₹1,600 crore, is the sum that can actually be deployed. Benefit beyond that is presentational.
• Regulatory recognition. The 50% haircut reflects the supervisor's suspicion of modelled dependence. Whatever the internal model says, the group must be able to survive on the recognised amount.
• Model and parameter risk. The correlation assumption is the least empirically supported input in the model. A benefit of this size resting on it should carry a margin.

So the defensible statement is not "we have ₹1,600 crore of diversification". It is: ₹800 crore is recognised for regulatory purposes, ₹500 crore is genuinely mobile, and the rest is a modelling result that should be stress-tested before it is spent.

Recommendation: allocate on a marginal (Euler) basis, with a fungibility overlay, and report standalone capital alongside it.

The method. Allocate each entity the capital it contributes at the margin - the change in group economic capital if that entity were removed, computed as the Euler allocation of the group quantile. This has the property that allocations sum exactly to group capital, and it rewards an entity for being diversified against the other. General insurance, being smaller and less correlated with life, will typically receive an allocation below its standalone figure; life, being the larger and dominant risk, will receive something close to or above its standalone share.

Why the CEO's objection is partially right. The general insurance CEO is correct that ₹1,400 crore understates the capital his business would need standing alone. Allocating below standalone is not a subsidy only if the benefit is real and reachable. The honest answer is: you receive this allocation because the group can absorb your losses with less total capital, but you do not get to bank the difference - and the quantum recognised for solvency is only the ₹800 crore the regulator allows, not the full ₹1,600 crore.

The fungibility overlay. Require each entity to hold at least its standalone regulatory minimum plus a buffer, regardless of allocation. The diversification benefit is then held at group level, not distributed. This removes the incentive for either CEO to argue for a lower allocation in order to flatter returns, because the allocation does not change what they must hold.

Reporting discipline. Publish both measures - allocated and standalone - and set return targets on the allocated figure with the standalone figure disclosed. If a business is being subsidised, show it. The Board's real question is whether the group's capital plan is credible, and dual reporting answers that better than a single contested number.

Immediate impact. The group solvency ratio falls by the amount of the withdrawn credit relative to own funds. If the discipline of the capital plan assumed ₹800 crore of recognised benefit, ₹400 crore of that disappears from the regulatory balance sheet overnight. The first step is to quantify the new ratio, the headroom over the board's risk appetite floor, and the distance to the regulatory minimum - and to do it before anyone commits to a response, because the three numbers may point to very different urgencies.

Diagnosis before action. Is the cut a permanent change of view on dependence, or a transitional measure pending a model review? The response differs. A permanent cut says the supervisor does not believe the tail-dependence assumption; the group should revisit its copula and correlation calibration, and should expect further challenge. A transitional cut says nothing about the model but constrains capital now.

Options, in order of preference.

1. Reduce the dependence, not the model. Genuine risk mitigation - diversify reinsurance panels, avoid shared counterparties, cap common exposure to a single sovereign or banking group - lowers correlation and makes the benefit more defensible. This is slow but it is the only response that survives a second review.
2. Free up fungibility. Negotiate with local regulators for contingent capital arrangements or intra-group guarantees that make more than ₹500 crore effectively mobile. This addresses the constraint that actually binds.
3. Hold more capital at group level. If the benefit cannot be defended, fund the gap. That may mean a hold on dividends or a subordinated debt issue; both should be modelled against the cost of shrinking the general insurance book.
4. Re-price or shrink. Reinstate standalone capital as the planning constraint for each entity. Books that only earn their return because of a diversification credit that the regulator has withdrawn should be reviewed for exit.

Governance point. The Board should not treat this as a modelling negotiation with the supervisor. It is a signal that the group's capital plan was leaning on a benefit it could not evidence. The response should be a revised appetite statement with standalone-based floors, and a report to the Board on which business lines fail on that basis.