Capital Allocation for Reinsurance Pricing presentation by Kevin Madigan Casualty Actuaries in Reinsurance Seminar on Reinsurance, Boston May 19-20, 2008

Crawl -> Walk -> Run At the risk of offending my audience, I want to spend a few moments talking about some basics and framing some issues. Why “allocate” capital? We need to make decisions under uncertainty Should we believe our answers?

Why Allocate Capital? Need a denominator for a return calculation Context is important. Are we allocating the capital of the firm, or deriving a method to compare alternative uses of capacity? Insurance is not physics – a grand unified theory is not required When calculating ROEs for transactions or LOBs or business units, it isn’t important to get the “right” one – a reasonable one will do

The Denominator Returns are extremely important, but they are relative measures You give me $x and I will target a return of y% – Capital markets / “normal” investments – Capital budgeting (gives me something to write against, but still exposes more than the allocated capital) – Pricing treaties (does this really make sense? I don’t know, but we need a metric)

How much capital? Solvency issues are crucial to determining how much capital a (re)insurer must hold relative to the risk they already have, or plan to put, on their books If you want a rating, the rating agencies determine the lower bound If you want to be regulated, the regulator also has a say

How much capital? We do not need fancy capital methodologies – the rating agencies and regulators tell us what we need. If we want to be unrated and unregulated, we promise our investors a numerator, and they give us a denominator.

Are we allocating real capital? Can this capital be divided into disjoint units and “allocated” to business units or contracts? Of course not Sometimes we behave as if it can (Katrina, adverse development in long tails)

So why do it? We have to service the capital we have, or give it back. Calculating expected ROEs or ROCs is an accepted (and pretty good) way to rank order business opportunities So we need a denominator

Random thoughts Order dependency – May not matter to cedent, may matter very much to the reinsurer – Should it be ignored / avoided / embraced ? What about rating agency or RDS constraints? – Can’t be ignored, but how do we incorporate?

Random thoughts Underwriter and management buy-in – Crucial or time and resources are wasted How to deal with parameter risk – Build into loss pick and fix ROE? – Build into capital allocated to transaction? – Don’t bother pretending to know the impact and target a higher ROE?