Financial Risk Management

Study guide: Exam 9

Financial Risk Management (FRM) is the discipline by which an insurer decides how much financial and insurance risk to bear, how much capital to hold against it, and how to charge each line and business unit for the capital it uses — so that pricing, underwriting, investment, reinsurance and capital decisions add to the value of the firm. It is the financial core of Enterprise Risk Management.

$V_{\text{firm}} = V_{\text{frictionless}} - \text{PV}(\text{frictional costs})$

Need. In a perfect (Modigliani–Miller) market, risk management cannot create value: shareholders can diversify or hedge on their own account. FRM earns its keep only by reducing the frictional costs of Insurance Market Imperfections — taxes on capital held inside the firm, financial distress, agency conflicts, costly external capital, and policyholders who, unlike bondholders, are customers averse to their insurer's default.
Purpose. Hold the amount of capital that balances the cost of holding capital against the cost of default risk (the insurer's Capital Structure); price business to earn the cost of the Risk Capital it consumes; and direct capital toward the units that earn more than that cost.
Design. Choose a Risk Measure and tolerance (TVaR at a chosen level, an expected policyholder deficit ratio, a rating target); build a model of the joint distribution of insurance and financial outcomes; and choose a capital allocation method — proportional, Merton–Perold, Shapley, Myers–Read or Euler, co-measures, or a direct allocation of margin. Different methods give materially different answers, so the choice is a management decision, not a technicality.
Execution runs as a loop: allocate capital → set risk-adjusted prices → measure Risk-Adjusted Performance (RAROC, EVA) → transfer or hedge what the firm should not keep — Reinsurance, CAT Bonds and other securitizations, asset–liability management of Interest Rate Risk, and limits on Credit Risk.
Allocation is a device. Capital is never physically divided: all of it stands behind every policy, because an insolvent insurer defaults on every line at once. What is really allocated is the cost of capital — which is why Mildenhall and Major argue for allocating margin directly rather than capital.

Reinsurance as a Substitute for Capital A catastrophe excess-of-loss treaty costs $\$13$ M and has expected recoveries of $\$10$ M. The insurer's capital model says the treaty reduces required capital by $\$35$ M. Investors require a $12\%$ return on capital; capital held inside the insurer is invested at $4\%$ . Ignore taxes.

Does the treaty add value?
Answer The net cost of reinsurance is the margin paid to the reinsurer:

$\$13\text{M} - \$10\text{M} = \$3.0\text{M}$

The capital saving is not $12\%$ of $\$35$ M. The capital would have earned $4\%$ while held, so the cost of holding it is only the spread:
 $\begin{align*} \text{Cost of capital saved} &= (0.12 - 0.04) \times \$35\text{M} \\ &= \$2.8\text{M} \end{align*}$ 
Net benefit $= 2.8 - 3.0 = -\$0.2$ M. Using the gross $12\%$ ( $\$4.2$ M) would have made the treaty look clearly worthwhile; on the net spread it slightly destroys value.

The decision is not closed, though. The capital saving depends on the risk measure — a TVaR model credits a tail cover far more than a volatility model — and the treaty also cuts distress costs (downgrade, lost renewals, forced capital raising after the event) that a capital model may not price. FRM's job is to put those on the same scale as the $\$3$ M.