Actuarial Notes

Insurance Market Imperfections

Study guide: Exam 9

Insurance Market Imperfections are the departures from a frictionless (Modigliani–Miller) market — taxes, costs of financial distress, agency conflicts, asymmetric information, regulation and costly external capital — that make capital expensive for an insurer to hold and to raise. They are why insurers behave as if they were risk-averse, why Reinsurance and hedging can add value, and why an insurance price must carry a margin beyond the market price of risk.

P = \text{PV}(E[L]) + \text{Expenses} + \text{Risk premium} + \text{Frictional costs}

  • In a perfect market the premium would stop at the first three terms: the market's charge for systematic risk only, since diversifiable risk is free. Imperfections add the frictional cost term, which depends on the insurer's total risk and on how much capital it holds — the Cost of Capital charged on Risk Capital.
  • Taxes. Investment income on capital held inside an insurer is taxed at the corporate level before shareholders receive it — a cost investors avoid by holding the same assets directly. Taxes are also convex: losses cannot always be offset in full or in time, so volatile income raises the expected tax bill.
  • Financial distress. Direct receivership costs are the smaller part. The larger costs are indirect: policyholders — who, unlike bondholders, are customers unable to diversify their insurer's default risk — move their business, agents and brokers steer away, a rating downgrade shuts the insurer out of commercial lines, and the franchise value of future renewals is lost.
  • Agency costs. Managers may spend surplus capital on low-return growth or acquisitions instead of returning it. Shareholders, protected by limited liability, gain from taking more asset or underwriting risk once premiums are collected — at the policyholders' expense. Capital requirements and ratings exist partly to police this.
  • Asymmetric information. Outsiders know less than management about reserve adequacy and exposure, so new equity raised after a large loss is sold at a discount, if at all. When external capital is costly the firm should act risk-averse toward risks it cannot hedge (the Froot–Stein argument). On the underwriting side the same problem appears as Adverse Selection and Moral Hazard.
  • Regulation. Minimum capital standards (Risk-Based Capital, the MCT), rate regulation and investment restrictions impose costs of their own and can bind before economic capital does.
  • Consequences. Insurers price in a cost of capital, diversify, buy reinsurance at more than its expected loss, manage Financial Risk, and after a catastrophe find capital scarce and prices rising — the hard-market side of the underwriting cycle.

Convex Taxes Reward Smoothing An insurer's pre-tax income next year is -\$100M or +\$300M with equal probability. Tax is 21\% of positive income, and a loss earns no tax credit. A hedge (at no cost) would fix pre-tax income at its mean of \$100M. What is the hedge worth?

Answer

\begin{align*}
E[\text{tax}]_{\text{unhedged}} &= 0.5(0) + 0.5(0.21 \times 300) \\
&= \$31.5\text{M} \\
E[\text{tax}]_{\text{hedged}} &= 0.21 \times 100 \\
&= \$21.0\text{M}
\end{align*}

Expected after-tax income rises from \$68.5M to \$79.0M, so the hedge is worth \$10.5M a year even though it leaves pre-tax income unchanged on average. In a world without convex taxes it would be worth nothing. Carryforwards soften the effect in practice but do not remove it, because a deferred credit is worth less than an immediate one.

Why Pay Twice the Expected Loss for Catastrophe Cover? An insurer buys catastrophe excess-of-loss cover whose premium is about twice the modelled expected recovery. A director argues that in an efficient market this simply transfers value to the reinsurer. Evaluate the argument.

Answer In a frictionless market the director is right: shareholders could diversify the catastrophe risk themselves, and paying a margin to shed it destroys value. The imperfections are what change the answer:

  1. Costly external capital. After a major event the insurer would have to raise equity when its information disadvantage is greatest and every competitor is raising at once — at a steep discount, or not at all.
  2. Distress costs. A large net loss risks a downgrade, the flight of default-averse policyholders, and the loss of renewal franchise value — none of which a shareholder's own diversification recovers.
  3. Regulatory and rating capital. The cover lowers required capital, and capital is costly to hold.
  4. Taxes. A catastrophe year wastes tax shields that a smoothed result would use.

So the right test is not whether the premium exceeds expected loss — it always will, since the reinsurer faces frictional costs too — but whether the margin paid is smaller than the frictional costs the cover removes. That comparison is the everyday work of Financial Risk Management.