CAT Bonds

Study guide: Exam 9

CAT Bonds (catastrophe bonds) are fully collateralised securities through which an insurer or reinsurer — the sponsor — buys multi-year catastrophe protection from capital-market investors. Investors earn a floating collateral yield plus a risk spread, and forfeit part or all of their principal if a defined catastrophe trigger is hit.

\text{Coupon rate} = r_{\text{mm}} + s

\text{Principal lost} = \text{Principal} \times \min\!\left(1,\ \frac{(I - A)^+}{E - A}\right)

• r_{\text{mm}} is the money-market return on the collateral, s the risk spread, I the trigger's measured value, A the attachment and E the exhaustion point. A cat bond is a layer — a tranche of the trigger's distribution (Structured Finance).
• Structure. The sponsor enters a reinsurance (or derivative) contract with a single-purpose reinsurer, usually offshore, and pays it premium. The SPV issues the notes, commonly for about three years, and places the proceeds in a collateral trust. Historically a total return swap converted the trust's yield to a floating rate; after Lehman Brothers' 2008 failure impaired several bonds that relied on it as swap counterparty, collateral moved mostly to Treasury money-market funds. If the trigger is hit the trust pays the sponsor; otherwise principal is repaid at maturity.
• Triggers, from least to most basis risk (and most to least moral hazard):
  • Indemnity — the sponsor's actual losses. No basis risk, but moral hazard in claims handling, disclosure of the sponsor's book, and slow settlement.
  • Modelled loss — the event's physical parameters run through an agreed catastrophe model on the sponsor's exposure. Basis risk equals the model's error.
  • Industry index — an industry loss estimate (PCS in the U.S.), often weighted by the sponsor's market shares by area. Transparent and quick; basis risk wherever the sponsor's book differs from the industry's.
  • Parametric — the physical event itself: magnitude and location, or wind speed in a defined box. Fastest and most transparent, with the most basis risk.
• Basis risk — the gap between the sponsor's actual loss and its recovery — is two-sided, and it has an accounting consequence: a non-indemnity bond may not qualify as reinsurance.
• Pricing. Offerings quote the attachment probability, the exhaustion probability and the expected loss (EL), and the spread is read as a multiple of EL. Cat losses are nearly independent of the economy, so theory says the spread need only cover EL; in practice it runs well above, reflecting model uncertainty, limited capacity and the reinsurance cycle. See Insurance-Linked Securities for the wider market and Securitization for why it exists.

Layer Metrics and the Investor's Outcome A sponsor issues \$150 million of notes covering 50\% of its indemnity losses between \$1.0 billion and \$1.3 billion from a single hurricane. The modelled attachment probability is 2.5\% and the exhaustion probability 1.2\%; the spread is 6.0\%. Estimate the EL (assume exceedance probability falls linearly across the layer) and the spread multiple, then find the principal lost if a hurricane costs the sponsor \$1.2 billion.

Answer

\begin{align*}
\text{EL} &\approx \frac{2.5\% + 1.2\%}{2} \\
&= 1.85\% \\[4pt]
\text{Multiple} &= \frac{6.0\%}{1.85\%} \\
&= 3.2
\end{align*}

For the event, I = \$1{,}200\text{M}, A = \$1{,}000\text{M}, E = \$1{,}300\text{M}:

\begin{align*}
\text{Principal lost} &= \$150\text{M} \times \frac{1{,}200 - 1{,}000}{1{,}300 - 1{,}000} \\
&= \$100\text{M}
\end{align*}

Investors lose two-thirds of their principal; in a quiet year they earn the money-market rate plus \$9 million of spread. The sponsor keeps the other half of the layer — a co-participation that gives it a stake in its own claims handling.

Industry-Index Trigger and Basis Risk A Florida insurer with about a 2\% market share buys an index bond paying 2\% of industry losses above \$25 billion, capped at \$200 million. An indemnity cover would instead pay its own losses above \$500 million, capped at \$200 million. Two hurricanes each cause \$32 billion of industry loss: storm X lands where the insurer is concentrated (its loss \$800 million), storm Y elsewhere (its loss \$450 million). Compare recoveries.

Answer The index bond pays the same for both storms:

\begin{align*}
\text{Index recovery} &= 0.02 \times (\$32\text{B} - \$25\text{B}) \\
&= \$140\text{M}
\end{align*}

• Storm X: indemnity would pay \min(\$800\text{M} - \$500\text{M},\ \$200\text{M}) = \$200\text{M}. The index pays \$140 million — a \$60 million shortfall, in the storm that hurt most.
• Storm Y: indemnity would pay nothing (the loss is inside the retention); the index pays \$140 million the insurer did not need.

Basis risk runs both ways, but the damaging side is systematic: the index under-recovers precisely when the insurer's concentration makes an event worse for it than for the market. Weighting the index by the insurer's share in each county, or a modelled-loss trigger, narrows the gap.