Risk Mitigation

Study guides: Exam 9, Exam CFE-101

Risk Mitigation is the set of actions — the ERM tools — that move an organisation's risk profile toward its risk appetite: avoid a risk, reduce its frequency or severity, transfer it to another party, or retain it and hold capital against it. A strategy's effectiveness is judged by how far it lowers a chosen risk measure, and the capital that measure implies, per unit of cost.

$\text{Net cost} = \text{Premium paid} - E[\text{Recoveries}]$

$\text{Value added} = r_{\text{CoC}}\,\Delta C - \text{Net cost}$

$\Delta C$ is the capital released, $C_{\text{before}} - C_{\text{after}}$ , where required capital is set by the risk measure (for example $C = \text{TVaR}_{99\%}(L) - E[L]$ ), and $r_{\text{CoC}}$ is the cost of capital. Transfer pays when the capital it frees is worth more than the margin it hands over.
The tools:
- Avoid — decline a class, exit a territory, turn down an account outside appetite.
- Reduce — underwriting standards, loss control, exposure and aggregate limits, diversification, and internal controls for operational risk.
- Transfer — Reinsurance (Quota Share, Excess of Loss), cat bonds and other ILS; for financial risk, hedging with derivatives (interest-rate swaps, equity puts, credit default swaps) and asset–liability matching (Immunization).
- Retain — keep the risk and hold capital: right when the risk is the business the firm is paid for, or when transfer costs more than the capital it saves.
Assessing effectiveness means checking the change in the risk measure against the net cost; the residual risk against appetite; basis risk, where the hedge pays on something other than the actual loss; counterparty risk, since transfer swaps the original risk for credit risk, concentrated in the scenario the cover exists for; changed behaviour (moral hazard); and whether the answer survives a different risk measure or model.
Mitigation shapes strategy. Capital released can support growth or be returned. Brehm puts reinsurance programmes on an efficient frontier of expected return against risk: a programme below the frontier is dominated, and the choice along it is a question of appetite. See Reinsurance Strategy and Business Risk.

Before and After an Excess-of-Loss Treaty Annual gross loss (in $$$$$M): $100$ with probability $70\%$ , $150$ with $20\%$ , $250$ with $8\%$ , $400$ with $1.5\%$ , $700$ with $0.5\%$ . The insurer can buy $250$ xs $250$ for a premium of $7.0$ . Capital is $\text{TVaR}_{99\%} - E[L]$ and the cost of capital is $10\%$ . Does the treaty add value?
Answer Gross. The worst $1\%$ is $0.5\%$ at $700$ and $0.5\%$ at $400$ .
 $\begin{align*} E[L] &= 70 + 30 + 20 + 6 + 3.5 \\ &= 129.5 \\ \text{TVaR}_{99\%} &= \frac{0.005(700) + 0.005(400)}{0.01} \\ &= 550 \\ C_{\text{gross}} &= 550 - 129.5 \\ &= 420.5 \end{align*}$ 
Ceded. The layer pays $150$ on a $400$ loss and $250$ on a $700$ loss:
 $\begin{align*} E[\text{Ceded}] &= 0.015(150) + 0.005(250) \\ &= 3.5 \\ \text{Net cost} &= 7.0 - 3.5 \\ &= 3.5 \end{align*}$ 
Net. Losses become $100$ ( $70\%$ ), $150$ ( $20\%$ ), $250$ ( $9.5\%$ ), $450$ ( $0.5\%$ ).
 $\begin{align*} E[L_{\text{net}}] &= 129.5 - 3.5 \\ &= 126.0 \\ \text{TVaR}_{99\%} &= \frac{0.005(450) + 0.005(250)}{0.01} \\ &= 350 \\ C_{\text{net}} &= 350 - 126.0 \\ &= 224.0 \\[4pt] \text{Value added} &= 0.10(420.5 - 224.0) - 3.5 \\ &= 16.15 \end{align*}$ 
The treaty frees $\$196.5$ M of capital, worth $\$19.65$ M a year, for a net cost of $\$3.5$ M: it adds about $\$16$ M of value a year. $\text{VaR}_{99\%}$ falls from $400$ to $250$ as well.

Quota Share or Excess of Loss? For the same insurer, the alternative is a $20\%$ quota share whose net cost — margin ceded, net of ceding commission — is $\$3.0$ M. Which strategy is more effective?
Answer A quota share scales every outcome by $0.8$ , so capital falls by $20\%$ :
 $\begin{align*} \Delta C_{\text{QS}} &= 0.20 \times 420.5 \\ &= 84.1 \\ \text{Value added}_{\text{QS}} &= 0.10(84.1) - 3.0 \\ &= 5.41 \end{align*}$ 
Capital freed per dollar of net cost is $196.5 / 3.5 = 56$ for the excess of loss against $84.1 / 3.0 = 28$ for the quota share. The excess of loss is twice as effective because it cedes only the tail that drives the capital measure; the quota share also gives away profitable attritional business.

The quota share still has a place: it cuts premium leverage and its ceding commission gives a growing insurer surplus relief, so a company constrained by premium-to-surplus rather than by tail risk might prefer it. And the excess-of-loss recoveries arrive in catastrophe years, when reinsurers are most stressed — the reinsurer's credit quality is part of the assessment.