Actuarium

Formula sheets

Every formula on the syllabus, rendered natively, with the traps examiners set for each. Print one per exam and keep it by your desk.

ERM — Enterprise Risk Management (CERA / FSA cross-track)

SOA

Economic capital   EC=VaR99.5%(L)−E[L]\;EC=VaR_{99.5\%}(L)-E[L] (or TVaR-based)

Aggregation with correlation   SCR=∑i∑jρijSCRiSCRj\;SCR=\sqrt{\sum_i\sum_j\rho_{ij}SCR_iSCR_j}; diversification benefit =∑iSCRi−SCR=\sum_iSCR_i-SCR

Tail dependence   λU=lim⁡u→1P(U2>u∣U1>u)\;\lambda_U=\lim_{u\to1}P(U_2>u\mid U_1>u): zero for Gaussian copula, positive for tt and Gumbel

Euler allocation   ρ(Xi∣S)=E[Xi∣S≥VaRα(S)]\;\rho(X_i\mid S)=E[X_i\mid S\ge VaR_\alpha(S)] for TVaR

RAROC   =expected profiteconomic capital\;=\dfrac{\text{expected profit}}{\text{economic capital}}

Traps to remember

  • Treating risk appetite, tolerance and limits as synonyms.

  • Assuming linear correlation captures tail dependence.

  • Forgetting to subtract expected loss when defining economic capital from VaR.

  • Confusing hedging (offsetting) with diversification (pooling).

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