CAS Exam 9 flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Pure vs speculative risk

Pure risk offers only loss or no-loss outcomes and is generally insurable; speculative risk offers gain or loss outcomes and is usually handled through capital markets or avoidance rather than insurance.

Expected aggregate loss formula

For Poisson claim count with mean lambda and independent severity X, expected aggregate loss equals lambda times E[X], and variance equals lambda times E[X squared].

Coefficient of variation

Standard deviation divided by the mean. It expresses risk per unit of expected value, allowing comparison of loss volatility across pools of different sizes or premium volumes.

Value at Risk definition

The loss threshold such that losses exceed it with probability one minus the confidence level. VaR is intuitive but not subadditive, so combining portfolios can appear riskier.

Tail Value at Risk

The expected loss conditional on exceeding the VaR threshold. TVaR is a coherent risk measure satisfying subadditivity and captures the severity of losses in the extreme tail.

Lundberg adjustment coefficient

The positive root R of the Lundberg equation. It yields the exponential upper bound on ruin probability, e to the minus R times initial surplus, for a surplus process with positive loading.

Moral hazard vs adverse selection

Moral hazard is behavior change after coverage that raises loss frequency or severity. Adverse selection is the tendency of higher-risk insureds to buy or retain more coverage before pricing is set.

Risk control techniques

Avoidance eliminates exposure; prevention lowers frequency; reduction lowers severity; separation and duplication limit correlated loss; transfer shifts risk to insurers, reinsurers, or derivative counterparties.

Portfolio variance two assets

Portfolio variance equals w1 squared times sigma1 squared plus w2 squared times sigma2 squared plus twice w1 w2 rho sigma1 sigma2. Covariance, not individual variance, drives diversification.

Minimum variance portfolio weight

For two assets, the weight in asset one is sigma2 squared minus rho sigma1 sigma2, divided by sigma1 squared plus sigma2 squared minus twice rho sigma1 sigma2.

CAPM expected return

Expected return equals the risk-free rate plus beta times the market risk premium. Beta is covariance with the market divided by market variance and prices only systematic risk.

Sharpe ratio

Excess expected return over the risk-free rate divided by portfolio standard deviation. The tangency portfolio on the efficient frontier maximizes the Sharpe ratio for a given risk-free asset.

Bond duration approximation

The percentage price change approximately equals minus modified duration times the yield change plus one half convexity times the squared yield change. Convexity adds a favorable second-order term.

Black-Scholes call formula

Call price equals stock price times N of d1 minus discounted strike times N of d2, where d1 includes drift and volatility terms and d2 equals d1 minus sigma root T.

Put-call parity

For European options on a non-dividend stock, call minus put equals stock price minus the discounted strike. Violations permit arbitrage through replication of the underlying position.

Option Greeks definitions

Delta measures price sensitivity to the underlying, gamma measures delta change, vega measures volatility sensitivity, theta measures time decay, and rho measures interest rate sensitivity.

Credit expected loss

Expected loss equals probability of default times loss given default times exposure at default. Unexpected loss is the volatility around that expectation and is covered by economic capital.

Diversification benefit in ERM

The difference between the sum of standalone risk capitals and the consolidated capital requirement. It shrinks when correlations rise during stress, so tail dependence must be modeled explicitly.

Risk appetite vs tolerance

Risk appetite is the amount and type of risk the firm chooses to pursue; risk tolerance sets quantitative boundaries around it, and limits translate tolerance into monitored line-level constraints.

COSO ERM components

Five components: governance and culture, strategy and objective-setting, performance, review and revision, and information, communication, and reporting. ERM is an integrated process, not a compliance checklist.

Three lines model

Business units own and manage risk as the first line; risk and compliance functions provide oversight frameworks as the second line; internal audit gives independent assurance as the third line.

Economic capital definition

Capital needed to keep the probability of insolvency below a target over a chosen horizon, often measured at a 99.5 percent one-year VaR or TVaR and allocated to business lines.

RAROC formula

Risk-adjusted return on capital equals expected return minus expected loss and expenses, divided by economic capital. It is compared with a hurdle rate to judge whether a line creates value.

Key risk indicators

Leading, measurable metrics tied to risk limits that signal rising exposure before losses appear. A breach should trigger escalation and review, not automatic trading or underwriting action.

Model risk management

Controls over models: conceptual soundness review, independent validation, backtesting, ongoing monitoring, and conservative overlays. Stress and scenario tests supplement models that fail in regime shifts.

Combined ratio

Loss ratio plus expense ratio. A combined ratio above 100 percent indicates an underwriting loss; investment income may still produce an overall profit for the insurer.

IBNR reserves

Reserves for claims incurred but not reported, plus development on known claims. Underestimating IBNR overstates current income and surplus until strengthening reduces both later.

Policyholders surplus

Admitted assets minus liabilities. It is the cushion absorbing adverse experience, and premium capacity is constrained because acquisition costs are paid before premium is earned.

RBC covariance formula

Risk-based capital combines squared charges for asset, credit, reserve, and premium risk under a square root, assuming independence across categories; a company action level begins at 200 percent.

Investment and total leverage

Investment leverage is invested assets divided by surplus; total leverage adds net written premium to invested assets before dividing by surplus. Both raise return on surplus and insolvency risk.

Reinsurance net leverage

Net written premium divided by surplus measures retained underwriting exposure after ceding. Reinsurance lowers net leverage and required capital but adds counterparty credit risk and ceded premium.

Operating cash flow for insurers

Premium collected minus losses and expenses paid. A growing insurer can show negative operating cash flow while solvent because claim payments lag premium collection.