Casualty Actuarial Society Credentials (ACAS/FCAS) Exam 9 — Financial Risk and Rate of Return Syllabus

Define market risk versus credit risk.

Market risk is the risk of loss from changes in market prices/rates (equity, interest rate, FX, commodity). Credit risk is the risk of loss from a counterparty or issuer failing to meet obligations (default, downgrade, spread widening).

What are the components of expected credit loss?

$$EL = PD \times LGD \times EAD$$ where PD = probability of default, LGD = loss given default ($=1-$ recovery rate), and EAD = exposure at default.

What is a credit spread and what does it compensate for?

The credit spread is the yield difference between a risky bond and a risk-free bond of equal maturity. It compensates investors for expected default loss, credit risk premium, and liquidity premium.

What is the purpose of Asset-Liability Management (ALM) for an insurer?

To coordinate management of assets and liabilities so that the firm can meet obligations as they come due while controlling risk to surplus. It addresses interest-rate, liquidity, and cash-flow mismatches between assets and liabilities.

What does it mean to immunize a portfolio against interest-rate risk?

To structure assets so that asset and liability values move together for small rate changes. Classical immunization sets asset duration equal to liability duration and asset present value $\geq$ liability present value, ideally with convexity matched.

What is duration matching and its key limitation?

Setting $D_{assets} = D_{liabilities}$ so first-order interest-rate sensitivities offset. Limitation: it only protects against small, parallel yield-curve shifts; it ignores convexity differences and non-parallel (twist/butterfly) movements.

What is cash-flow matching in ALM and how does it compare to immunization?

Cash-flow matching structures asset cash inflows to exactly meet liability outflows on each date, eliminating reinvestment and rebalancing needs. It is more precise but more costly and less flexible than duration-based immunization.

Distinguish funding (cash-flow) liquidity risk from market (trading) liquidity risk.

Funding liquidity risk is the inability to meet cash obligations as they fall due without incurring losses. Market liquidity risk is the inability to sell or unwind a position quickly without significantly moving the price.

What is the liquidity premium in asset returns?

The additional expected return investors demand for holding less-liquid assets that are costly or slow to convert to cash. Insurers with predictable, illiquid liabilities can harvest this premium by holding illiquid assets.

What characteristics make an insurer's liabilities suitable for an illiquid investment strategy?

Long duration, predictable timing, low surrender/lapse risk, and limited acceleration of claims. Such stable liabilities allow the insurer to hold illiquid, higher-yielding assets and capture the liquidity premium.

Define the Sharpe ratio.

$$S = \frac{E(R_p) - R_f}{\sigma_p}$$ Excess return per unit of total risk (standard deviation). Higher is better; used to rank portfolios on a total-risk basis.

Define the Treynor ratio and contrast it with the Sharpe ratio.

$$T = \frac{E(R_p) - R_f}{\beta_p}$$ Excess return per unit of systematic risk (beta). Treynor uses $\beta$ (appropriate for well-diversified portfolios); Sharpe uses total $\sigma$ (appropriate for standalone portfolios).

What is Jensen's alpha?

$$\alpha = R_p - [R_f + \beta_p(R_m - R_f)]$$ The portfolio's return in excess of its CAPM-predicted return. Positive $\alpha$ indicates outperformance relative to risk taken.

What is RAROC (Risk-Adjusted Return on Capital)?

$$\text{RAROC} = \frac{\text{Risk-adjusted return (expected profit)}}{\text{Economic (risk) capital}}$$ It evaluates profitability per unit of risk capital and is used for performance measurement and capital allocation.

What is the information ratio?

$$IR = \frac{R_p - R_b}{\sigma(R_p - R_b)}$$ Active return (over a benchmark $R_b$) divided by tracking error. It measures consistency of active outperformance.

Name the three common methods for estimating the cost of equity capital.

(1) CAPM, $r_e = R_f + \beta(R_m-R_f)$; (2) Dividend Discount / Gordon Growth Model, $r_e = \frac{D_1}{P_0}+g$; (3) Fama-French / multi-factor models. Bond-yield-plus-risk-premium is a fourth practical approach.

State the Gordon (constant-growth) Dividend Discount Model for cost of equity.

$$r_e = \frac{D_1}{P_0} + g$$ where $D_1$ is next period's dividend, $P_0$ the current price, and $g$ the constant dividend growth rate.

Write the Weighted Average Cost of Capital (WACC) formula.

$$\text{WACC} = \frac{E}{V} r_e + \frac{D}{V} r_d (1 - \tau)$$ where $E$ and $D$ are market values of equity and debt, $V = E+D$, $r_e$ and $r_d$ the costs of equity and debt, and $\tau$ the marginal tax rate.

How do you unlever and relever beta when estimating cost of capital (Hamada)?

$$\beta_L = \beta_U\left[1 + (1-\tau)\frac{D}{E}\right]$$ Unlever a comparable firm's $\beta_L$ to $\beta_U$, then relever using the target firm's own $D/E$ to reflect its financial leverage.

List the main capital allocation methods used by insurers.

Proportional/marginal methods such as: VaR/percentile, Tail-VaR (TVaR/CTE), the Myers-Read marginal method, the RMK (Ruhm-Mango-Kreps) co-measure method, covariance/correlation allocation, and the Merton-Perold marginal surplus approach.

Describe the Myers-Read capital allocation method.

A marginal allocation that distributes total capital so that the marginal default value (option value of insolvency) per dollar of liability is equal across all lines. It produces an additive allocation summing exactly to total capital and accounts for diversification.

What is the key feature of the RMK (Ruhm-Mango-Kreps) co-measure capital allocation approach?

It allocates total risk capital by each line's contribution conditional on the firm's total outcome being in the tail (co-measures). Allocations are additive and naturally reflect each line's dependence on adverse aggregate scenarios.

Contrast the Merton-Perold and Myers-Read allocation approaches.

Merton-Perold allocates capital based on the marginal cost of adding a whole business (stand-alone vs with-without), and allocations need not sum to total. Myers-Read uses infinitesimal marginal allocation, is fully additive, and sums exactly to total capital.

In financial pricing models for insurance, what does the Net Present Value / DCF approach require for the premium?

The premium is set so the present value of premiums equals the present value of losses, expenses, and taxes, discounted at risk-adjusted rates, plus a target return on the capital committed. Investment income on reserves and surplus is explicitly recognized.

What is the Insurance CAPM (Fairley) formula for the underwriting profit margin?

$$r_u = -k\, r_f + \beta_u\,[E(R_m) - r_f]$$ where $r_u$ is the underwriting profit margin, $k$ is the funds-generating (reserves-to-premium) factor, and $\beta_u$ is the underwriting beta. The $-k r_f$ term credits the insurer for investment income on policyholder funds.

Describe the Myers-Cohn discounted cash flow model for fair insurance premium.

The fair premium equals the present value of losses, expenses, and the present value of the tax on investment and underwriting income, with all flows discounted at risk-appropriate rates (risk-free for the IRS tax timing, risk-adjusted for losses). It explicitly charges for the tax on the investment income of the surplus supporting the policy.

What is the underwriting profit provision and how does the target total return relate to it?

The underwriting profit provision is the portion of premium intended as profit from underwriting (before investment income). Because insurers earn investment income on reserves and surplus, the underwriting provision needed to hit a target total return on equity can be small or even negative for long-tailed lines.

How does the funds-generating coefficient $k$ affect the required underwriting profit margin?

$k$ measures how long and how much policyholder-supplied funds (reserves) are held per dollar of premium. A larger $k$ (longer-tailed line) means more investment income is earned on held funds, so a lower (more negative) underwriting profit margin is needed to reach the target return.

What is the economic rationale for reinsurance and risk transfer for a primary insurer?

Reinsurance reduces volatility of results, lowers required risk capital and cost of capital, increases underwriting capacity, provides catastrophe protection, stabilizes surplus, and reduces frictional costs (taxes, financial distress, agency). It is justified when the cost of capital saved exceeds the reinsurance loading.

In risk-transfer economics, when is purchasing reinsurance value-adding to shareholders?

When the cost of ceded reinsurance (premium load above expected losses) is less than the value of the capital released plus the reduction in frictional/distress costs and the diversification benefit. Reinsurance adds value if it lowers WACC or frees capital for higher-return uses more cheaply than raising equity.

What distinguishes proportional from non-proportional reinsurance, and give the basic loss-sharing formulas.

Proportional (quota share / surplus): reinsurer takes a fixed fraction $c$ of premiums and losses, ceded loss $= c\,L$. Non-proportional (excess of loss): reinsurer pays loss above a retention $R$ up to a limit, ceded loss $= \min(\max(L-R,0),\,\text{limit})$. Non-proportional targets large/cat losses and transfers more tail risk per premium dollar.