Institute and Faculty of Actuaries (IFoA) Exams Pensions, Health and Investment Specialisms (SP4, SP1, SP5, SP6, SP9) Syllabus

What is the deferred period in income protection and how does it affect pricing?

The deferred period is the time a claimant must be incapacitated before benefit payments begin (e.g. 4, 13, 26, 52 weeks). A longer deferred period reduces claim incidence and cost, lowering the premium, and aligns with other sick-pay arrangements.

Distinguish the inception/disability annuity approach used to reserve income protection claims.

The Manchester Unity (inception–annuity) approach values IP using a claim inception rate (probability of becoming sick) multiplied by an annuity factor for the expected duration of sickness. It separates the frequency of claims from their continuance/duration.

What are the key drivers of the cost of a Private Medical Insurance (PMI) product?

Claim frequency (number of treatments), claim severity (cost per treatment, driven by medical inflation), the scope of cover/excess, age and health of insured, and expense/commission loadings. Medical inflation typically exceeds price inflation.

State the basic equivalence (premium) principle for pricing an insurance contract.

$$\text{EPV(premiums)} = \text{EPV(benefits)} + \text{EPV(expenses)} + \text{EPV(profit/contingency loading)}$$ The premium is set so the expected present value of income equals that of outgo plus required margins.

Why must health insurance reserves include an IBNR component, and what is it?

IBNR (Incurred But Not Reported) reserves provide for claims that have occurred but not yet been reported/settled at the valuation date. Health claims have reporting delays, so reserving only on reported claims would understate liabilities.

What is a disabled life reserve (claims reserve) for income protection?

It is the reserve held for lives currently in claim, equal to the EPV of future benefit payments expected during the remaining period of disability, allowing for recovery and mortality of claimants (claim termination/continuance rates).

Define risk classification (risk rating) in health/protection underwriting.

Risk classification groups applicants into homogeneous risk categories using rating factors (age, sex where permitted, smoker status, occupation, medical history) so that premiums reflect expected claims cost, controlling against anti-selection.

What is anti-selection (adverse selection) and how does underwriting counter it?

Anti-selection is the tendency for higher-risk individuals to buy more/cheaper-than-fair cover when the insurer cannot distinguish risk. Underwriting (medical evidence, questionnaires, exclusions, loadings) and rating factors counter it by aligning premiums with true risk.

List common underwriting decisions/outcomes for a substandard life.

Accept at ordinary rates; accept with a premium loading (extra mortality/morbidity rating); accept with an exclusion clause; impose a benefit restriction or reduced sum assured; postpone the decision; or decline the application.

What is moral hazard, and how does it differ from anti-selection?

Moral hazard is the change in a policyholder's behaviour because they are insured (e.g. claiming more readily, reduced care). Anti-selection concerns who buys cover based on pre-existing risk; moral hazard concerns behaviour after cover is in force. Excesses, no-claims discounts and exclusions mitigate moral hazard.

In the SP5 context, what is the distinction between active and passive investment management?

Active management seeks to outperform a benchmark through stock selection and timing, accepting higher costs and tracking error. Passive management replicates an index to match the benchmark return at low cost, accepting market (beta) returns only.

State the expected return of a portfolio and its variance for two assets.

$$E[R_p] = w_A E[R_A] + w_B E[R_B]$$ $$\sigma_p^{2} = w_A^{2}\sigma_A^{2} + w_B^{2}\sigma_B^{2} + 2 w_A w_B \rho_{AB}\sigma_A \sigma_B$$ where $w$ are weights and $\rho_{AB}$ is the correlation.

State the Capital Asset Pricing Model (CAPM) equation.

$$E[R_i] = R_f + \beta_i\,(E[R_m] - R_f)$$ where $R_f$ is the risk-free rate, $E[R_m]$ the expected market return, and $\beta_i = \dfrac{\operatorname{Cov}(R_i,R_m)}{\sigma_m^{2}}$ measures systematic risk.

Define the Sharpe ratio and what it measures.

$$S = \frac{E[R_p] - R_f}{\sigma_p}$$ It measures excess return per unit of total risk (standard deviation); a higher Sharpe ratio indicates better risk-adjusted performance.

Define the information ratio in active portfolio management.

$$IR = \frac{\alpha}{\omega} = \frac{E[R_p] - E[R_b]}{\text{tracking error}}$$ It is the active (excess over benchmark) return divided by the tracking error (standard deviation of active returns), measuring skill per unit of active risk.

What does Modern Portfolio Theory's efficient frontier represent?

The efficient frontier is the set of portfolios offering the maximum expected return for each level of risk (or minimum risk for each return). Rational mean-variance investors hold only portfolios on this frontier.

State put-call parity for European options on a non-dividend-paying stock.

$$C - P = S_0 - K e^{-rT}$$ where $C$ and $P$ are call and put prices, $S_0$ the spot price, $K$ the strike, $r$ the risk-free rate and $T$ the time to maturity.

What are the five inputs to the Black–Scholes option pricing formula and the price of a European call?

Inputs: spot $S_0$, strike $K$, time $T$, risk-free rate $r$, volatility $\sigma$. $$C = S_0\,N(d_1) - K e^{-rT} N(d_2),\quad d_1 = \frac{\ln(S_0/K) + (r + \tfrac{1}{2}\sigma^{2})T}{\sigma\sqrt{T}},\quad d_2 = d_1 - \sigma\sqrt{T}$$

Define the option Greeks delta and gamma.

Delta $\Delta = \dfrac{\partial V}{\partial S}$ is the rate of change of option value with the underlying price (the hedge ratio). Gamma $\Gamma = \dfrac{\partial^{2} V}{\partial S^{2}}$ is the rate of change of delta with the underlying, measuring convexity/hedge stability.

Distinguish a forward contract from a futures contract.

A forward is an OTC bilateral agreement to buy/sell an asset at a set price on a future date, customisable but with counterparty risk and no daily settlement. A futures contract is exchange-traded, standardised, margined and marked-to-market daily, with the clearing house reducing counterparty risk.

What is an interest-rate swap and its typical use in investment/ALM?

An interest-rate swap exchanges fixed-rate for floating-rate interest payments on a notional principal. It is used to convert exposure (e.g. fix floating liabilities), hedge interest-rate risk, or alter portfolio duration without trading the underlying bonds.

Define Value at Risk (VaR).

VaR at confidence level $\alpha$ over horizon $T$ is the loss that will not be exceeded with probability $\alpha$: $$P(L \leq \text{VaR}_\alpha) = \alpha$$ e.g. a 1-day 99% VaR of £1m means a 1% chance of losing more than £1m in a day.

Define Expected Shortfall (Tail VaR / Conditional VaR) and why it is preferred to VaR.

$$\text{ES}_\alpha = E[\,L \mid L \geq \text{VaR}_\alpha\,]$$ It is the expected loss given that the loss exceeds VaR. It is preferred because it captures tail severity beyond VaR and is a coherent (sub-additive) risk measure, whereas VaR is not generally sub-additive.

State the four properties of a coherent risk measure.

For a risk measure $\rho$: (1) Monotonicity; (2) Sub-additivity $\rho(X+Y)\leq\rho(X)+\rho(Y)$; (3) Positive homogeneity $\rho(\lambda X)=\lambda\rho(X)$ for $\lambda\geq0$; (4) Translation invariance $\rho(X+c)=\rho(X)-c$.

Compare the three main approaches to calculating VaR.

Variance–covariance (analytic): assumes normal returns, fast but poor for fat tails/options. Historical simulation: re-prices using past return distribution, no distributional assumption but limited by history. Monte Carlo simulation: simulates from a model, flexible for non-linear payoffs but computationally intensive and model-dependent.

What is Enterprise Risk Management (ERM) and how does it differ from traditional siloed risk management?

ERM is a holistic, organisation-wide framework for identifying, assessing, responding to and monitoring all risks in an integrated way, aligned to strategy and risk appetite. Unlike siloed management, it captures risk interactions, diversification and aggregate exposure, treating risk as a source of value, not just downside.

Name a widely used ERM framework and its core components.

The COSO ERM framework. Core components: governance & culture; strategy & objective-setting; performance (risk identification, assessment, prioritisation, response); review & revision; and information, communication & reporting.

Define risk appetite and risk tolerance in an ERM context.

Risk appetite is the amount and type of risk an organisation is willing to accept in pursuit of its objectives (high-level, strategic). Risk tolerance is the acceptable variation around specific objectives/limits (operational, often quantified), translating appetite into measurable boundaries.

List the four main risk responses available under an ERM framework.

Avoid (do not undertake the activity), Reduce/Mitigate (controls to lower likelihood or impact), Transfer/Share (insurance, reinsurance, hedging, outsourcing), and Accept/Retain (retain within risk appetite, possibly with capital held).

What is economic capital and how is it typically defined for risk quantification?

Economic capital is the amount of capital an organisation needs to remain solvent over a defined horizon at a chosen confidence level, given its risk profile. It is often defined as the VaR or Expected Shortfall of the change in net asset value (e.g. 99.5% over one year, as in Solvency II).

What is a risk register and a key risk indicator (KRI) in risk reporting?

A risk register is a structured record of identified risks with their likelihood, impact, owner, controls and response actions. A KRI is a quantifiable metric that gives early warning of rising risk exposure (e.g. claims ratio, staff turnover), monitored against thresholds to trigger management action.