CAS Exam 9Financial Risk & Rate of Return
Syllabus learning objectives
Paraphrased from the CAS syllabus so the study-plan builder and practice sets track the topics you will actually be examined on. Weights are the official topic ranges.
Portfolio theory, CAPM & market efficiency
- Compute portfolio expected return and variance and construct the efficient frontier under modern portfolio theory.
- Apply the Capital Asset Pricing Model to determine required return given systematic risk (beta).
- Describe the forms of market efficiency and their implications for active investment management.
- Evaluate risk-adjusted portfolio performance using Sharpe, Treynor and Jensen's alpha measures.
Asset-liability management & fixed income
- Compute duration and convexity of fixed-income assets and liabilities and apply immunization techniques.
- Construct an ALM strategy matching asset cash flows to insurance liability cash flows.
- Assess yield curve risk and reinvestment risk in a fixed-income portfolio.
- Apply key rate duration analysis to non-parallel yield curve shifts.
Financial risk management, options & risk measures
- Price options using binomial and Black-Scholes models and apply put-call parity.
- Compute Greeks (delta, gamma, vega) and construct simple hedging strategies.
- Apply VaR and other risk measures to assess financial risk of an investment portfolio.
- Evaluate the use of derivatives to hedge interest-rate, equity and currency risk.
Rate of return, capital & underwriting profit
- Compute an insurer's return on equity incorporating underwriting and investment income.
- Apply the insurance CAPM / internal rate of return models to determine a target underwriting profit provision.
- Assess the impact of premium-to-surplus leverage on required rate of return.
- Evaluate the relationship between cost of capital and target profit loads in ratemaking.
Lecture videos for this exam
Open the full video library โPricing Insurance Risk: Theory and Practice
Stephen Mildenhall ยท Pricing & GLMs
How to Derive the Black-Scholes Equation
Roman Paolucci ยท Derivatives & Quantitative Finance
Overview
Exam 9 connects finance to insurance: CAPM and portfolio theory (Bodie, Kane & Marcus), fixed-income and ALM, option pricing intuition, coherent risk measures and capital allocation, and the insurance-specific profit-provision literature (Ferrari, Robbin, Feldblum, Mango, Kreps).
- Duration
- 4 hours
- Questions
- 25 written-answer items
- Style
- Computer-based written answer
- Credit
- Required for FCAS
Syllabus map
Key formulas
CAPM
Ferrari total return
Normal VaR / TVaR ,
Coherence monotonic, subadditive, positively homogeneous, translation invariant. VaR fails subadditivity in general; TVaR is coherent.
Modified duration ; surplus duration .
Kreps' reinsurer risk load risk load marginal standard deviation or marginal variance of the combined portfolio.
Study strategy
Learn the BKM finance chapters as a mini-MBA: draw the CML/SML, know what alpha and beta mean and how to compute them from regressions.
For each profit-provision paper, memorize its target return concept and the leverage relationships it uses.
Practice the risk-measure calculations under normal and lognormal assumptions until VaR/TVaR conversions are automatic.
Write short argument paragraphs for the 'critique this method' style of question.
Common traps
Beta from the regression slope of excess returns โ not raw returns โ when risk-free rates vary.
Confusing VaR (a quantile) with TVaR (a conditional mean) and their coherence properties.
Applying duration to surplus without leveraging by and .
Sign errors in Ferrari: underwriting loss reduces total return but the leverage still magnifies investment income.