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CAS Exam 9Financial Risk & Rate of Return

Fellowship (FCAS)
4 hoursยท25 written-answer itemsยทโ‰ˆ450 study hours

Syllabus learning objectives

Official syllabus

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

25%
  • 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

20%
  • 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

25%
  • 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

30%
  • 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 โ†’

Pricing 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

Asset-liability management & fixed income
20%
Financial risk management, options & risk measures
25%
Rate of return, capital & underwriting profit
30%

Key formulas

CAPM โ€…โ€ŠE[ri]=rf+ฮฒi(E[rM]โˆ’rf)\;E[r_i]=r_f+\beta_i\left(E[r_M]-r_f\right)

Ferrari total return โ€…โ€ŠTS=IA(1+RS)+UPโ‹…PS\;\dfrac{T}{S}=\dfrac{I}{A}\left(1+\dfrac{R}{S}\right)+\dfrac{U}{P}\cdot\dfrac{P}{S}

Normal VaR / TVaR โ€…โ€ŠVaRฮฑ=ฮผ+zฮฑฯƒ\;VaR_\alpha=\mu+z_\alpha\sigma, โ€…โ€ŠTVaRฮฑ=ฮผ+ฯƒฯ•(zฮฑ)1โˆ’ฮฑ\;TVaR_\alpha=\mu+\sigma\dfrac{\phi(z_\alpha)}{1-\alpha}

Coherence โ€…โ€Š\; monotonic, subadditive, positively homogeneous, translation invariant. VaR fails subadditivity in general; TVaR is coherent.

Modified duration โ€…โ€ŠDmod=Dmac/(1+y)\;D_{mod}=D_{mac}/(1+y); surplus duration โ€…โ€ŠDS=ADAโˆ’LDLS\;D_S=\dfrac{A D_A-L D_L}{S}.

Kreps' reinsurer risk load โ€…โ€Š\; risk load โˆ\propto marginal standard deviation or marginal variance of the combined portfolio.

Study strategy

  1. 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.

  2. For each profit-provision paper, memorize its target return concept and the leverage relationships it uses.

  3. Practice the risk-measure calculations under normal and lognormal assumptions until VaR/TVaR conversions are automatic.

  4. 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 A/SA/S and L/SL/S.

  • Sign errors in Ferrari: underwriting loss reduces total return but the leverage still magnifies investment income.

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