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CAS Exam 9 study materials
CAS Exam 9 study resources

CAS Exam 9: Financial Risk Management and Portfolio Theory

CAS Exam 9 · Work through your exam, one topic at a time.

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Financial Risk Management and Portfolio Theory

The Financial Risk Management and Portfolio Theory domain is the most quantitative on Exam 9: mean-variance portfolio construction, equilibrium asset pricing, performance measurement, derivative pricing and interest rate risk. Questions reward clean algebra and a clear idea of which risk measure belongs with which decision.

Portfolio mathematics

  • Expected return is a weighted average of component returns; risk is not. Variance requires the covariance term: σp² = w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2.
  • The efficient frontier is the upper half of the feasible set in mean–standard deviation space; the minimum-variance portfolio sits at its left edge.
  • With a risk-free asset, two-fund separation holds: every efficient investor holds a mix of the risk-free asset and the tangency portfolio. The capital market line's slope is the Sharpe ratio of the tangency portfolio.
  • Diversification drives unsystematic risk toward zero as holdings broaden, so only systematic (covariance) risk earns a premium.

Pricing equilibrium and performance

  • CAPM: E(Ri) = rf + βi[E(Rm) − rf], with βi = Cov(Ri, Rm)/σm².
  • The SML plots expected return against beta and prices any asset; the CML plots return against total risk and applies only to efficient portfolios.
  • Performance measures: Sharpe (Rp − rf)/σp; Treynor (Rp − rf)/βp; Jensen's alpha Rp − [rf + βp(E(Rm) − rf)]. Sharpe suits a portfolio that is the investor's entire holding; Treynor and alpha suit a sleeve inside an already diversified fund.

Derivatives and fixed income

  • Put-call parity for non-dividend stocks: C − P = S − PV(K). Black-Scholes adds lognormal returns, constant volatility and continuous hedging.
  • Duration measures price sensitivity to parallel yield shifts; immunization matches asset and liability duration and present value.

Worked example

60% in A (E = 10%, σ = 20%), 40% in B (E = 6%, σ = 10%), ρ = 0.25. E = 0.6(10) + 0.4(6) = 8.4%. Variance in %²: 0.36(400) + 0.16(100) + 2(0.6)(0.4)(0.25)(20)(10) = 144 + 16 + 24 = 184, so σ = 13.56%. The weighted-average σ is 16%, so diversification saved 2.44 points; at ρ = 1 the portfolio σ would be exactly 16%.

Traps

Dropping the covariance term; using σ instead of β to judge a well-diversified portfolio; quoting the CML for an individual stock; comparing Sharpe ratios across portfolios with different leverage; sign errors in put-call parity; assuming a high Sharpe ratio and a positive alpha are the same claim.