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

Exam 9 — Financial Risk and Rate of Return syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Exam 9 — Financial Risk and Rate of Return in Casualty Actuarial Society Credentials (ACAS/FCAS), not a summary of it.

1. 1

   Portfolio Theory and Asset Pricing

   3 topics

   • Modern Portfolio Theory
     • Efficient frontier and diversification
     • Risk-return tradeoff and utility
   • Asset Pricing Models
     • Capital Asset Pricing Model (CAPM)
     • Arbitrage Pricing Theory and multifactor models
     • Market efficiency hypotheses
   • Fixed Income and Derivatives
     • Bond pricing and duration/convexity in portfolios
     • Option pricing (Black-Scholes) and Greeks
2. 2

   Financial Risk Management

   3 topics

   • Market and Credit Risk
     • Value at Risk and stress testing
     • Credit risk modeling and default probabilities
   • Asset-Liability Management
     • Duration matching and immunization for insurers
     • Interest rate risk in the insurance balance sheet
   • Liquidity and Investment Strategy
     • Liquidity risk for insurers
     • Strategic asset allocation under constraints
3. 3

   Capital Allocation and Cost of Capital

   3 topics

   • Risk-Adjusted Performance
     • RAROC and risk-adjusted return measures
     • Allocating capital to lines of business
   • Cost of Capital Estimation
     • Estimating the insurer cost of equity
     • Weighted average cost of capital for insurers
   • Capital Allocation Methods
     • Marginal and co-measure allocation approaches
     • Myers-Read and proportional allocation
4. 4

   Rate of Return and Insurance Pricing Models

   3 topics

   • Financial Pricing Models for Insurance
     • Insurance CAPM and underwriting beta
     • Discounted cash flow / internal rate of return models
     • Risk-adjusted discounted cash flow
   • Profit Provisions and Target Returns
     • Setting the underwriting profit provision
     • Investment income offset in ratemaking
   • Reinsurance and Risk Transfer Economics
     • Financial impact of reinsurance on returns
     • Capital relief and risk transfer value

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

18 of 51 cards from the Exam 9 — Financial Risk and Rate of Return deck — real questions with worked answers.

1. In Modern Portfolio Theory, what is the expected return of a two-asset portfolio with weights $w_1$ and $w_2$?

   $$E(R_p) = w_1 E(R_1) + w_2 E(R_2)$$ It is the weighted average of the individual expected returns.

2. What is the variance of a two-asset portfolio in MPT?

   $$\sigma_p^{2} = w_1^{2}\sigma_1^{2} + w_2^{2}\sigma_2^{2} + 2 w_1 w_2 \rho_{12}\sigma_1\sigma_2$$ where $\rho_{12}$ is the correlation between the two assets.

3. In MPT, what defines the efficient frontier?

   The set of portfolios that offer the maximum expected return for a given level of risk (variance), or equivalently the minimum risk for a given expected return. Rational investors choose only portfolios on this frontier.

4. What is the Capital Market Line (CML) and its equation?

   The CML connects the risk-free asset to the market portfolio and describes efficient portfolios: $$E(R_p) = R_f + \frac{E(R_m)-R_f}{\sigma_m}\,\sigma_p$$ Its slope is the market Sharpe ratio.

5. State the Capital Asset Pricing Model (CAPM) equation for expected return.

   $$E(R_i) = R_f + \beta_i\,[E(R_m) - R_f]$$ where $\beta_i = \frac{\operatorname{Cov}(R_i,R_m)}{\sigma_m^{2}}$ and $E(R_m)-R_f$ is the market risk premium.

6. In CAPM/MPT, what is the difference between systematic and unsystematic risk?

   Systematic (market) risk is non-diversifiable and is priced via $\beta$. Unsystematic (idiosyncratic/specific) risk is diversifiable and earns no risk premium in equilibrium.

7. What does the Security Market Line (SML) plot, and how does it differ from the CML?

   The SML plots expected return against beta ($\beta$) and applies to all assets and portfolios. The CML plots expected return against total standard deviation ($\sigma$) and applies only to efficient portfolios.

8. What is the general form of the Arbitrage Pricing Theory (APT) model?

   $$E(R_i) = R_f + \sum_{k=1}^{K} \beta_{ik}\,\lambda_k$$ where $\beta_{ik}$ is the sensitivity of asset $i$ to factor $k$ and $\lambda_k$ is the risk premium for factor $k$. APT is multi-factor and relies on no-arbitrage rather than mean-variance equilibrium.

9. Name the three factors in the Fama-French three-factor model.

   Market excess return ($R_m - R_f$), SMB (Small Minus Big, the size factor), and HML (High Minus Low book-to-market, the value factor).

10. How is the price of a coupon bond computed from its cash flows?

    $$P = \sum_{t=1}^{n} \frac{C}{(1+y)^{t}} + \frac{F}{(1+y)^{n}}$$ where $C$ is the periodic coupon, $F$ the face value, and $y$ the yield per period.

11. Define Macaulay duration of a bond.

    The weighted-average time to receipt of cash flows, weights being present values: $$D_{Mac} = \frac{\sum_{t} t\cdot \frac{CF_t}{(1+y)^{t}}}{P}$$ It is measured in years.

12. How are modified duration and Macaulay duration related, and what does modified duration measure?

    $$D_{mod} = \frac{D_{Mac}}{1+y}$$ Modified duration approximates the percentage price change for a unit change in yield: $\frac{\Delta P}{P} \approx -D_{mod}\,\Delta y$.

13. What is convexity and how does it improve the duration-based price approximation?

    Convexity measures curvature of the price-yield relationship. The second-order estimate is $$\frac{\Delta P}{P} \approx -D_{mod}\,\Delta y + \tfrac{1}{2}\,C\,(\Delta y)^{2}$$ It corrects the underestimation of duration alone; positive convexity benefits the bondholder.

14. State the put-call parity relationship for European options.

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

15. What is the payoff at maturity of a long call and a long put option?

    Long call: $\max(S_T - K,\,0)$. Long put: $\max(K - S_T,\,0)$, where $S_T$ is the underlying price at expiration and $K$ the strike.

16. In the Black-Scholes model, what is the formula for a European call price?

    $$C = S_0 N(d_1) - K e^{-rT} N(d_2)$$ with $d_1 = \frac{\ln(S_0/K) + (r+\tfrac{1}{2}\sigma^{2})T}{\sigma\sqrt{T}}$ and $d_2 = d_1 - \sigma\sqrt{T}$.

17. Define the forward price of an asset with no income under no-arbitrage.

    $$F_0 = S_0 e^{rT}$$ For an asset paying continuous yield $q$: $F_0 = S_0 e^{(r-q)T}$.

18. What is Value at Risk (VaR) and how is it interpreted?

    VaR is the maximum loss over a given horizon at a stated confidence level $1-\alpha$. E.g., a one-day 99% VaR of \$1M means there is a 1% probability of losing more than \$1M in one day. Formally, $P(\text{Loss} > \text{VaR}) = \alpha$.

See more Exam 9 — Financial Risk and Rate of Return flashcards →

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

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