Investment Analysis and Risk
This domain tests risk measurement, portfolio theory and the pricing of risk. Expect CAPM, beta, Sharpe and Treynor ratios, bond duration and yield, and VaR questions with a conceptual edge.
Core tools
- Total risk = standard deviation; systematic risk = beta.
- Diversification removes unsystematic risk, not market risk.
- CAPM: E(R) = Rf + β(Rm − Rf).
- Sharpe = (Rp − Rf)/σp; Treynor = (Rp − Rf)/βp.
- Bond price moves inversely with yield; duration measures sensitivity; convexity corrects for larger moves.
- VaR estimates a loss threshold at a confidence level over a horizon.
Worked example
Risk-free rate 7%, market return 12%, beta 1.4. Required return = 7% + 1.4 × (12% − 7%) = 7% + 7% = 14%. If the analyst expects 16%, alpha is +2%: the stock is undervalued on a CAPM basis. If beta were 0.8, required return would be 11%, and the same 16% expectation would imply a larger alpha.
Traps
- Saying diversification eliminates all risk; it leaves systematic risk.
- Using standard deviation in Treynor or beta in Sharpe.
- Treating duration as time to maturity; it is the weighted average time of cash flows and a price-sensitivity measure.
- Assuming YTM is the realised return when coupons are reinvested at a different rate.
- Reading VaR as a maximum possible loss.