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SIDC PrepStudyingModule 6
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Investment advice and corporate finance
Module 12Investment Management and Corporate FinanceModule 12 · Topic 3
Section 3 of Module 12 can supply up to 25% of the paper, and nearly every item is a short calculation: a utility score, a two-asset standard deviation, a CAPM required return, a beta or an APT expected return. The pass mark is 70% and the paper is closed book, so you must carry the formulas in your head and know the standard slips examiners turn into wrong options: penalising σ instead of σ², dropping the ½, multiplying beta by the market return instead of the premium, adding standard deviations instead of variances, or reading 'above the SML' as overvalued.
8 min read7 sections
Checked 12 October 2026 against Bodie, Kane and Marcus, Investments (chapters on capital allocation, optimal risky portfolios, index models, the CAPM and APT); CFA Institute 2026 Level I refresher readings Portfolio Risk and Return Parts I and II (cfainstitute.org); Ross (1976), Journal of Economic Theory; and the SIDC Module 12 Study Outline for July to December 2026 examinations, Section 3, Topic 6. All worked figures computed in Python. As at October 2026. Independent prep, not endorsed by SIDC or the SC.
The SIDC syllabus (Module 12 Topic 6.1) starts with how investors trade risk for return. The standard mean-variance utility function (Bodie, Kane and Marcus) is U = E(r) − 0.5Aσ², where A measures risk aversion. Work in decimals: 12% is 0.12 and a 20% standard deviation gives σ² = 0.04.
| Portfolio (A = 3) | E(r) | σ | U = E(r) − 1.5σ² |
|---|---|---|---|
| X | 10% | 15% | 0.10 − 0.0338 = 6.63% |
| Z | 8% | 10% | 0.08 − 0.0150 = 6.50% |
| Y | 14% | 25% | 0.14 − 0.0938 = 4.63% |
| W | 18% | 35% | 0.18 − 0.1838 = −0.38% |
U is the certainty-equivalent rate: the risk-free return the investor would accept instead of the risky portfolio. If U is below the Treasury bill rate, the investor prefers the bill. More risk-averse investors have steeper indifference curves; a risk-neutral investor (A = 0) ranks by expected return alone.
Trap: dropping the ½ (doubling the penalty), penalising σ instead of σ², or quoting the penalty 0.5Aσ² as the utility.
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Takeaway: U = E(r) − ½Aσ² in decimals; compare U with the risk-free rate to accept or reject a risky portfolio.
Expected portfolio return is always the weighted average of expected returns, with short positions carrying negative weights. Portfolio risk is not: the covariance term means risk falls below the weighted average whenever ρ < +1 (Topic 6.2).
Worked example: 60% in A (σ 20%), 40% in B (σ 30%), ρ = 0.25. σp² = 0.0144 + 0.0144 + 0.0072 = 0.0360, so σp = 18.97%, against a weighted average of 24%.
Trap: forgetting the 2 in the covariance term, forgetting the square root, or giving the larger weight to the riskier asset in a zero-risk or minimum-variance portfolio.
Takeaway: Returns average; risk does not. Correlation below +1 is the whole source of diversification benefit.