Risk aversion and the portfolio

Example numbers — returns, swings and risk aversion are for illustration. This is not investment advice.

Two assets (% a year) Risk-free return rf Risky asset expected return E Risky asset standard deviation σ

Risk aversion A

The higher, the more you dislike swings 2

Keep the risky share within 0–100% (no borrowing or short selling)

Share in the risky asset w81.3% risk-free 18.8%

The more you dislike risk (higher A), the less of the risky asset you hold at the same reward. With no extra reward you hold none; with enough reward even a risk-averse person holds some.

Risk–return line (solid 0–100%, dashed = borrowing) Indifference curve (higher is better) Chosen mix

Price of risk (slope)	0.325	(8.5 − 2) ÷ 20
Calculated w*	0.812	(0.085 − 0.02) ÷ (2 × 0.2²) — model assumption
Expected return E_p	7.28%	2 + 0.8125 × (8.5 − 2)
Swing σ_p	16.25%	0.8125 × 20

Model assumption: the share comes from mean–variance utility U = E − (A/2)σ². Only the direction (more risk aversion, less of the risky asset) is in the study guide; the formula is a learning supplement.

Not in this calculation

Several risky assets — co-movement (correlation) and diversification are a different calculation
Borrowing to buy more or short selling — clipped to 0–100% by default
Taxes and fees
Anyone’s real risk aversion — the slider is an assumption
That expected returns and swings stay the same
Investment advice

Using the example values

Tool: Renuary (CC BY 4.0) · Numbers are examples. Method and limits on the original page.