Which risk earns a return?
Build the market portfolio, compare the CML with the SML, and use beta to judge returns and prices. Solve has 10 questions worked step by step.
Shared forecasts lead to one risky portfolio
- Compare expected return and standard deviation over one period.
- Use the same forecasts for every asset.
- Borrow and lend at the same risk-free rate.
- Pay no taxes or trading costs.
- Take prices as given: one investor cannot move them.
| Holding | Share of wealth |
|---|---|
| Common market basket | 60.00% |
| T-bills | 40.00% |
Shared forecasts lead to one risky portfolio
E[R] means expected return; σ is standard deviation; σ² is variance. Rf is the effective annual risk-free rate, M is the market portfolio, y is the share of wealth held in M, β is beta and α is forecast return minus required return.
The CML uses total SD and applies to efficient T-bill–market mixes. The SML uses beta and prices every asset or portfolio. For how the optimal risky basket is found, see the tool “Diversification and efficient portfolios”.
Build a market portfolio from market values
- Find total market value and each asset’s market-value weight.
- Find the market’s expected return and its risk premium above the risk-free rate.
- Does the asset with the highest expected return necessarily have the largest market weight? Explain what sets the weights.
| Asset | Market value | Weight | Expected return |
|---|---|---|---|
| Thistlegear | $2,000,000 | ? | 6% |
| Mothglass | $3,000,000 | ? | 10% |
| Velvetcog | $5,000,000 | ? | 14% |
| Market | ? | ? | ? |
Exam coming up and the CML and the SML keep swapping places?
Bring your problem sets. We work through them together until every type feels routine.
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