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Lesson 10 of 13 · 12 min
Theory assumptions, risk-aversion measures and the Sharpe ratio of the CAL
Portfolio theory rests on a few simplifying assumptions; within it, the slope of the capital allocation line is the Sharpe ratio, the same for every mix on the line, and a steeper line is always better.
In short
- Key assumptions: investors are rational and risk averse, have a single-period horizon, pay no taxes or costs, and can borrow and lend freely at one risk-free rate.
- Large institutions making many small independent trades behave almost as if risk neutral: by the law of large numbers their outcomes become nearly certain.
- Absolute risk aversion: how utility responds to more risk at fixed wealth. Relative risk aversion: the share of wealth an investor is willing to risk. Risk aversion can vary with wealth.
- An indifference curve's slope is the marginal rate of substitution between risk and return; for risk-averse investors the curves are convex.
- The CAL's slope is the Sharpe ratio; every point on one CAL has the same Sharpe ratio.
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