What the Valley Pays You to Carry the Drought - risk premium, beta, CAPM and the Sharpe ratio

The board says “the valley pays you to carry the drought nobody can mix away; that pay is the risk premium”. This lesson works out how much it pays, and why it pays for that drought and not for any other.

Education, not financial advice.

Before you start. From One Cloud Over Every River - diversification, correlation and Markowitz you need the two kinds of risk. A river’s local weather (idiosyncratic risk) cancels when you own many rivers, for free. The cloud that rains on every river at once (systematic risk) does not cancel, however many you own. From A Day That Should Never Have Happened - volatility, the bell curve and fat tails you need volatility, the typical size of a swing.

The idea in 30 seconds

In 1964 William Sharpe, after a rejection in 1962, asked what prices come out if everyone diversifies. Others reached the same answer around the same time.
The valley will not pay you for local weather, because anyone who mixes can carry it for free. It pays only for the shared cloud: that pay is the risk premium.
The risk-free rate is the safe well’s sure return; the premium is measured on top of it.
Beta says how much one asset moves with the whole market. CAPM says expected return = risk-free rate + beta × the market’s premium: a straight line.
The Sharpe ratio is extra return over the safe rate per unit of volatility, and shows when risk is being carried for no pay.
Tests found the real line flatter than CAPM predicts. The idea of paid and unpaid risk lasted; the exact line did not.

Read the story · Skip to the numbers