Why Excess-Return CAPM Lines Have Zero Intercepts

Summary

The document clarifies how to interpret the intercepts of the Security Market Line and Capital Market Line when their vertical axis shows excess returns. The question notes that these plots use beta or standard deviation as the horizontal measure and appear to intersect the vertical axis at zero, although plots of expected returns are often associated with a risk-free-rate intercept.

The answer confirms that subtracting the risk-free rate changes the intercept: when returns are expressed in excess of the risk-free rate, the CAPM line has a zero intercept. For the Security Market Line, expected excess return is proportional to beta, with the market price of risk setting the slope. This is a conceptual clarification of axis definition and model interpretation; the document does not provide empirical tests or discuss departures from CAPM assumptions.

Key ideas

• The vertical-axis definition determines how to interpret a CAPM line's intercept.
• When returns are measured above the risk-free rate, the CAPM line has a zero intercept.
• The Security Market Line relates expected excess return to beta.
• The market price of risk determines the slope in the stated relationship.

Tags

# Intrepreting the Capital Market Line plot


# Intrepreting the Capital Market Line plot












I am looking at plots of the Security Market (SML) line and Capital market line (CML).

The X axis is the beta for the SML and Standard deviation for CML; the y axis is labeled with excess return.

Normally it would be expected return. The CML ans SML both have an Inteercept (y axis) at 0%. The intercept should normally be at the risk-free rate.

Is the Intercept at 0% and not at the risk free rate because the y axis is plotting the EXCESS returns?

## Answer by phdstudent (score 0, accepted)

https://quant.stackexchange.com/a/18869

Yes. If on the y axis you have excess returns, then the intercept of the line is zero. This are the implications of the CAPM model. E.g. for the SML: $E[R_i,t^e]=\beta \lambda_t$, where $R_i,t^e$ is the excess return on stock $i$ at time $t$ and $\lambda$ is the market price of risk.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.