# Slope of SML

The equation for the SML is: SML = rf + Beta(return market - rf) Can someone please explain why the slope of the SML is the market risk premium, and not beta. For the linear function y = a + b(x), the slope is b, so am confused with this.

And if you graph the SML, the x-axis is beta, so the slope, as you pointed out, is the coefficient on beta: MRP.

I wrote an article on this that may be of some help: http://financialexamhelp123.com/cal-vs-cml-vs-sml/.

On the SML graph the X-axis is Beta . And on Y axis it starts with Risk free rate . So the slope is obviously Market risk premium which is the coefficient.

I’m still unsure why beta is not the coefficient of the SML formula? SML formula = risk free + [Beta (expected return market - risk free)]

_ It is _ the coefficient of the SML formula.

You may be misinterpreting the graph: the x-axis is beta , so the coefficient on x is (expected return market – risk free) = MRP.

But the text says that the slope of the SML is the market risk premium. And the slope of the coefficient isn’t it?

Think that in the market, investors should only be compensated for non-diversifiable risk. The risk free rate is just that-- at no systematic risk, what will the Expected return be? As the systematic risk increases by one unit (beta increases by one), what happens to the expected return? So as S2000 is saying, beta is on the x-axis, and the slope of this line relating expected return to beta, is the MRP. If it helps, beta is non-diversifiable risk, relative to the market. Market has a beta of 1 and a standard method for estimating a slope is change in rise over change in run. So change y from rf to E(Rm) = E(Rm)-Rf and change beta from zero to 1 = 1-0

so (E(Rm)-Rf) / (1-0) =MRP.

The market risk premium is the slope coefficient. Beta is the variable: the x-axis is beta.