Security market line

Overview

Security market line (SML) is the representation of the capital asset pricing model. It displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk. The risk of an individual risky security reflects the volatility of the return from the security rather than the return of the market portfolio. The risk in these individual risky securities reflects the systematic risk.

Formula

The Y-intercept of the SML is equal to the risk-free interest rate. The slope of the SML is equal to the market risk premium and reflects the risk return tradeoff at a given time:

S M L

: E (

R

i

) =

R

f

+

β

i

[ E (

R

M

) −

R

f

]

{\displaystyle \mathrm {SML} :E(R_{i})=R_{f}+\beta _{i}[E(R_{M})-R_{f}]\,}

where:

Security Market Line, Treynor ratio and Alpha

All of the portfolios on the SML have the same Treynor ratio as does the market portfolio, i.e.

E (

R

i

) −

R

f

β

i

= E (

R

M

) −

R

f

.

{\displaystyle {\frac {E(R_{i})-R_{f}}{\beta _{i}}}=E(R_{M})-R_{f}.}

In fact, the slope of the SML is the Treynor ratio of the market portfolio since

β

M

See also

Capital allocation line Capital market line Efficient frontier Market portfolio Modern portfolio theory Security characteristic line