Security market line
Security market line (SML) is the graphical 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 (its beta).[1]
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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 trade off at a given time:
![\mathrm{SML}�: E(R_i) = R_f %2B \beta_{i}[E(R_M) - R_f]\,](/2012-wikipedia_en_all_nopic_01_2012/I/072996f0c22f3d8b5b08be34f38cd9f8.png)
When used in portfolio management, the SML represents the investment's opportunity cost (investing in a combination of the market portfolio and the risk-free asset). All the correctly priced securities are plotted on the SML. The assets above the line are undervalued because for a given amount of risk (beta), they yield a higher return. The assets below the line are overvalued because for a given amount of risk, they yield a lower return.[2]
There is a question what the SML is when beta is negative. A rational investor should reject all the assets yielding sub-risk-free returns, so beta-negative returns have to be higher than the risk-free rate. Therefore, the SML should be V-shaped.
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.
In fact, the slope of the SML is the Treynor ratio of the market portfolio since 
.
A stock picking rule of thumb for assets with positive beta is to buy if the Treynor ratio is above the SML and sell if it is below (see figure above). Indeed, from the efficient market hypothesis, it follows that we cannot beat the market. Therefore, all assets should have a Treynor ratio less than or equal to that of the market. In consequence, if there is an asset whose Treynor ratio is bigger than the market's then this asset gives more return for unity of systematic risk (i.e. beta), which contradicts the efficient market hypothesis.
This abnormal extra return over the market's return at a given level of risk is what is called the alpha.
See also
- Capital allocation line
- Capital market line
- Market portfolio
- Modern portfolio theory
- Security characteristic line
References
External links
- CFA Level 1 - The Security Market Line
- RISK, DIVERSIFICATION, AND THE SECURITY MARKET LINE (SML)
- Chapter 11 Capital Asset Pricing Model (CAPM)