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[[Image:SML-chart.png|thumb|right|320px|Security market line]] | |||
'''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, [[Systematic risk|non-diversifiable risk]] (its [[Beta (finance)|beta]]).<ref>[http://www.bettertrades.net/financial-terms/security-market-line.asp Security Market Line]</ref> | |||
==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: | |||
:<math>\mathrm{SML} : E(R_i) = R_f + \beta_{i}[E(R_M) - R_f]\,</math> | |||
where: | |||
:''E(R<sub>''i''</sub>)'' is an expected return on security | |||
:''E(R<sub>''M''</sub>)'' is an expected return on market portfolio M | |||
:''β'' is a nondiversifiable or systematic risk | |||
:''R<sub>M</sub>'' is a market risk | |||
:''R<sub>f</sub>'' is a risk-free rate | |||
When used in [[Investment management|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.<ref>[http://www.investopedia.com/terms/s/sml.asp Investopedia explains Security Market Line - SML]</ref> | |||
There is a question about what the SML looks like when beta is negative. A [[rational investor]] will accept these assets even though they yield sub-risk-free returns, because they will provide "recession insurance" as part of a well-diversified portfolio. Therefore, the SML continues in a straight line whether beta is positive or negative.<ref>{{cite book|last=Berk, DeMarzo, Stangeland|title=Corporate Finance, Second Canadian Edition|year=2012|publisher=Pearson Canada|isbn=978-0-321-70872-4|page=390}}</ref> A different way of thinking about this is that the [[absolute value]] of beta represents the amount of risk associated with the asset, while the sign explains when the risk occurs.<ref>Geurts and Pavlov, "Calculating the Cost of Capital for REITs: A Classroom Explanation." Real Estate Review 34 (Fall 2006).</ref> | |||
==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. | |||
:<math>\frac{E(R_i) - R_f}{\beta_i} =E(R_M) - R_f.</math> | |||
In fact, the slope of the SML is the Treynor ratio of the market portfolio since <math>\beta_M=1</math>. | |||
A [[stock picking]] rule of thumb for assets with positive beta is to buy if the Treynor ratio will be above the SML and sell if it will be 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 will be 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 (investment)|alpha]]. | |||
==See also== | |||
* [[Capital allocation line]] | |||
* [[Capital market line]] | |||
* [[Market portfolio]] | |||
* [[Modern portfolio theory]] | |||
* [[Security characteristic line]] | |||
==References== | |||
{{Reflist}} | |||
==External links== | |||
* [http://www.rhsmith.umd.edu/faculty/gphillips/courses/Bmgt640/Sml.pdf RISK, DIVERSIFICATION, AND THE SECURITY MARKET LINE (SML)] | |||
{{stock market}} | |||
{{DEFAULTSORT:Security Market Line}} | |||
[[Category:Investment]] | |||
Revision as of 08:40, 15 October 2013
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 (its beta).[1]
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:
where:
- E(Ri) is an expected return on security
- E(RM) is an expected return on market portfolio M
- β is a nondiversifiable or systematic risk
- RM is a market risk
- Rf is a risk-free rate
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 about what the SML looks like when beta is negative. A rational investor will accept these assets even though they yield sub-risk-free returns, because they will provide "recession insurance" as part of a well-diversified portfolio. Therefore, the SML continues in a straight line whether beta is positive or negative.[3] A different way of thinking about this is that the absolute value of beta represents the amount of risk associated with the asset, while the sign explains when the risk occurs.[4]
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 will be above the SML and sell if it will be 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 will be 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
43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.
External links
- ↑ Security Market Line
- ↑ Investopedia explains Security Market Line - SML
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Geurts and Pavlov, "Calculating the Cost of Capital for REITs: A Classroom Explanation." Real Estate Review 34 (Fall 2006).