Security market line (SML) is the representation of the

capital asset pricing model In finance, the capital asset pricing model (CAPM) is a model used to determine a theoretically appropriate required rate of return of an asset, to make decisions about adding assets to a well-diversified portfolio. The model takes into ac ...

. 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 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 A risk premium is a measure of excess return that is required by an individual to compensate being subjected to an increased level of risk. It is used widely in finance and economics, the general definition being the expected risky return less t ...

and reflects the risk return tradeoff at a given time: :

\mathrm : E(R_i) = R_f + \beta_(R_M) - R_f,

where: : is an expected return on security : is an expected return on market portfolio :''β'' is a nondiversifiable or systematic risk : is a market rate of return : 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. In a market in perfect equilibrium, all securities would fall on the SML. 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. A different way of thinking about this is that the

absolute value In mathematics, the absolute value or modulus of a real number x, is the non-negative value without regard to its sign. Namely, , x, =x if is a positive number, and , x, =-x if x is negative (in which case negating x makes -x positive), ...

of beta represents the amount of risk associated with the asset, while the sign explains when the risk occurs.

Tom Geurts Tom Geerd Geurts (born in Dedemsvaart on April 2, 1964) is a Dutch economist currently employed by The George Washington University and an Honorary Professor at the Technische Universität Berlin. Current Chair of the Education Committee of the Am ...

and Andrey Pavlov, "Calculating the Cost of Capital for REITs: A Classroom Explanation." Real Estate Review 34 (Fall 2006).

Security Market Line, Treynor ratio and Alpha

All of the portfolios on the SML have the same

Treynor ratio The Treynor reward to volatility model (sometimes called the reward-to-volatility ratio or Treynor measure), named after Jack L. Treynor, is a measurement of the returns earned in excess of that which could have been earned on an investment that h ...

as does the market portfolio, i.e. :

\frac =E(R_M) - R_f.

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

\beta_M=1

. A

stock picking In financial markets, stock valuation is the method of calculating theoretical values of companies and their stocks. The main use of these methods is to predict future market prices, or more generally, potential market prices, and thus to profit f ...

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 The efficient-market hypothesis (EMH) is a hypothesis in financial economics that states that asset prices reflect all available information. A direct implication is that it is impossible to "beat the market" consistently on a risk-adjusted bas ...

, 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 unit of

systematic risk In finance and economics, systematic risk (in economics often called aggregate risk or undiversifiable risk) is vulnerability to events which affect aggregate outcomes such as broad market returns, total economy-wide resource holdings, or aggreg ...

(i.e. beta), which contradicts the

. This ''abnormal'' extra return above the market's return at a given level of risk is what is called the

alpha Alpha (uppercase , lowercase ; grc, ἄλφα, ''álpha'', or ell, άλφα, álfa) is the first letter of the Greek alphabet. In the system of Greek numerals, it has a value of one. Alpha is derived from the Phoenician letter aleph , whi ...

References

{{DEFAULTSORT:Security Market Line Investment

Formula

Security Market Line, Treynor ratio and Alpha

See also

References