Security market line

Security market line (SML): The SML displays the expected rate of return of an individual security as a function of systematic, non-diversifiable risk (Beta).

In finance, the capital asset pricing model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset. ^[1]

Inventors

The CAPM was introduced by Jack Treynor (1961, 1962), William F. Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) independently, building on the work of Harry Markowitz. ^[2]

Formula and the SML

The Security Market Line (SML) graphs the results of the CAPM. The slope of the SML is equal to the market risk premium:

${\displaystyle E(R_{i})=R_{f}+\beta _{i}(E(R_{m})-R_{f})}$

where:

• ${\displaystyle E(R_{i})}$ is the expected return on the asset.
• ${\displaystyle R_{f}}$ is the risk-free rate.
• ${\displaystyle \beta _{i}}$ is the systematic risk (beta).
• ${\displaystyle E(R_{m})-R_{f}}$ is the market premium.

All correctly priced securities are plotted on the SML. Assets above the line are **undervalued**, while assets below the line are **overvalued**. ^[3]

Security Market Line, Treynor ratio and Alpha

All portfolios on the SML share the same Treynor ratio as the market portfolio:

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

The "abnormal" extra return above the market's return at a given level of risk is called alpha ($\alpha$).

Modified betas

Research has explored mean-reverting betas (adjusted beta) and consumption-based betas. ^[4] However, traditional CAPM often outperforms these models in empirical tests. ^[5]

Asset-specific required return and WACC

In corporate finance, the required return $E(R_i)$ is used as the cost of equity within the **Weighted Average Cost of Capital (WACC)** for evaluating **operating activities**:

${\displaystyle {\text{WACC}}=w_{d}\cdot [K_{d}(1-t)]+w_{pf}\cdot K_{pf}+w_{ce}\cdot K_{ce}}$

When issuing new common equity, the cost must be adjusted for **flotation costs** ($F$):

${\displaystyle K_{e}={\frac {D_{1}}{P_{0}(1-F)}}+g}$

Fundamental Valuation

Once $E(R_i)$ or WACC is established, it is used to determine an asset's intrinsic value:

${\displaystyle PV=\sum _{t=1}^{n}{\frac {E(CF_{t})}{(1+E(R_{i}))^{t}}}}$

Criticisms

Economists Eugene Fama and Kenneth French argue that empirical failures imply many applications of the model are invalid. ^[6]

See also

• Capital market line
• Modern portfolio theory
• Treynor ratio

References

1. Sharpe, William F. (1964). "Capital Asset Prices". Journal of Finance. 19 (3): 425–442.
2. Markowitz, Harry (1952). "Portfolio Selection". The Journal of Finance. 7 (1): 77–91.
3. Investopedia explains SML
4. Blume, Marshall E. (1971). "On the Assessment of Risk". The Journal of Finance. 26 (1): 1–10.
5. Fama, Eugene F.; French, Kenneth R. (2004). "The CAPM: Theory and Evidence". Journal of Economic Perspectives. 18 (3): 25–46.
6. Fama; Eugene F.; French, Kenneth R. (2004). "The CAPM: Theory and Evidence". Journal of Economic Perspectives.