Security market line

The security market line (SML) is a graphical representation of the relationship between the expected return of an individual security and the expected return of the broad market. The SML plots expected return on the y-axis (vertical axis) and the risk on the x-axis (horizontal axis). It is used to show the risk/return relationship for a portfolio of securities, and it is used to determine the appropriate level of risk for any given level of expected return. The SML is sometimes referred to as the characteristic line because it shows the relationship between the expected return of the security and its systematic risk.

Security market line calculation

To calculate the SML, you need to calculate the expected return and risk of a security. The expected return is calculated by taking the expected future cash flows and discounting them using the appropriate discount rate. The expected risk is calculated by measuring the volatility of the security's returns over time. Once these two values are calculated, the security can be plotted on the SML, and its expected return and risk can be compared to the expected return and risk of the broad market.

The expected return of a security can be calculated using the following formula:

$E[r]=\sum _{i=1}^{n}{\frac {C_{i}}{(1+r)^{i}}}$

Where E[r] is the expected return, C_i is the expected cash flow in period i, and r is the discount rate.

The expected risk of a security can be calculated using the following formula:

$\sigma ={\sqrt {{\frac {1}{N}}\sum _{i=1}^{N}(r_{i}-\mu )^{2}}}$

Where \sigma is the expected risk, r_i is the return in period i, and \mu is the average return.

Other market lines

Other similar market lines include the Capital Market Line (CML), which is similar to the SML except that it shows the relationship between the expected return and the risk-free rate; and the Market Portfolio Line (MPL), which is similar to the SML but plots the expected return against the expected return of the market portfolio. Additionally, the Capital Allocation Line (CAL) is similar to the SML but plots the expected return against the expected return of a portfolio of risky assets and the risk-free asset.

• Security Market Line (SML): Graphical representation of the relationship between the expected return of an individual security and the expected return of the broad market. Plots expected return on the y-axis (vertical axis) and risk on the x-axis (horizontal axis).
• Capital Market Line (CML): Similar to SML except it shows the relationship between the expected return and the risk-free rate.
• Market Portfolio Line (MPL): Similar to SML but plots the expected return against the expected return of the market portfolio.
• Capital Allocation Line (CAL): Similar to the SML but plots the expected return against the expected return of a portfolio of risky assets and the risk-free asset.

Suggested literature

• Jylhä, P. (2018). Margin requirements and the security market line. The journal of Finance, 73(3), 1281-1321.
• Jylhä, P. (2013). Margin constraints and the security market line. Working Paper, Imperial College London.
• Stulz, R. M. (1981). On the effects of barriers to international investment. The Journal of Finance, 36(4), 923-934.