DEFINITION of 'Characteristic Line'
A line formed using regression analysis that summarizes a particular security or portfolio's systematic risk and rate of return. The rate of return is dependent on the standard deviation of the asset's returns and the slope of the characteristic line, which is represented by the asset's beta.
INVESTOPEDIA EXPLAINS 'Characteristic Line'
A characteristic line of a stock is the same as the security market line, and is very useful when employing the capital asset pricing model, or when using modern portfolio formation techniques. The slope of the line, which is a measure of systematic risk, determines the riskreturn tradeoff. According to this metric, the more risk you take on  as measured by variability in returns  the higher the returns you can expect to earn.
There is considerable controversy regarding the use of beta as a measure of risk and return.

Systematic Risk
The risk inherent to the entire market or entire market segment. ... 
Standard Deviation
1. A measure of the dispersion of a set of data from its mean. ... 
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Capital Market Line  CML
A line used in the capital asset pricing model to illustrate ... 
Beta
A measure of the volatility, or systematic risk, of a security ...

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