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# Characteristic Line

## What Is a Characteristic Line?

A characteristic line is a straight line formed using regression analysis that summarizes a particular security's systematic risk and rate of return. The characteristic line is also known as the security characteristic line (SCL).

The characteristic line is created by plotting a security's return at various points in time. The y-axis on the chart measures the excess return of the security. Excess return is measured against the risk-free rate of return. The x-axis on the chart measures the market's return in excess of the risk free rate.

### Key Takeaways

• A characteristic line indicates a security's systematic risk and rate of return.
• This line shows the security's performance versus the market's performance.
• The characteristic line is also referred to as the security characteristic line.

The security's plots reveal how the security performed relative to the market in general. The regression line formed from the plots will show the security's excess return over the measured period of time as well as the amount of systematic risk the security demonstrates. The y-intercept is the security's alpha, which represents its rate of return in excess of the risk-free rate, which cannot be accounted for by that market’s specific risks. According to Modern Portfolio Theory (MPT), the alpha stands for the asset’s rate of return above and beyond its risk-free return, adjusted for the asset’s relative riskiness. The slope of the characteristic line is the security's systematic risk, or beta, which measures the correlated variability of the specific asset’s price when compared to that of the market as a whole.

### What the Characteristic Line Shows

The characteristic line presents a visual representation of how a specific security or other asset performs when compared to the performance of the market as a whole. The return, and correlated risk, of a specific asset, relative to the market in general, are represented by both the slope of the characteristic line and its standard deviation.

## How a Characteristic Line Works

The characteristic line is part of a wider suite of security and market performance assessment tools known as Modern Portfolio Theory (MPT). In addition to the characteristic line regression, other qualities of a security or the overall market can be plotted and regressed to help an investor measure risk and make decisions.

### Other MPT Tools

Other analytic tools in the Modern Portfolio Theory family are the security market line (SML), the capital market line (CML), the capital allocation line (CAL), and the capital asset pricing model (CAPM). Calculating the characteristic line is a means of graphically portraying the CAPM. All of these systems use various constructions of risk, excess return, overall market performance, security beta, and individual security performance to assess the risk/return tradeoff and inform investment decisions.

According to MPT and the CAPM, rates of return should increase relative to the riskiness of an asset. When risk goes up, returns go up as well. Rates of return are therefore said to depend on risk and risk can be measured in terms of the variability of returns. Returns higher than the risk-free interest rate plus an additional level of compensation for assuming higher risk are said to be abnormal. However, assets often exhibit abnormal returns. Those exhibiting abnormally high returns are said to be undervalued, while those with abnormally low returns are said to be overvalued.

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