capital allocation line
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Capital allocation line (CAL) is a graph created by investors to measure the risk of risky and risk-free assets. The graph displays the return to be made by taking on a certain level of risk. Its slope is known as the "reward-to-variability ratio".


Formula

The capital allocation line is a straight line that has the following equation: :\mathrm : E(r_) = r_F + \sigma_C \frac In this formula ''P'' is the risky portfolio, ''F'' is riskless portfolio, and ''C'' is a combination of portfolios ''P'' and ''F''. The slope of the capital allocation line is equal to the incremental return of the portfolio to the incremental increase of risk. Hence, the slope of the capital allocation line is called the reward-to-variability ratio because the
expected return The expected return (or expected gain) on a financial investment is the expected value of its return (of the profit on the investment). It is a measure of the center of the distribution of the random variable that is the return. It is calculated b ...
increases continually with the increase of risk as measured by the
standard deviation In statistics, the standard deviation is a measure of the amount of variation or dispersion of a set of values. A low standard deviation indicates that the values tend to be close to the mean (also called the expected value) of the set, whil ...
.


Derivation

If investors can purchase a risk free asset with some return ''rF'', then all correctly priced risky assets or portfolios will have expected return of the form : = r_F + b \sigma_P where ''b'' is some incremental return to offset the risk (sometimes known as a
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 σP is the risk itself expressed as the standard deviation. By rearranging, we can see the risk premium has the following value :b = \frac Now consider the case of another portfolio that is a combination of a risk free asset and the correctly priced portfolio we considered above (which is itself just another risky asset). If it is correctly priced, it will have exactly the same form: :E(R_C) = r_F + \sigma_C b Substituting in our derivation for the risk premium above: :E(R_C) = r_F + \sigma_C \frac This yields the Capital Allocation Line.


See also

* Capital market line *
Security market line Security market line (SML) is the representation of the capital asset pricing model. 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 re ...
*
Security characteristic line Security characteristic line (SCL) is a regression line, plotting performance of a particular security or portfolio against that of the market portfolio at every point in time. The SCL is plotted on a graph where the Y-axis is the excess return on ...
*
Market portfolio Market portfolio is a portfolio consisting of a weighted sum of every asset in the market, with weights in the proportions that they exist in the market, with the necessary assumption that these assets are infinitely divisible. Richard Roll's cr ...
*
Sharpe ratio In finance, the Sharpe ratio (also known as the Sharpe index, the Sharpe measure, and the reward-to-variability ratio) measures the performance of an investment such as a security or portfolio compared to a risk-free asset, after adjusting for its ...
, which equals the slope of the Capital Allocation Line


References

Investment management {{investment-stub