# Capital allocation line

Canonical: https://web4.xpay.bi/en/wiki/wp-en-22199186/

Language: en

Published: 2026-10-25T17:15:23.071Z

Updated: 2026-10-25T17:15:23.071Z

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".

## Key facts

## Overview

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:

C           A           L

:         E         (

r

C

)         =

r

F

+

σ

C

E               (

r

P

)               −

r

F

σ

P

\{\\displaystyle \\mathrm \{CAL\} :E(r\_\{C\})=r\_\{F\}+\\sigma \_\{C\}\{\\frac \{E(r\_\{P\})-r\_\{F\}\}\{\\sigma \_\{P\}\}\}\}

## 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

E           (

R

P

)

=

r

F

+         b

σ

P

\{\\displaystyle \{E(R\_\{P\})\}=r\_\{F\}+b\\sigma \_\{P\}\}

where b is some incremental return to offset the risk (sometimes known as a risk premium), and σP is the risk itself expressed as the standard deviation. By rearranging, we can see the risk premium has the following value

b         =

E               (

R

P

)               −

r

F

## See also

Capital market line Security market line Security characteristic line Market portfolio Sharpe ratio, which equals the slope of the Capital Allocation Line

## Sources

- Capital allocation line · Wikipedia: https://en.wikipedia.org/?curid=22199186

Source: Wikipedia contributors — https://en.wikipedia.org/?curid=22199186&oldid=1361243558

Licence: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/

Adaptation notice: Reformatted for XPay; the source may be abridged, restructured or translated. Consult the cited revision for the original.