Capital allocation line
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".
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
Wikipedia contributors · Capital allocation line · revision 1361243558 · CC BY-SA 4.0 · Plain text extracted and formatting adapted; tags derived from linked topics.