SML and CML Comparison

The beta coefficient of an asset can be expressed as a function of the asset's correlation with the market as follows:

Substitute this expression for beta into the Security Market Line $($SML$),$ equation below.

SML: ri $=$ rRF $+($rM $-$ rRF$)$bi $=$ rRF $+($RPM$)$bi

This results in an alternative form of the SML$.$

ri $=$ rRF $+($rM $-$ rRF$)$

ri $=$ rRF $+($rM $+$ rRF$)$

ri $=$ rRF $+($rRF $-$ rM$)$

ri $=$ rM $+($rM $-$ rRF$)$

The correct equation is

III

$.$

Compare your answer to part a with the Capital Market Line $($CML$),$ equation below.

CML:

What similarities do you observe? What conclusions can you drawn?

When in this form, the CML and SML

have the same market price of risk

$.$

The measure of risk in the

CML

is $\backslash$sigma p$.$ The measure of risk in the

SML

is $\backslash$rho iM$\backslash$sigma i$,$ and is

less

than for all assets except those which are perfectly positively correlated with the market.