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Capital Market Line (CML) and Security Market Line (SML)

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

bi=rho iM si / sM
rho iM = correlation between the security's returns and market returns
si= standard deviation of security's returns
sm= standard deviation of market's returns

1. Substitute this expression for beta into the Security Market Line (SML) This will result in the alternative form of SML.

2. Compare your answer to part with the Capital Market Line (CML) What are the similarities and what conclusion can be drawn?

Solution Preview

See attached file where formatting is conserved:

1. Substitute this expression for beta into the Security Market Line (SML) This will result in the alternative form of SML.

SML is expressed as
ri = r f + beta i (r m - r f)
where

r f = risk free rate
beta i = beta of stock/portfolio of stocks
r m = return on market portfolio
r i = required return on stock / portfolio of stocks

beta i can also be written as

beta i = s im / s m 2

where
s im = covariance between stock / portfolio and the market portfolio

s m 2 = variance of ...

Solution Summary

The solution looks at similarities between Capital Market Line (CML) and Security Market Line (SML).

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