SECURITY MARKET LINE (SML)

Starting from the CML and assuming all the hypotheses of the CAPM, one of the fundamental results is the derivation SML. For a diversified portfolio, the relationship is expressed by the CML; while for an asset or a generic portfolio, whether located on the CML or not, perfectly or not completely diversified, we have the following relationship:
                                                    , or
                                                   .

This equation describes the Security Market Line (SML). This equation does not represent the efficient frontier as the CML does. In equilibrium, this equation represents the relation between risk and return for single assets or portfolios (diversified or not). The SML is unique in a space. It also represents the portfolios on the CMLand portfolios from the efficient frontier derived by the minimum-variance one. 
In the space, the SML and CML differ because of the SML slope that represents the correlation coefficient. The could be expressed as . The two curves are equivalent only if (i.e., portfolio i is perfectly correlated with the market portfolio); if , and E(Ri) is equal, the CML has a higher slope with respect to the SML; with , the SML will have a negative slope.
Bibliography
Saltari, E., 1997, Introduzione all’Economia Finanziaria, NIS (La Nuova Italia Scientifica), Roma;
Editor: Rocco CICIRETTI
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