Question

You find an asset that does not lie on the security market line (SML). Is there an arbitrage opportunity? Explain, with reference to Arbitrage Pricing Theory.

Answer 1

ANS: The Security market Line (SML) is a line drawn on a chart that serves as a graphical representation of the Capital Assets Pricing Model (CAPM).

The Formula of CAPM = Risk Free Return + Beta (Market Return - risk free return)*

* The Difference of market return & risk free return is also known as Risk Premium.

The Sloping of Security Market Line is Up-ward sloping because securities with higher beta has higher expected return.

Features of Assets (securities) on the graph :-

• Assets plotted on the SML are correctly priced.
• Assets above the line are Under-valued because for the given Beta, they yield a higher return.
• Assets below the line are Over-valued because for the given beta, they yield a lower return.

So, as the Assets that are not plotted on the SML are either Over-valued or Under-Valued, that further leads to the Arbitrage opportunities. Investors may buy the securities at a lower price & able to sell them at a higher price & makes the arbritage profit.

NOTE : The concept of Beta is central to the CAPM & SML. The Beta of a security is a measure of its systematic risk which cannot be eliminated by way of diversification.