Question

Draw the Security Market Line (SML) and plot Asset C such that it has less risk than the market but plots above the SML, and Asset D such that it has more risk than the market and plots below the SML. (Be sure to indicate where the market portfolio and risk-free returns are on your graph and provide the formula and the slope of the SML.) Explain how Assets C or D can plot as they do and explain why such pricing cannot persist in a market that is in equilibrium.                                                                                                     

Answer 1

The security market line (SML) is a line drawn on a chart that serves as a graphical representation of the capital asset pricing model (CAPM). The SML can help to determine whether an investment product would offer a favorable expected return compared to its level of risk.

Formula for plotting the SML is

Rreturn = risk-free rate of return + beta(market return- risk-free rate of return).

Let us hypothesis two portfolio as below

Investment	expected return	beta
A	10	1
B	12	2

Now consider a portfolio E made up of one half of portfolio A and B. From the facts stated in table, the expected return on this portfolio is 11 and it's beta is 1.5.

Now hypothesize a new asset/security C that has a return of 8% and the beta of 1.5. such an investment cannot exist for very long. All decision are made in terms of higher return and same risk as portfolio E. Hence it would pay arbitragerus to step in and buy portfolio E while selling security C short.

Similarly if security were to exist with a return of 14%and beta of 1.5( designated by D). This portfolio offers a higher return and same risk as portfolio E. As all decision are made on same risk and return, so investors will sell E short and buy D.

Such arbitrage would take place until C,D,& E all yield the same return. This is just another example of the adage that two things that are equivalent cannot sell at different prices.

Let's understand how arbitrage happens

An investor could sell $100 worth of the portfolio E short and with the $100 buy portfolio D.if the investor were to do so, the characteristics of the arbitraged portfolio would be as follow: -

Particular	Cash invested($)	Expected return	Beta
Portfolio E	-100	-11	-1.5
Security D	+100	14	1.5
Arbitrage portfolio	00	03	0

From this example it is clear that as long as security lies above or below the straight line, then opportunity would exist for arbitrage until all the investment converged to the line.