Question

Consider a two factor model of expected returns where the risk free rate is 6% and the expected risk premiums on the factor portfolios are 3% and 7%. If the factor portfolios are “ideal” and tradable, determine if an arbitrage opportunity exists for the portfolio given below and specify how can it be exploited.

portfolio	Bf1	Bf2	Expected return
A	1.4	0.8	0.41

 

 

Answer 1

Given

Risk free rate is 6%

Factor 1 risk premium = 3%

Factor 2 risk peridium = 7%

Factor 1 beta = 1.4

Factor 2 beta = 0.8

 

SML return or required return = Rf + BF1 * Risk premium at F1 + BF2 * Risk premium at F2

                                                       = 0.06 + 1.4*(0.03)+0.8*(0.07)

                                                       = 0.158 

 

But given

Expected return = 0.41

 

Expected return (0.41) > SML return (0.158) - there is an existence of arbitrage opportunity.

 

So the portfolio is under valued in the market so buy or hold the portfolio to gain advantage of arbitrage.

So the portfolio is under valued in the market so buy or hold the portfolio to gain advantage of arbitrage.