Question

Assume that you are using a two-factor APT model to find the expected return on a well-diversified portfolio Q that promises an expected return of 18%. The relevant factor portfolios, their betas, and their factor risk premiums are shown in the table below. The assumed risk-free rate is 3.5%.

Factor	Factor Beta	Factor risk premium
A	1.4	12.0%
B	0.8	-3.5%

What is the arbitrage strategy?

Answer 1

Factor	Factor Beta	Factor Risk Premium
A	1.4	12%
B	0.8	-3.5%

Risk free interest = Rf=3.5%

Expected return under APT or Arbitrage Pricing Theory=

ER= Rf+ B1(Risk premium for factor1) + B2( Risk premuim for Factor2)

=> ER= 3.5% + (1.4*12%) +(0.8* -3.5%)

=>ER= 3.5%+16.8%+(-2.8%) =17.5%

Actual return promised by Portfoli Q =18%

The idea behind a no-arbitrage condition is that if there is a mispriced security in the market, investors can always construct a portfolio with factor sensitivities similar to those of mispriced securities and exploit the arbitrage opportunity.

Here the actual return is 18% and the minimum expected return of the investor is 17.5%. It means the portfoli will earn more return than its minimum required retrun. Hence the portfolio is underpriced now and the value of portfoli will increase in near future.

The arbitrage strategy in this case is to borrow t risk free interest @3.5% and invest it in the portfolio. In future sell the portfolio at higher value and pay off the risk free borrowing and earn the arbitrage profit.