Question

Recall that the definition of arbitrage required the satisfaction of three conditions: one about weights, one about risk and one about returns. Consider the following scenario in a one-factor APT:

	E[r]	B1
Asset X	3.7%	0.1
Asset Y	4.5%	2.1
Asset Z	14.9%	3.1

What is the expected return of an arbitrage portfolio composed of all three assets, X, Y and Z? Weights will be between +1 and -1.

Answer in percentage without the symbol, i.e. #.##% --> #.##

Answer 1

Ans - Following steps are taken to get arbitrage opportunity -

1. First of all optimal weights are taken so that factor sensitivity of combines security is equal to factor sensitivity of other security i.e. Beta (B1)
2. After that sell security or borrow from market at lower rate of return and put that money into higher return security
3. After that sell the portfolio of higher return and from that pay the money which you have taken from the market.
4. The left over amount is your gain

NOTE - Remember choose that securities which have same sensitivity, because we are taking the same risk i.e on one hand taking risk and on the other hand forgiving risk. So in this way we are taking no risk but earning money. This is known as arbitrage opportunity