Question

Stock prices are determined by a 2 factor APT model. You have 3 investments available to you:

Portfolio	Expected Excess Return	Beta 1	Beta 2
A	4.9%	1	0
B	4.0%	0	1
C	4.9%	0.5	0.5

What would the expected excess return be on an arbitrage portfolio, given this information?

Answer 1

For an Arbitrage opportunity, Betas of 2 portfolios should be same.

Beta of Portfolio C is 0.5 & 0.5, whereas Beta of Portfolio A & B are 1 & 0 and 0 & 1 respectively.

If we make an Portfolio with 50% in A and 50% in B, then Beta of that combined Portfolio will become 0.5 & 0.5 i.e. same as Portfolio C.

Expected Return of above portfolio i.e. combination of A & B = Sum of [Weight*Return] = [0.5*4.9] + [0.5*4] = 4.45%

Now, we have 2 Portfolios as follows:

1) A+B, which has an Expected Return of 4.45% and Beta of 0.5 & 0.5

2) C, which has an Expected Return of 4.9% and Beta of 0.5 & 0.5

Therefore, To make an Arbitrage Gain, Portfolio (1) should be Sold and Portfolio (2) should be Bought.

Expected Excess Return = 4.9%-4.45% = 0.45%