Question

Given the following three assets, determine whether an arbitrage opportunity exists according to the arbitrage pricing theory. If so, please calculate the excess return of the arbitrage portfolio; if there is no arbitrage opportunity, please enter zero as your answer. (Assume the weight in A is standardized to 1 or -1 depending on the position)
Answers must be entered with 2 decimal places and no dollar signs , e.g. 6 as 6.00; 32.346 as 32.35.

Asset	E(r) (%)	Beta
A	9	1.0
B	14	1.4
C	3	0.0

The arbitrage excess return is ?

Answer 1

The existence of arbitrage opportunities can be tested by calculating their respective Treynor ratios.

A: (9.0% - 3.0%) / 1 = 6%

B: (14.0% - 3.0%) / 1.4 = 7.85%

C: (3.0% - 3.0%) / 0 = 0%

as the Treynor (A) and Treynor(C) is lower than the Treynor (B) = 7.85;

i.e., our arbitrage is to buy the "cheap" Portfolio B (with the higher Treynor) and sell the "expensive" blend of Portfolios (A) and (C).

Arbitrage Excess Return:

Expected Return from B: By CAPM 3% + (9% - 3%) * 1.4 = 11.4

Expected Return from B = 14%

Excess Return: 14% - 11.4% = 2.6%

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