Hi Everyone:
It seems like I can get some crazy tough topics on this exam, but for some reason I’m having a hard time with finding the arbitrage opportunity - like #2 in the Concept Checkers in the Schweser Curriculum in the “Intro to Multifactor Models.” If someone that has done this problem explain their thinking process, etc… to get to the answer that would be great. What do I need to do in order to understand that I need to allocate 30% long to security A, etc…? Again, I’m feeling dumb, because the answer is probably obvious. Thanks!
Multiply 2 of the associated risk factors with the weights given in the options.
The portfolio that yields the highest return relative to risk is the one you go long on
In this problem, you have the factor sensitivities - there are no weights given in the options - all you have are expected returns and the factor sensitivities. Therefore, the part I’m having a hard time with has to do with how do I find how much weight I need to give to each portfolio based on that expected return and factor sensitivity?
The problem works the following way:
Portfolio A has Expected Return of 10% and factor sensitivity is 1.2
Portfolio B has Expected Return of 20% and factor sensitivity is 2
Portfolio C has Expected Return of 13% and factor sensitivity is 1.76
The question is the following: An arbitrage strategy would most likely involve a short position in which portfolio?
A. Portfolio A
B. Portfolio B
C. Portfolio C
The answer is portfolio C - the explanation in the answers says the following: “An arbitrage portfolio can be constructed consisting of 30% long portfolio A, 70% long portfolio B, and a 100% short position in portfolio C. The factor sensitivity of this portfolio will be (0.3)(1.2) + (0.7)(20) - 1(1.76) = 0. Expected return on zero risk, zero investment portfolio will be (0.3)(10)+(0.7)(20)-1(13)=4%.”
I’m confused as to what I do on this problem to get the weights for each asset. Why 30%, why 70%, and how can I solve this quickly on exam day?
AFAIK its usually the weighted sum of the portfolios with the highest and lowest risk. The weights could be done by trial and error. Start with 50% and add/subtract 10% each time.
The higher risk portfolio is usually under weighted and the low risk portfolio is usually over weighted.
But tbh I am sure there is a faster way.
Yes, I’m in agreement with you on principle. However, since I consider myself pretty good at math, I know there must be some formulaic way to do this…or at least some way to use the info given to us in a more efficient way. Maybe someone can come to the rescue.
Yea just hope Magician comes to our rescue.