Timeline for Law of large numbers necessary for APT derivation?
Current License: CC BY-SA 3.0
8 events
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| Jan 15, 2015 at 14:54 | comment | added | Drew | No worries. Im glad it made sense. its true, APT is a limiting result. and that's correct, and the true intuition behind the more advanced stochastic calculus conditions. FYI, another interesting point, the APT is a one factor model, not a multi factor one. Try deriving it, it's a good exercise. | |
| Jan 15, 2015 at 7:33 | comment | added | vanguard2k | To upvote and accept your answer I had to edit it first so I added the resource. Your explanation is not different from the paper but my question was aiming at something different. The shanken paper answered it though. What confused me was that the APT equation is only an approximate result! (which is unusual for an arbitrage argument and very seldomly stressed in the literature) Of course, $x^\prime \varepsilon=0$ can never hold for independent $\varepsilon_i$ and thus there will never be an arbitrage portfolio, even if arbitrage possibilities are present. | |
| Jan 15, 2015 at 7:27 | vote | accept | vanguard2k | ||
| Jan 15, 2015 at 7:26 | history | edited | vanguard2k | CC BY-SA 3.0 |
added the paper so i can upvote and accept the answer
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| Jan 14, 2015 at 14:59 | comment | added | Drew | Enlighten me as to how my explanation is different | |
| Jan 14, 2015 at 14:59 | comment | added | Drew | thats fine. But its a short answer because the question seems a little too obvious to me to have a detailed answer. If you really can't get it, Jay Shanken in his seminal papers addresses it at a high-school level: home.business.utah.edu/finmll/fin787/papers/shanken1982.pdf | |
| Jan 14, 2015 at 8:36 | comment | added | vanguard2k | I am sorry I have to downvote this answer. To get the APT relation you could simply assume $x^\prime \varepsilon = 0$ for an arbitrage portfolio... If you think its about the assumptions, feel free to be more specific about "some extent making assumptions of linear regression". Please also explain in detail where these assumptions are needed and how they imply the need for the law of large numbers with respect to the no-arbitrage argument! | |
| Jan 13, 2015 at 18:01 | history | answered | Drew | CC BY-SA 3.0 |