Godfrey Cadogan is a Research Scientist in Risk and Uncertainty at the Institute for Innovation and Technology Management, Ted Rogers School of Management, Ryerson University. His research focus is on application of diverse branches of mathematics such as algebraic topology, number theory, group... More

On the recent controversy over whether portfolio managers can consistently deliver positive alpha 0 comments

Dec 24, 2011 10:15 AM

There is an old African proverb when loosely translated states "When elephants fight, the grass gets trampled". That said, the "elephants" or "giants" of financial economics disagree on whether portfolio managers can consistently deliver positive alpha--the bane of existence of this site. As some may know, I recently developed a reasonably sophisticated mathematical model of portfolio manager behavior which provides a trade strategy representation theorem for active portfolio management available here http://ssrn.com/abstracts=1920605. That theorem has been supported by empirical evidence reported by the SEC concerning the flash crash of May 10, 2010 available at http://www.sec.gov/news/studies/2010/marketevents-report.pdf Basically, the theorem shows why high frequency traders engage in price reversal strategies. I subsequently came across a paper written by Prof. Robert Jarrow entitled Active Portfolio Management and Positive Alphas: Fact or Fantasy?available here http://www.iijournals.com/doi/abs/10.3905/jpm.2010.36.4.017 That paper asserts that positive alphas are illusionary. I subsequently applied the alpha representation theorem in thee context of what I call Jarrow's alpha, and found that what Jarrow calls an illusionary alpa is actually portfolio manager's compensation for trade strategy. So positive alphas reflect portfolio manager reward for trade strategy. They are not illusionary. This I titled the paper "Positive Jensen-Jarrow Alpha , Active Portfolio Management, and Zero Sets of CAPM" and made it available here http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1976082 The key result is that mathematical models of equilibrium asset pricing exists on a set of measure zero. So the market is always in a state of disequilibrium. Thus, there are always trading opportunities to be exploited--something that practitioners know as evidenced by the vast sums spent on delegated portfolio management. We have to start computer trading models somewhere. So academic models on market equilibrium serve a useful building block purpose. In any event, for those who are mathematically inclined and who care about "exotic options" the rejoinder to Jarrow may be edifying.

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## On the recent controversy over whether portfolio managers can consistently deliver positive alpha 0 comments

There is an old African proverb when loosely translated states "When elephants fight, the grass gets trampled". That said, the "elephants" or "giants" of financial economics disagree on whether portfolio managers can consistently deliver positive alpha--the bane of existence of this site. As some may know, I recently developed a reasonably sophisticated mathematical model of portfolio manager behavior which provides a trade strategy representation theorem for active portfolio management available here http://ssrn.com/abstracts=1920605. That theorem has been supported by empirical evidence reported by the SEC concerning the flash crash of May 10, 2010 available at http://www.sec.gov/news/studies/2010/marketevents-report.pdf

Basically, the theorem shows why high frequency traders engage in price reversal strategies. I subsequently came across a paper written by Prof. Robert Jarrow entitled

Active Portfolio Management and Positive Alphas:

Fact or Fantasy?available here http://www.iijournals.com/doi/abs/10.3905/jpm.2010.36.4.017That paper asserts that positive alphas are illusionary. I subsequently applied the alpha representation theorem in thee context of what I call Jarrow's alpha, and found that what Jarrow calls an illusionary alpa is actually portfolio manager's compensation for trade strategy. So positive alphas reflect portfolio manager reward for trade strategy. They are not illusionary. This I titled the paper "Positive Jensen-Jarrow Alpha , Active Portfolio Management, and Zero Sets of CAPM" and made it available here http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1976082

The key result is that mathematical models of equilibrium asset pricing exists on a set of measure zero. So the market is always in a state of disequilibrium. Thus, there are always trading opportunities to be exploited--something that practitioners know as evidenced by the vast sums spent on delegated portfolio management. We have to start computer trading models somewhere. So academic models on market equilibrium serve a useful building block purpose. In any event, for those who are mathematically inclined and who care about "exotic options" the rejoinder to Jarrow may be edifying.

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