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Active Portfolio Management, Positive Jensen-Jarrow Alpha, and Zero Sets of CAPM

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  • G. Charles-Cadogan

Abstract

We present conditions under which positive alpha exists in the realm of active portfolio management- in contrast to the controversial result in Jarrow (2010, pg. 20) which implicates delegated portfolio management by surmising that positive alphas are illusionary. Specifically, we show that the critical assumption used in Jarrow (2010, pg. 20), to derive the illusionary alpha result, is based on a zero set for CAPM with Lebesgue measure zero. So conclusions based on that assumption may well have probability measure zero of occurrence as well. Technically, the existence of [Tanaka] local time on a zero set for CAPM implies existence of positive alphas. In fact, we show that positive alpha exists under the same scenarios of "perpetual event swap" and "market systemic event" Jarrow (2010) used to formulate the illusionary positive alpha result. First, we prove that as long as asset price volatility is greater than zero, systemic events like market crash will occur in finite time almost surely. Thus creating an opportunity to hedge against that event. Second, we find that Jarrow's "false positive alpha" variable constitutes portfolio manager reward for trading strategy. For instance, we show that positive alpha exists if portfolio managers develop hedging strategies based on either (1) an exotic [barrier] option on the underlying asset - with barrier hitting time motivated by the "market systemic" event, or (2) a swaption strategy for the implied interest rate risk inherent in Jarrow's triumvirate of riskless rate of return, factor sensitivity exposure, and constant risk premium for a perpetual event swap.

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File URL: http://arxiv.org/pdf/1206.4562
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Paper provided by arXiv.org in its series Papers with number 1206.4562.

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Date of creation: Jun 2012
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Handle: RePEc:arx:papers:1206.4562

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  1. George Chacko, 2002. "Pricing Interest Rate Derivatives: A General Approach," Review of Financial Studies, Society for Financial Studies, vol. 15(1), pages 195-241, March.
  2. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  3. Carhart, Mark M, 1997. " On Persistence in Mutual Fund Performance," Journal of Finance, American Finance Association, vol. 52(1), pages 57-82, March.
  4. Tom Nohel & Z. Jay Wang & Lu Zheng, 2010. "Side-by-Side Management of Hedge Funds and Mutual Funds," Review of Financial Studies, Society for Financial Studies, vol. 23(6), pages 2342-2373, June.
  5. Shleifer, Andrei & Vishny, Robert W, 1997. " The Limits of Arbitrage," Journal of Finance, American Finance Association, vol. 52(1), pages 35-55, March.
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  7. Vikas Agarwal, 2004. "Risks and Portfolio Decisions Involving Hedge Funds," Review of Financial Studies, Society for Financial Studies, vol. 17(1), pages 63-98.
  8. Godfrey Charles-Cadogan, 2012. "Alpha Representation For Active Portfolio Management and High Frequency Trading In Seemingly Efficient Markets," Papers 1206.2662, arXiv.org.
  9. Henriksson, Roy D & Merton, Robert C, 1981. "On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecasting Skills," The Journal of Business, University of Chicago Press, vol. 54(4), pages 513-33, October.
  10. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-87, September.
  11. Breeden, Douglas T., 1979. "An intertemporal asset pricing model with stochastic consumption and investment opportunities," Journal of Financial Economics, Elsevier, vol. 7(3), pages 265-296, September.
  12. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  13. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  14. Merton, Robert C, 1981. "On Market Timing and Investment Performance. I. An Equilibrium Theory of Value for Market Forecasts," The Journal of Business, University of Chicago Press, vol. 54(3), pages 363-406, July.
  15. Amit Goyal, 2012. "Empirical cross-sectional asset pricing: a survey," Financial Markets and Portfolio Management, Springer, vol. 26(1), pages 3-38, March.
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