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Investment Model Uncertainty and Fair Pricing

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  • Los, Cornelis A.
  • Tungsong, Satjaporn

Abstract

Modern investment theory takes it for granted that a Security Market Line (SML) is as certain as its "corresponding" Capital Market Line. (CML). However, it can be easily demonstrated that this is not the case. Knightian non-probabilistic, information gap uncertainty exists in the security markets, as the bivariate "Galton's Error" and its concomitant information gap proves (Journal of Banking & Finance, 23, 1999, 1793-1829). In fact, an SML graph needs (at least) two parallel horizontal beta axes, implying that a particular mean security return corresponds with a limited Knightian uncertainty range of betas, although it does correspond with only one market portfolio risk volatility. This implies that a security' risk premium is uncertain and that a Knightian uncertainty range of SMLs and of fair pricing exists. This paper both updates the empirical evidence and graphically traces the financial market consequences of this model uncertainty for modern investment theory. First, any investment knowledge about the securities risk remains uncertain. Investment valuations carry with them epistemological ("modeling") risk in addition to the Markowitz-Sharpe market risk. Second, since idiosyncratic, or firm-specific, risk is limited-uncertain, the real option value of a firm is also limited-uncertain This explains the simultaneous coexistence of different analyst valuations of investment projects, particular firms or industries, included a category "undecided." Third, we can now distinguish between "buy", "sell" and "hold" trading orders based on an empirically determined collection of SMLs, based this Knightian modeling risk. The coexistence of such simultaneous value signals for the same security is necessary for the existence of a market for that security! Without epistemological investment uncertainty, no ongoing markets for securities could exist. In the absence of transaction costs and other inefficiencies, Knightian uncertainty is the necessary energy for market trading, since it creates potential or perceived arbitrage (= trading) opportunities, but it is also necessary for investors to hold securities. Knightian uncertainty provides a possible reason why the SEC can't obtain consensus on what constitutes "fair pricing." The paper also shows that Malkiel's recommended CML-based investments are extremely conservative and non-robust.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 8859.

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Date of creation: 24 May 2008
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Handle: RePEc:pra:mprapa:8859

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Keywords: capital market line; security market line; beta; investments; decision-making; Knightian uncertainty; robustness; information-gap; Galton's Error; real option value;

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  1. William F. Sharpe, 1964. "Capital Asset Prices: A Theory Of Market Equilibrium Under Conditions Of Risk," Journal of Finance, American Finance Association, vol. 19(3), pages 425-442, 09.
  2. Robert J. Elliott & John van der Hoek, 2003. "A General Fractional White Noise Theory And Applications To Finance," Mathematical Finance, Wiley Blackwell, vol. 13(2), pages 301-330.
  3. Jamdee, Sutthisit & Los, Cornelis A., 2007. "Long memory options: LM evidence and simulations," Research in International Business and Finance, Elsevier, vol. 21(2), pages 260-280, June.
  4. Cornelis A. Los, 2004. "Galton's Error and the Under-Representation of Systematic Risk," Finance 0409041, EconWPA.
  5. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, 03.
  6. Cornelis A. Los, 1991. "A Scientific View of Economic Data Analysis: Reply," Eastern Economic Journal, Eastern Economic Association, vol. 17(4), pages 526-531, Oct-Dec.
  7. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, vol. 13(3), pages 341-360, December.
  8. Cornelis A. Los, 1991. "A Scientific View of Economic Data Analysis," Eastern Economic Journal, Eastern Economic Association, vol. 17(1), pages 61-71, Jan-Mar.
  9. Yakov Ben-Haim, 2005. "Value-at-risk with info-gap uncertainty," Journal of Risk Finance, Emerald Group Publishing, vol. 6(5), pages 388-403, November.
  10. Bryan Beresford-Smith & Colin J. Thompson, 2007. "Managing credit risk with info-gap uncertainty," Journal of Risk Finance, Emerald Group Publishing, vol. 8(1), pages 24-34, January.
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