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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 …nancial 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 …rm-speci…c, risk is limited-uncertain, the real option value of a …rm is also limited-uncertain This explains the simultaneous coexistence of di¤erent analyst valuations of investment projects, particular …rms 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 ine¢ ciencies, 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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