Donald J. Brown

Document Type

Discussion Paper

Publication Date


CFDP Number


CFDP Pages


Journal of Economic Literature (JEL) Code(s)

B31, C91, D9


Ambiguous assets are characterized as assets where objective and subjective probabilities of tomorrow’s asset-returns are ill-defined or may not exist, e.g., bitcoin, volatility indices or any IPO. Investors may choose to diversify their portfolios of fiat money, stocks and bonds by investing in ambiguous assets, a fourth asset class, to hedge the uncertainties of future returns that are not risks. (IR)rational probabilities are computable alternative descriptions of the distribution of returns for ambiguous assets. (IR)rational probabilities can be used to define an investor’s (IR)rational expected utility function in the class of non-expected utilities. Investment advisors use revealed preference analysis to elicit the investor’s composite preferences for risk tolerance, ambiguity aversion and optimism. Investors rationalize (IR)rational expected utilities over portfolios of fiat money, stocks, bonds and ambiguous assets by choosing their optimal portfolio investments with (IR)rational expected utilities. Subsequently, investors can hedge future losses of their optimal portfolios by purchasing minimum-cost portfolio insurance.

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