The numeraire portfolio, also called the optimal growth portfolio, allows simple derivations of the main results of financial theory. The prices of self financing portfolios, when the optimal growth portfolio is the numeraire, are martingales in the 'true' (historical) probability. Given the dynamics of the traded securities, the composition of the numeraire portfolio as well as its value are easily computable. Among its numerous properties, the numeraire portfolio is instantaneously mean variance efficient. This key feature allows a simple derivation of standard continuous time CAPM, CCAPM, APT and contingent claim pricing. Moreover, since the Radon-Nikodym derivatives of the usual martingale measures are very simple functions of the numeraire portfolio, the latter provides a convenient link between the standard Capital Market Theory a la Merton and the probabilistic approach a la Harrison-Kreps-Pliska.Martingale Pricing Equilibrium Pricing Numeraire Portfolio Theory,

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Closed-form solutions for HARA optimal portfolios are obtained in a dynamic portfolio optimization model in three assets (stocks, bonds and cash) with stochastic interest rates. A Vasicek-type model of stochastic interest rates with a correlated stock price is assumed. The HARA solution can be expressed as a buy and hold combination of a zero-coupon bond with maturity matching the investor's horizon and a "CRRA mutual fund," which is the optimal portfolio for a CRRA investor expressed in terms of the weights on cash, stock, a constantduration bond fund and the (redundant) bond with maturity matching the investor's horizon (a generalization of the Merton's (1971) result of constant weight in stock for a CRRA investor, derived for two assets with constant interest rates). This simple characterization facilitates insights about investor behavior over time and under different economic scenarios and allows fast computation time (without simulation or other numerical methods). We use the model to provide explanations of the Canner-Mankiw-Weil (1997) asset allocation puzzle, the use of "convex" (momentum) and "concave" (contrarian) investment strategies and other features of popular investment advice. The model illuminates clearly the role of the different market parameters, the composition of initial investor wealth, and relative risk aversion in portfolio strategies.

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