Maximal Compounded Wealth for Portfolios of Stocks and Options
نویسندگان
چکیده
In the context of multi-period stock market investment with options, we provide characterization of the wealth of constantly rebalanced portfolios of stocks and options. This characterization takes advantage of a correspondence between certain combinations of options and pure gambling opportunities. Through this equivalence, prices to be set for the options correspond to payoff odds on the gambles. Portfolios of a sufficiently complete set of options correspond to betting fraction in gambles on state securities. We use this correspondence to examine the compounded wealth and to show it has a decomposition into a product of three easily interpretable factors. The best portfolio and price strategies with hindsight are identified. We provide universal portfolio strategies that yield the minimax drop in wealth from the maximal compounded wealth for portfolios of stock options.
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