Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate

Martin Gremm

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arXiv · 1605.03551

Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate

Martin Gremm

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Abstract

We define risk-free portfolios using three gauge invariant differential operators that require such portfolios to be insensitive to price changes, to be self-financing, and to produce a zero real return so there are no risk-free profits. This definition identifies the risk-free rate as the return of an infinitely diversified portfolio rather than as an arbitrary external parameter. The risk-free rate measures the rate of global price rescaling, which is a gauge symmetry of economies. We explore the properties of risk-free rates, rederive the Black Scholes equation with a new interpretation of the risk-free rate parameter as a that background gauge field, and discuss gauge invariant discounting of cash flows.

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Martin Gremm. 2016-05-11. Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate. https://arxiv.org/abs/1605.03551

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