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

17 Pages Posted: 12 May 2016

Date Written: May 9, 2016

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.

Keywords: Gauge Theory, Risk Free Rate, Option Pricing

Suggested Citation

Gremm, Martin, Global Gauge Symmetries, Risk-Free Portfolios, and the Risk-Free Rate (May 9, 2016). Available at SSRN: https://ssrn.com/abstract=2777814 or http://dx.doi.org/10.2139/ssrn.2777814

Martin Gremm (Contact Author)

Pivot Point Advisors ( email )

Bellaire, TX 77401
United States

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