Munich Personal RePEc Archive

Die Theorie der fairen geometrischen Rendite

Sonntag, Dominik (2018): Die Theorie der fairen geometrischen Rendite.


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The theory of fair geometric returns, F theory for short, rejects the generally accepted notion that volatility is the risk of risky assets. Instead, it claims that capital market volatility, in turn, constitutes the maximum achievable geometric return. In order to get to the point, F theory, in addition to its own ideas, resorts to information theoretical considerations (centrally Shannon, 1948). The starting point of the analysis is a specific initial observation concerning the geometric mean return (G): Consecutive geometric returns of fairly (properly) exchange-traded assets ex post almost always turn out to be unequal. The author proposes two consequences to be drawn from this observation, which can be made daily at the financial market: (1) E[G]≠G dominates E[G]=G. Then what is E[G]? When does E[G]=G hold? (2) Since (it seems) there is volatility in G, is this volatility usable as part of a contrarian "buy low, sell high" strategy? If yes, how? In answer to these and other questions, the master's degree candidate presents a formulae system along with qualitative context, which essentially comprises: a formula for the expected geometric mean return; a measure of the abnormal return on an asset; movement probabilities in relation to the return process; an equivalent to Claude Shannon's famous information flow formula; the (here so-called) concept of the fugue – a novel countercyclical investment strategy borrowed from music theory; as well as an F-theory consistent option price and self-insurance model.

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