The geometry of risk adjustments

Hans-Peter Bermin () and Magnus Holm
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Hans-Peter Bermin: Lund University
Magnus Holm: Hilbert Group

Decisions in Economics and Finance, 2024, vol. 47, issue 1, No 3, 83-120

Abstract: Abstract We present a geometric approach to portfolio theory with a focus on risk-adjusted returns, in particular Jensen’s alpha. We find that while the alpha/beta approach has severe limitations, especially in higher dimensions, only minor conceptual modifications (e.g., using orthogonal Sharpe ratios rather than risk-adjusted returns) are needed to identify the efficient trading strategies. We further show that, in a complete market, the so-called market price of risk vector is identical to the growth optimal Kelly vector, albeit expressed in coordinates of a different basis. This implies that a derivative, having an orthogonal Sharpe ratio of zero, has a price given by the minimal martingale measure.

Keywords: Jensen’s alpha; Kelly criterion; Market price of risk; Option pricing; Geometry (search for similar items in EconPapers)
JEL-codes: G11 G12 G13 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s10203-023-00421-1

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