Leverage and risk relativity: how to beat an index

Hans-Peter Bermin and Magnus Holm
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Hans-Peter Bermin: Knut Wicksell Centre for Financial Studies, Lund University, Postal: Knut Wicksell Centre for Financial Studies, Lund University School of Economics and Management, P.O. Box 7080, S-220 07 Lund, Sweden
Magnus Holm: Hilbert Capital

No 2021/1, Knut Wicksell Working Paper Series from Lund University, Knut Wicksell Centre for Financial Studies

Abstract: In this paper we show that risk associated with leverage is fundamentally relative to an arbitrary choice of reference asset or portfolio. We characterize leverage risk as a drawdown risk measure relative to the chosen reference asset. We further prove that the growth optimal Kelly portfolio is the only portfolio for which the relative drawdown risk is not dependent on the choice of the reference asset. Additionally, we show how to translate an investor’s viewpoint from one choice of reference asset to another and establish conditions for when two investors can be said to face identical leverage risk. We also prove that, for a given reference asset, the correlation between two arbitrary portfolios with identical leverage risk equals the ratio of their Sharpe ratios if and only if the leverage risk is consistently traded. More surprisingly, we observe that leverage applied to the growth optimal Kelly strategy affects the drawdown risk in much the same way as the speed of light affects velocities in Einstein’s theory of special relativity. Finally, we provide details on how to trade in order to beat an arbitrary index for a given leverage risk target.

Keywords: Leverage; Drawdown risk; Generalized Kelly strategy; Numéraire invariance; Risk relativity (search for similar items in EconPapers)
JEL-codes: E20 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2021-01-25
New Economics Papers: this item is included in nep-ban, nep-cwa and nep-rmg
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