Peters (2011a) defined an optimal leverage which maximizes the time-average growth rate of an investment held at constant leverage. We test the hypothesis that this optimal leverage is attracted to 1, such that  leveraging an investment in the market portfolio cannot yield long-run outperformance. Historical data support the hypothesis. This places a strong constraint on the stochastic properties of  traded assets, which we call "leverage efficiency." Market conditions that deviate from leverage efficiency are unstable and may create leverage-driven bubbles. This result resolves the equity premium puzzle , informs interest rate setting , and constitutes a theory of noise in financial markets  .
Peters (2011a) defined an optimal leverage which maximizes the time-average growth rate of an investment held at constant leverage. It was hypothesized that this optimal leverage is attracted to 1, such that , e.g., leveraging an investment in the market portfolio cannot yield long-term outperformance. This places a strong constraint on the stochastic properties of prices of traded assets, which we call "leverage efficiency." Market conditions that deviate from leverage efficiency are unstable and may create leverage-driven bubbles. Here we expand on the hypothesis and its implications. These include a theory of noise that explains how systemic stability rules out smooth price changes at any pricing frequency; a resolution of the so-called equity premium puzzle ; a protocol for central bank interest rate setting to avoid leverage-driven price instabilities; and a method for detecting fraudulent investment schemes by exploiting differences between the stochastic properties of their prices and those of legitimately-traded assets. To submit the hypothesis to a rigorous test we choose price data from different assets: the S P500 index, Bitcoin, Berkshire Hathaway Inc., and Bernard L. Madoff Investment Securities LLC. Analysis of these data supports the hypothesis .
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We test the hypothesis
It was hypothesized
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, e.g.,
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long-run outperformance. Historical data support the hypothesis.
long-term outperformance.
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prices of
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This result resolves the
Here we expand on the hypothesis and its implications. These include a theory of noise that explains how systemic stability rules out smooth price changes at any pricing frequency; a resolution of the so-called
R
, informs
; a protocol for central bank
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, and constitutes a theory of noise in financial markets
to avoid leverage-driven price instabilities; and a method for detecting fraudulent investment schemes by exploiting differences between the stochastic properties of their prices and those of legitimately-traded assets. To submit the hypothesis to a rigorous test we choose price data from different assets: the S
A
P500 index, Bitcoin, Berkshire Hathaway Inc., and Bernard L. Madoff Investment Securities LLC. Analysis of these data supports the hypothesis