Foreword: Fixed Leverage vs Margin Leverage (parity conditions, example)

It is well know that fixed-leveraged instruments price is eroded by the volatility of the underlying assets. While buy-and-hold strategies inevitable suffer from long-term price decay, it may be argued that such decay reduces the cost of a plethora of instruments which can be used to gain short-term exposure in volatile markets without the risks of unlimited losses involved in margin leverage.

In this section I will derive a simple parity condition between margin leverage and fixed leverage for a generic underlying instrument. Building on Avellaneda and Zhang (2010) I will show that such parity requires a moderate exposure precisely because of the compound-induced erosion in the fixed leverage instrument price. Some actual example in commodity and volatility markets will be provided.

in progress

References

Avellaneda, Marco, and Stanley Zhang. "Path-dependence of leveraged ETF returns." SIAM Journal on Financial Mathematics 1.1 (2010): 586-603.