> For the complete documentation index, see [llms.txt](https://docs.btcd.fi/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.btcd.fi/readme/omega-o-the-language-of-exposure.md).

# Omega (ω): The Language of Exposure

Throughout the protocol, we use the symbol $$\omega$$ (omega) to describe how an asset's value moves with BTC price. Formally, $$\omega$$ is the log-log elasticity of an asset's value, $$V$$, with respect to BTC price, $$P$$, though we often refer to $$\omega$$ as simply the "exposure" of the asset:

$$\omega = \frac{\partial \log V}{\partial \log P}$$

Intuitively, $$\omega$$ is the "Bitcoin-ness" of an asset:

* $$\omega =1$$: pure BTC exposure (e.g. wBTC)
* $$\omega=0$$: pure USD exposure (e.g. USDC, assuming a stable peg)
* $$\omega=0.5$$: 50/50 BTC/USD exposure (e.g. the BTCD peg)
* $$\omega>1$$: leveraged BTC exposure
* $$\omega < 0$$: short BTC exposure

Omega is additive across a portfolio: the portfolio's overall $$\omega$$ is the value-weighted average of the $$\omega$$ of each asset it holds. This makes it an unusually clean tool for thinking about hedging and exposure management.

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