> 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/the-50-50-peg.md).

# The 50 / 50 Peg

BTCD is not pegged to a fixed dollar value. It is pegged to a portfolio that maintains continuous 50% BTC / 50% USD exposure — the same exposure a Uniswap V2 LP position would have if it were continuously rebalanced.

Mathematically, the BTCD peg price $$p\_{btcd}$$ tracks the square root of the BTC price $$P$$:

$$P\_{btcd}(t) = P\_{btcd}(t\_0) \sqrt{\frac{P(t)}{P(t\_0)}}$$

The square-root scaling $$P\_{btcd} \propto \sqrt{P}$$  is the signature of a continuously rebalanced 50/50 portfolio. It means that when BTC doubles, the BTCD peg increases by a factor of $$\sqrt{2}-1$$ or roughly 41%. When BTC halves, the BTCD peg falls by a factor of $$1 − \frac{1}{\sqrt{2}}$$ or roughly 29%.

The result: BTCD's dollar-denominated volatility is roughly half of BTC's. Holders get exposure to the BTC trend with the spikes smoothed out.

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