> 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/cr-collateral-ratio.md).

# CR: Collateral Ratio

The collateral ratio (CR) is the ratio of portfolio value to the value of the peg liability:

$$\mathrm{CR} = \frac{V}{P\_{btcd}S}$$

where $$V$$ is the total portfolio value, $$P\_{btcd}$$ is the peg price of BTCD, and $$S$$ is the total supply of BTCD tokens.

When $$\mathrm{CR} > 1$$, the protocol is overcollateralized. Excess collateral above the peg is the source of yield distributed to sBTCD holders.

Because the $$P\_{btcd}\propto \sqrt{P}$$, maximizing CR over time is equivalent to growing portfolio value faster than $$\sqrt{P}$$ — i.e., outperforming a continuously rebalanced 50/50 portfolio. To ensure that the collateral ratio is insensitive to BTC price moves, the portfolio must be hedged to such that $$\omega\_V = 0.5$$. When the portfolio is properly hedged, CR growth is driven purely by yield earned minus rebalancing costs.

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