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# Power Perpetuals

Power Perpetuals are a form of perpetual whose index price tracks the price of an asset raised to a power. Read more about them here.
Power Perpetuals allow users to get exposure to convex payouts similar to options, without having to deal with different expiries and strikes.

### Funding

$power = 2$
$funding = mark - index^{power}$
For all powers > 1, the funding rate will almost always be positive since the perp will trade above the mark price because of convex nature of the payout.

### Example

$SOL$
perp is trading at $100 and the $SOL^3$ perp is trading at$1,000,000. If
$SOL$
goes up 10%, the
$SOL^3$
perp will be worth
$1.1^3 = 1.331$
or gain
$33.1$
%. If
$SOL$
goes down 10%, the
$SOL^3$
perp will be worth
$0.9^3 = 0.729$
or lose
$27.9%$
%.
For power perps where power > 1, the longs get asymmetric upside. This benefit comes at the cost of increased demand to be long, causing mark price to trade above index price and require longs to pay funding to shorts in most cases.
For power perps where power < 1, the shorts get asymmetric upside. This benefit will cause the perps to have negative funding in almost all situations.

### Perp Assets

For now, Entropy will support:
• POWER-2 SOL perps
• POWER-0.5 SOL perps

#### POWER-2 SOL

POWER-2 SOL perps allow users to get options-like exposure. The funding rate on POWER-2 SOL perps can be viewed as the implied volatility of the asset, and most closely mimics the payoff structure of an options contract.

#### POWER-0.5 SOL

POWER-0.5 SOL perps mimic the payoff structure of an LP position. Shorting the POWER-0.5 perp allows users to directly hedge impermanent loss from LPing. The funding rate can be viewed as a combination of the implied volatility of the asset with some additional higher order terms.
$\sqrt{1+x}$
can be expanded into a Taylor series
$1 + \frac{x}{2} - \frac{x^2}{8}+\frac{x^3}{8}...$