It is a slight oversimplification, but directionally correct to say:

Funding Rate (F) = Interest Rate (I) + Premium (P)

Where the premium is the amount a perpetual market differs from its underlying index.

This means that the funding rate is not exactly equal to the price discrepancy between the perp market and the underlying index.  There is an offset called the interest rate component.  The interest rate component is meant to deal with carry (yield) differences between the quote asset and the base asset.

The interest rate should be a constant value unique to each market.  Currently most exchanges either set the interest rate to zero or a fixed constant across all markets, often 0.01% every 8 hours. This has implications for the average difference between perpetual futures prices and their underlying prices. In some cases this is very significant.

What is the Interest Rate Component Trying to Achieve

The purpose of the funding rate is to keep the price of the perp and the index price in line.  This means as close to each other as possible and not biassed in either direction. The interest rate component takes care of potential perp price bias above or below the underlying index.

Theoretically an optimal distribution of the funding premium (difference between perp price and index price) would be normally distributed around zero with low variance.

The interest rate component helps translate the distribution of funding premiums one way or the other so it is centred around zero.

Some example of how non-differentiated interest rate components affect the distribution of the premium can be seen in the ETH and CRV markets on dYdX. Notice how the ETH market is relatively normally distributed divergence around the 0.01% IR component, while the CRV market divergence has a big left skew. This affects the variance of the divergence with the CRV market seeing much higher deviations on average.

How does the Interest Rate Component Improve Convergence

Perpetual futures prices diverge from their underlying index when there is a mismatch in the demand for volume traded on either side of the market.  Think more buyers than sellers or vice versa.  When this happens market makers accumulate inventory on the other side of the market.  To compensate they begin skewing prices to incentivise the side of their spread that would reduce their position.

How can the funding rate offset a sustained mismatch in demand for longs and shorts?

Perpetuals as a Hedge for Underlying Yield

Let’s start with an example where the quote asset can generate substantial yield.  Here perps could be a perfect hedge for movements in the price of the asset while capturing the yield.

Imagine Alice owns speculative token ABC that has a staking yield of 500% APY.  ABC PERPS are implemented the same as most perpetual markets currently with an interest rate component of 0.01% per 8 hours or ~11.6% APY.  

She buys and stakes ABC tokens for 500% APY and sells ABC PERPS.  For simplicity the APY in this example is in the same currency as the funding payments.

ABC PERPS in this example are likely to trade below the price of ABC on average as many traders will employ Alice’s strategy.  This will potentially cause regular depegs and diminish the ability of the funding rate to properly incentivise convergence.  

If not, Alice’s strategy is going to be highly profitable.  When prices are in-line on average then the average funding rate is the interest rate component.  In the example above, this is 11.6% APY which Alice also receives since she is short the perp.  Alice could earn 511.6% APY if the markets trade in line on average!

If this were possible other traders would likely notice and there would be more capital chasing short exposure than long exposure leading to the perp market trading below the price of ABC tokens.  Without frictions the perp market would likely average around 0.47%* below its index.

This is not optimal from a traders standpoint who want to trade instruments that track their index.  Because margin and hence liquidations happen using the index price, this also means that short positions are more likely to be liquidated than short positions as they have negative P&L immediately due to the divergent market.  Not the experience traders expect from their exchange.

More importantly it introduces a heightened risk of bad debt on the protocol as longs have less room for their liquidations to clear.  This in turn limits the amount of leverage that can safely be allowed on the exchange, limiting its ability to grow the market.

A solution in this market is to reduce the APY of the interest rate component to a negative rate.  This would incentivise participants to hold long positions in the ABC PERP market, balancing the mismatch between long demand and short demand.

* Exp[Funding Rate] = exp[(500%+11.6%)/(3*365)]-1 = 0.47%

Measuring the Performance of the Interest Rate Component

The interest rate component impacts the average divergence between the perpetual future market and its underlying index.  This could either be measured as the mean divergence or the median divergence, depending on how prone a market is to outliers on one side or the other.

We propose monitoring both as there could be tradeoffs where unusual trading dynamics happen in a market.

Interest Rates derived from Trading Activity

If the performance of the interest rate component is measured by a market’s average price skew, then it makes sense to calibrate it using this measure.  The specifics of how this is achieved are beyond the scope of this post, but the following ideas could help choose a rate that fits a market:

• Adjust the interest rate component by the observed mean divergence (perp price – index price) over some time period.  The observed divergence would need to be deducted from the current parameter.
• Do the same as above, but average the mean and median to better set an unbiased market.

Floating Rates derived from Money Markets

An interesting idea would be to allow this rate to float within some bounds using a lending index.  This could allow the interest rate component to respond to market conditions autonomously.  In this case the funding rate could be set as the money market rate on stablecoins less the money market rate of the base token.  Money market rates could be a better forward looking measure of the demand for exposure.  

Bounding the rates is necessary to protect against attacks and manipulations.  Presumably as long as rates are constrained to a reasonable range, an attack manipulating a lending index is not profitable.

Implementing floating rates requires robust interest rate indices and oracles.  This rate would need to account for the wide differential between borrow and lend rates.  There is still lots to develop before this is practical.

Conclusion

The interest rate component makes sure that PERP prices are equally likely above or below their index.  

The current implementation on most exchanges of 0.01% every 8 hours on all markets does not take tokens unique characteristics into account.  Just like commodity futures markets in traditional finance have very different carry profiles, crypto perps should also tailor their interest rates to their market.