## Background

Institutions and retail traders regularly pursue cash-and-carry strategies to earn yields while remaining delta neutral. Some of the most lucrative risk-adjusted opportunities in the crypto asset class are seen in covered interest rate parity arbitrages. This is demonstrated by the steadily increasing notional volume on BTC futures contracts across exchanges, among which CME’s BTC product represents the highest open interest.

The mechanics of each strategy vary as per the risk profile of the arbitrageur, but the underlying concept remains the same: a trader takes simultaneous long and short positions between some combination of futures contracts or spot contracts of equal notional value, and nets the interest rate differential in the process. The pair of contracts chosen for each leg of the trade will depend on the shape of the interest rate curve i.e. alternate with markets in contango or backwardation.

Traders can pursue more sophisticated strategies by taking a directional position on the shape of the interest rate curve by trading two futures contracts with different maturities, or even considering multiple term structures and rolling contracts as they expire i.e. calendar spreads. Other traders perform volatility arbitrages i.e. capturing the mean reverting nature of basis by entering and exiting both legs of the trade as and when basis values fluctuate.

Most arbitrage strategies are however capital inefficient and require participation on centralized exchanges. Traders often need to actively monitor positions and margin requirements, and keep track of an increasing number of trades if they aim to hedge directional trades.

Since futures basis is mean reverting, perp.fi’s vAMM construction is a natural fit. A BTC futures basis perpetual swap contract would allow users to take leveraged directional positions on the shape of the interest rate curve, without needing to participate in centralized exchanges, manage a large number of trades, or deposit traditionally required amounts of collateral.

## Construction

CME futures contracts are fairly unique in their construction, since each contract is worth 5 BTC. The contract is settled linearly in USD (in contrast to with some inverse or quanto futures on other centralized exchanges like Bittrex or Kraken), and settles to the CME CF Bitcoin Reference Rate, which includes prices from Bitstamp, GDAX, itBit, and Kraken. This is one specific example, but we can construct the basis perp using any fixed expiry futures product (FTX, Binance, OKEx etc.) as long as the contract specifications around position size, settlement currency, and reference price index are known and considered.

Let’s take the Skew Analytics formula for annualized rolling 1-month futures basis as the index price. For a given date t, this is calculated by taking a time-weighted average of the basis spread between two futures with expiries such that T_1 < t + 30 < T_2. The skew analytics definition takes the following forward yield formula

and constructs a weighted average using the T_1 basis and forward yield

The interpretation of this formula is: If there were to exist a future contract that would expire exactly one month from today, what would be the annualized basis of that contract?

## Use Case

Let’s take an example. If today is 23rd February, and BTC is trading at $48,000. FEB21 is trading at $48,100 and has 3 days to expiry and MAR21 is trading at $50,000 and has 34 days to expiry, and the APR21 contract is trading at $52,000 (Assume these are CME futures)

A trader could short one unit of FEB21 contract and purchase 5 BTC spot in order to net a profit of ($48,100 - $48,000)*5 = $500 in three days when the contract expires – this is the traditional cash-and-carry trade.

Given the upward slope of basis, the trader could long one unit of FEB21 and short one unit of the MAR21 contract. Upon expiry of the FEB21 contract, the trader could long the MAR21 contract and close the position, or simultaneously short the APR21 and “short-roll” the position, thereby capturing the interest rate differential between the March and February contracts – such a trade is sometimes referred to as a “curve flattener”, because it is inherently the short basis difference between the front and back dated futures. Once the March contracts expire, the trader could choose to continue the sequence of trades using the JUN21 futures.

Alternatively, the trader could “long-roll” their futures by shorting the backdated futures and longing the front dated futures – such a trade could be described as “curve steepener”, because it is inherently long the basis difference between the front and back dated futures. Some advanced traders will enter and exit these positions as basis values fluctuate, capturing greater amounts of theta i.e. volatility arbitrages.

Traders can arbitrage the basis on the PERP market vs basis on the exchange to keep the market in line. **The perp index would allow leveraged exposure to change in theta captured in the types of trades above, without needing to purchase the underlying futures or calendar spreads. Note that the product would not allow users to capture the basis itself directly, but rather speculate on the change in basis over time, which is what is being done when choosing whether or how to roll contracts.**

## Open Questions

Is there a way to source a reliable price feed for this product?