# Bitcoin Futures Basis Trading: Lesson 2

*Note: This article explains the 2015 and 2016 futures products. Please go to our product page for the most up to date details.

Lesson 1 explained the time value of money and how to calculate the annualised basis of a futures contract. Lesson 2 will focus on the basis term structure and different ways to profit from curve shifts.

The basis term structure is a graphical representation of the annualised percentage basis for different maturity futures contracts.

### Contango Term Structure

For a Bitcoin/USD future, being in contango means that the USD interest rate is higher than Bitcoin’s. Or put another way, traders believe that Bitcoin will appreciate in the future vs. the USD.

Assume there are three futures contracts:

`Spot = \$250`

`XBTU15 (September 2015): \$260, t = 0.08 (days until expiry, Days/360)`

`XBTZ15 (December 2015): \$290, t = 0.25`

`XBTH16 (March 2016): \$340, t = 0.5`

Below is a graphical representation of the upward sloping term structure. The best trading strategy for playing an upward sloping yield curve is a carry trade. Selling the longer dated XBTH16 and buying the shorter dated XBTU15 allows traders to capture the interest rate differential. When XBTU15 expires, the trader will purchase the XBTZ15; after XBTZ15 expires, the trader purchases XBTH16 to close the position.

Numerical Example:

T0 days:

`Buy 1,000 contracts XBTU15 @ \$260`

`Sell 1,000 contracts XBTH16 @ \$340`

T12 days:

`XBTU15 expires at the spot price of \$250`

`XBTZ15 = \$258`

`XBTU15 Realised PNL = (\$250 - \$260) * 1,000 * 0.00001 BTC = -0.1 BTC`

`Buy 1,000 XBTZ15 contracts @ \$258 (this replaces the long XBTU15 position)`

T30 days:

`XBTZ15 expires at the spot price of \$250`

`XBTH16 = \$310`

`XBTZ15 Realised PNL = (\$250 - \$258) * 1,000 * 0.00001 BTC = -0.08 BTC`

`Buy 1,000 XBTH16 contracts @ \$310 (this closes out the XBTH16 position)`

`XBTH16 Realised PNL = (\$310 - \$340) * -1,000 * 0.00001 BTC = 0.3 BTC`

Total PNL:

`-0.1 BTC from XBTU15`

`-0.08 BTC from XBTZ15`

`+0.3 BTC from XBTH16`

`Total Profit = 0.12 BTC`

As time elapsed the trader gained profited more from the fall in XBTH16’s price, than the loss experienced when XBTU15 & XBTZ15 expired. This is called positive carry, or positive Theta. The risk to this strategy is that the interest rate differential between XBTU15 & XBTZ15 or XBTZ15 & XBTH16 increases dramatically when the trader short rolls the position. The trader is short rolling, because he is short the near month contract and must buy it back, and then short the farther month contract to stay hedged against his long XBTH16.

### Backwardation Term Structure

For a Bitcoin/USD future, being in backwardation means that the USD interest rate is lower than Bitcoin’s. Or put another way, traders believe that Bitcoin will depreciate in the future vs. the USD.

`Assume there are three futures contracts:`

`Spot = \$250`

`XBTU15 (September 2015): \$240, t = 0.08`

`XBTZ15 (December 2015): \$200, t = 0.25`

`XBTH16 (March 2016): \$120, t = 0.5`

Below is a graphical representation of the downward sloping term structure: The best trading strategy for playing a downward sloping yield curve is a carry trade. Buying the longer dated XBTH16 and selling the shorter dated XBTU15 allows traders to capture the interest rate differential. When XBTU15 expires, the trader will sell the XBTZ15; after XBTZ15 expires, the trader sells XBTH16 to close the position.

Numerical Example:

T0 days:

`Sell 1,000 contracts XBTU15 @ \$240`

`Buy 1,000 contracts XBTH16 @ \$120`

T12 days:

`XBTU15 expires at the spot price of \$250`

`XBTZ15 = \$240`

`XBTU15 Realised PNL = (\$250 - \$240) * -1,000 * 0.00001 BTC = -0.1 BTC`

`Sell 1,000 XBTZ15 contracts @ \$240 (this replaces the short XBTU15 position)`

T30 days:

`XBTZ15 expires at the spot price of \$250`

`XBTH16 = \$163.33`

`XBTZ15 Realised PNL = (\$250 - \$240) * -1,000 * 0.00001 BTC = -0.1 BTC`

`Sell 1,000 XBTH16 contracts @ \$163.33 (this closes out the XBTH16 position)`

`XBTH16 Realised PNL = (\$163.33 - \$120) * 1,000 * 0.00001 BTC = 0.43 BTC`

Total PNL:

`-0.1 BTC from XBTU15`

`-0.1 BTC from XBTZ15`

`+0.43 BTC from XBTH16`

`Total Profit = 0.23 BTC`

As time elapsed the trader gained profited more from the rise in XBTH16’s price, than the loss experienced when XBTU15 & XBTZ15 expired. This is another example of positive carry or Theta. The risk to this strategy is that the interest rate differential between XBTU15 & XBTZ15 or XBTZ15 & XBTH16 decreases dramatically when the trader long rolls the position. The trader is long rolling, because he is long the near month contract and must sell it, and then buy the farther month contract to stay hedged against his short XBTH16 position.

In the Lesson 3, I will explain some basics about risk management. The terms Delta, Dollar Value of 1% (DV01), and Theta (time value) will be introduced.

# Bitcoin Futures Basis Trading: Lesson 1

Basis trading is an alternative set of trading strategies to profit from the interest rate differentials in futures contracts on the same underlying asset but with different maturities. This is the first in a series of lessons designed to provide the basic tools for traders to execute these more advanced trading strategies. These trading strategies will use the BitMEX 25x leveraged XBT series futures contracts.

## Lesson 1: Time Value of Money

Before beginning to basis trade, it is necessary to understand the basic concept of the time value of money. When the interest rate is positive, money today is worth more than money in the future.

If you borrow \$100 from the bank for one year at an interest rate of 10%, you owe the bank \$110 in one year.

`FV = Future Value`

`P = Principal`

`r = Annualised Interest Rate`

`FV = P * (1 + r) = \$100 * (1.1) = \$110`

Your friend John said he would give you \$100 in one year’s time. What is that money worth in today’s dollars assuming the interest rate is 10% per annum? If you had the \$100 today, you could earn \$10 by loaning it out. \$100 of future dollars is worth \$90.90 today.

`PV = Present Value`

`P = Principal`

`r = Annualised Interest Rate`

`PV = P / (1 + r) = \$100 / (1.1) = \$90.90`

In many university finance classes, they continuously compounded interest payments. However in the real world, you get paid interest once per day. Therefore as traders we must use simple interest.

### Continuously Compounding Interest

`FV = Future Value`

`P = Principal`

`e = Base of Natural Logarithm, approximately 2.78128`

`r = Annualised Interest Rate`

`t = Time in Years`

`FV = P * e^(r * t)`

### Simple Interest

`FV = Future Value`

`P = Principal`

`r = Annualised Interest Rate`

`t = Time in Years`

`FV = P * (1 + r * t)`

Let’s put this in context with a futures contract on apples. You want to buy one apple in a year’s time. The future price of apples is \$110 and the current cost to buy and apple right now is \$100, what is the cost of money? Remember that when you buy a futures contract you essentially borrow money to purchase an asset today you that will receive in the future.

`FV = \$110`

`PV = \$100`

`t = 1`

`r = (FV / PV - 1) / t = (\$110 / \$100 - 1) / 1 = 10%`

If you borrowed \$110 at 10% for one year and bought an apple today, it would be the same as if you bought an apple future for delivery in one year at \$110.

Let’s extend this to BitMEX 25x leveraged XBT futures contracts.

`Basis (B) = Future Price (F) - Spot Price (S)`

The above calculation expresses Basis as a nominal value. For example, if the futures price is \$250 and the spot price is \$230, basis is \$20. Basis trading is all about comparing futures contracts with different maturities. To do that we convert basis into an annual percentage difference.

XBTZ15 December 2015 has 90 days until expiry, or 0.25 years.

`F = \$250`

`S = \$230`

`t = 0.25 years`

`B = (\$250 / \$230 - 1) / 0.25 = 34.78% annualised`

XBTH16 March 2016 has 180 days until expiry, or 0.5 years.

`F = \$275`

`S = \$230`

`t = 0.5 years`

`B = (\$275 / \$230 - 1) / 0.5 = 39.13% annualised`

XBTH16 is more expensive than XBTZ15. This is because the annualised basis is higher. When evaluating the richness or cheapness of futures contracts, calculate the annualised basis and then compare.

In Lesson 2, I will explain the basis term structure and how to trade it.