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.