Based on BitMEX Blog Materials
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.
Lesson 2:
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.
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.
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.
In the third and final lesson, I will explain some basic risk management policies relating to basis trading. First I will explain the risk management metrics Delta, Bitcoin Value of 1% (BV01), and Theta. For each of these metrics, I will always present them in Bitcoin terms.
Delta
The performance of a Bitcoin futures contract is made up of three components, spot, interest rates, and time. The delta of a portfolio of Bitcoin futures contracts refers to the portfolio’s exposure to the movements in the spot price.
Delta = Spot Price * BTC Multiplier * Contracts
For example a the December 2015 25x leverage Bitcoin / USD futures contract (XBTZ15), settles on the TradeBlock XBX Index price. The current value of the XBX Index price is the spot price for XBTZ15.
Assume the following:
Spot = $250
BTC Multiplier = 0.00001
Contracts = 100,000
XBTZ15 Delta = $250 * 0.00001 BTC * 100,000 Contracts = 250 BTC
Because the portfolio is long, if the spot price moves up 1%, the profit is 2.5 BTC. If the spot price moves down 1%, the portfolio loses 2.5 BTC.
Delta PNL (Profit and Loss) = % Change in Spot * Delta
Notice that we use the spot price not the current price of the futures contract to calculate delta. The basis or difference between the spot and futures price is expressed through the BV01 and Theta metrics.
Bitcoin Value of 1% (BV01)
The BV01 refers to the amount that will be made or lost if the interest rate changes by 1%.
t = Days to Expiry / 360
% Basis = (Futures Price / Spot Price – 1) / t
BV01 = 1% * t * Spot Price * BTC Multiplier * Contracts
Assume the following:
Spot = $250
BTC Multiplier = 0.00001
Contracts = 100,000
t = 0.5
BV01 = 1% * 0.5 * $250 * 0.00001 BTC * 100,000 = 1.25 BTC
If the % basis rises by 10% in annualised terms:
BV0L PNL = 10 * 1.25 BTC = 12.5 BTC
Theta
Theta is the amount of money that a portfolio will gain or lose as time passes. Because a futures contract will equal the spot price at settlement, each day the basis between the future and spot price will get smaller.
Basis = Future Price - Spot Price
Depending on whether the basis is positive or negative a long or short futures position will have a positive or negative Theta. When calculating Theta multiply the result by -1 to get the correct result. Below is a table summarising in which situations Theta is positive or negative.
Theta = (Basis / Days Until Expiry) * BTC Multiplier * Contracts * -1
Assume the following:
Spot = $250
XBTH16 = $300
BTC Multiplier = 0.00001
Contracts = 100,000
Days = 180
Basis = $300 - $250 = $50
Theta = ($50 / 180 Days) * 0.00001 BTC * 100,000 * -1 = -0.28 BTC
Putting It All Together
Let’s construct a sample portfolio and examine the interplay between Delta, BV01, and Theta. The futures term structure is in contango and a trader wants to earn the carry between the December 2015 and March 2016 futures contracts.
To properly evaluate whether this is a good trade or not, let’s consider a few scenarios.
Scenario 1:
XBTZ15 is held until maturity, and the % basis does not change.
The portfolio will lose money due to the negative Theta.
30 days * -0.28 BTC Theta = 8.4 BTC loss
Scenario 2:
XBTZ15 is held until maturity, and a parallel shift in the % basis.
The % basis will need to parallel shift downwards by 33.60% for the portfolio to break even due to the Theta loss.
8.4 BTC / 0.25 BTC BV01 = 33.60% change in interest rates
If the % basis parallel shifted upwards, the portfolio would lose money both on the Theta and the BV01.
Scenario 3:
The term structure changes and you intend to exit the position before XBTZ15 expires.
Daily Curve PNL = Portfolio Theta + XBTH16 BV01 PNL + XBTZ15 BV01 PNL
If the % basis differential widens (a curve steepener) in any magnitude, you have an unrealised loss from BV01 and Theta. If the % basis differential narrows (a curve flattener), you have an unrealised gain if the BV01 profit is greater than the daily Theta loss.
Basis trading is a bit more complicated than out right position trading. However, due to the lack of understanding by many Bitcoin traders about the interplay between time and interest rates as it applies to Bitcoin futures contracts, there are many more opportunities to earn above average risk adjusted profits.
Start Trading Bitcoin Futures on BitMEX
Use the following link to open the BitMEX account:
https://www.bitmex.com/register/Q1nfNX
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