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.

Futures Position | Basis | Theta |

Long | Positive | Negative |

Short | Positive | Positive |

Long | Negative | Positive |

Short | Negative | 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.

Symbol | Contracts | Spot Price | Days | t | Multiplier | % Basis | Futures Price | Basis | BTC Delta | BTC Theta | BV01 |

XBTZ15 | 100,000 | $100 | 30 | 0.25 | 0.00001 BTC | 100% | $125 | $25 | 100 BTC | -0.83 BTC | 0.25 BTC |

XBTH16 | -100,000 | $100 | 180 | 0.5 | 0.00001 BTC | 200% | $200 | $100 | -100 BTC | 0.56 BTC | -0.50 BTC |

Total | 0 BTC | -0.28 BTC | -0.25 BTC |

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.

The below is a table shows the Daily Curve PNL depending on changes in the % basis differential.

XBTH16 | ||||||

XBTZ15 | % Basis Change | -2% | -1% | 0% | 1% | 2% |

-2% | 0.22 BTC | -0.28 BTC | -0.78 BTC | -1.28 BTC | -1.78 BTC | |

-1% | 0.47 BTC | -0.03 BTC | -0.53 BTC | -1.03 BTC | -1.53 BTC | |

0% | 0.72 BTC | 0.22 BTC | -0.28 BTC | -0.78 BTC | -1.28 BTC | |

1% | 0.97 BTC | 0.47 BTC | -0.03 BTC | -0.53 BTC | -1.03 BTC | |

2% | 1.22 BTC | 0.72 BTC | 0.22 BTC | -0.28 BTC | -0.78 BTC |

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 Bitocin futures contracts, there are many more opportunities to earn above average risk adjusted profits.