## What is the Hedge Ratio?

Following the correlation analysis, which determines whether the futures contract is at all suitable for hedging the cash position, the number of required futures contracts (the hedge ratio) must be determined.The following factors generally play a role:

- Size of cash position
- Futures contract size
- Price sensitivity of the cash position
- Price sensitivity of the futures contract

Hedge Ratio = Number of futures used

If one ignores the potential various, strong price fluctuations between future and cash, the hedge-ratio calculation is simple.

### Examples of simple hedge ratios:

Hedge ratio | = | Nominal value (bonds) |

Nominal contract value (future) |

With a nominal hedge, the nominal value of the portfolio´s bonds is divided by the contract size of the futures contract selected previously. Euro Schatz, Euro Bobl or Euro Bund Futures will be used, depending on the bonds´ average maturity or correlation analysis.
A more detailed analysis of the different price sensitivity of the bonds to be hedged and the futures contract is not carried out.

Advantages: easy to calculate

Disadvantage: not precise, especially given larger portfolios

Hedge ratio | = | EUR 1,000,000 | = | 10,000 Kontrakte |

EUR 100,000 |

Ten futures contracts are sold for a short hedge. Ten futures contracts are bought for a long hedge.

Hedge Ratio | = | Value of the equity portfolio |

Index level* x Index multiplier |

A simple hedge places the value of the equity portfolio in relation to the value of a futures contract.

*Index per equity portfolio, or established correlation of the portfolio.

Example:

Value of the equity portfolio (DAX shares): | EUR 2,100,000 |

DAX index level: | 6,000 |

DAX Future index multiplier: | EUR 25 |

Hedge ratio | = | EUR 2,100,000 | = | 14 ontrakte |

6,000 x 25 |

### Adjusted hedge ratio:

Hedgeratio | = | Market value_{Bonds} x CF_{CTD} |
x | MD_{Bonds} |

price_{CTD} x 1,000 |
MD_{CTD} |

CTD | = | Cheapest to deliver |

CF | = | Conversion factor |

MD | = | Modified Duration |

Mathematical indicators that estimate bond price sensitivity when changes in market interest rates occur are used to calculate the different price sensitivities of the bonds to be hedged, and the price sensitivity of futures contract (Modified Duration).

The price sensitivity of the bonds or equity portfolio to be hedged (MD bonds) is compared to the price sensitivity of the CTD, using the Modified Duration as an indicator.

Example:

MD_{Bonds} |
= | 7.5 | = | 1.07 |

MD_{CTD} |
7 |

As the bonds in the portfolio are much more sensitive to price changes compared to the CTD bonds, 1.07 futures contracts per EUR 100,000 nominal value of the portfolio must be traded, to hedge the portfolio.

Hedge ratio | = | Value of the equity portfolio x Portfolio beta |

Index level x Index multiplier |

The individual risk of the equity portfolio is taken into account by including the portfolio beta in a beta hedge. The portfolio beta calculates the extent to which the equity portfolio reacts more strongly (or more weakly) to the general price fluctuations of the index to which it is compared.

Please refer to the following pages for detailed information on the portfolio beta and beta hedge.