# How to compute interest rate futures spread ratio?

I am confused on how to compute the spread ratio.

For example, this is example I came across with my broker -

Consider 2 contracts Bobl and Euribor.

The DV01 of Bobl i 44.8 and Euribor is 25. To equalize DV01, we need 44.8/25=1.792 contracts of Euribor for every 1 contract of Bobl. However, tick sizes are different. 1 Bobl Tick is 10 Euros and similar Euribor tick is 25. So the ratio will be for 1 Bobl we need 1.79*(25/10) = 4.475 contracts of Euribor.

I understand DV01 sensitivity to compute the hedge ratio. However, I don't understand how is he using tick sizes. If he related tick sizes to basis points, it would have made more sense to me.

Does someone understand this?

DV01 is your cash exposure to a BP change. Once you have €45 and €25 as DV01s for Bobl and Euribor respectively, you simply divide the two to figure out your DV01 neutral position sizes. In my particular example buy 180 Euribors to sell 100 Bobls for no raw duration risk.

You can also choose weighing schemes that account for varying volatilities and correlations of the two rates. For example Bobl rates are currently more volatile than Euribor, hence the hedge ratio will be closer to 200 ER for 100 Bobls.

Actually the classical definition of a tick is the minimum price movement of a future (set by the exchange). This is often misrepresented semantically as most instruments have a genuine tick size of 0.01 (e.g. Bobl, Bund or Short Sterling contracts) but some do not (e.g. Euribor has 0.005 tick, Schatz has 0.005 and Buxl has 0.02). So some finance practitioners say a tick when they actually mean a cent, which is a 0.01 price deviation. Be aware of that.

Secondly with respect to your question; 1) The notional on a Bobl contract specification means that one cent (0.01) is worth 10EUR. If Bobl has a DV01 of 44.8EUR this is a movement of 4.48 cents or 4.48 ticks for each bp. 2) The notional on a Euriobor contract spec means one cent is worth 25EUR. If one contract has a DV01 of 25EUR this is a movement of 1.0 cents or 2 ticks for each bp. To get the hedge ratio of number of contracts divide 100 Bobls of 4480 DV01 by 25 to get 179 Euribor contracts.

Of course you will have a superior hedge if you trade all different contracts (to a total of 179) rather than a single contract (e.g. Sep 18). If you wanted to approximate an asset swap then you would have to trade something slightly different to a linear pro-rata of different contracts, although with current yield levels it will probably be minimally different.

Minimum price movement for Bobl is 1 basis point with a value of €10. Minimum price movement for Euribor is 0.5 basis point with a value of €12.50. This is usually called a half-tick. So a full-tick would have the value €25.

With these definitions, a tick is a basis point move for both the Bobl and the Euribor.

Tick size relates to the notional value of the contracts, so first you need to look at the equinotional hedge ratios and then adjust them by the ratio of the notional values to arrive at the relative number of contracts.

• Doesn't DV01 already account for notional value of the contract? It measures the change in the contract net value with 1 basis point change in interest rates. So why do we need tick size? It looks like we are doing the same thing twice. – Sam Hayen Sep 9 '12 at 17:15
• I am not sure what exactly the broker is telling you, but I assume that you first use something like DLV on Bloomberg to calculate dv01 for the bond futures. Could you post the exact wording from the broker document? – Strange Sep 9 '12 at 21:35