Euro BUND Future CTD Bond

Question

I'm trying to understand valuation of the Euro BUND Future.

As to my understanding, the price of the future should be:

• The price of a government bond issued by the Federal Republic of Germany
• That bond must have a maturity date between 8.5 and 10.5 years from expiration of the futures contract
• The bond must have an issue volume of at least 5 billion EUR
• The price is converted by a conversion factor. That factor depends on the coupon. The conversion factor crosses 1 at a coupon of 6%.

Now, the current price of the September contract of the Euro BUND future (FGBLU19) is (at the time of writing) 172.35 EUR.

Now I looked up bonds that meet the criteria, and found: ISIN DE0001135143 (in German, it's tricky getting quotes for German bonds in English).

Now to my checklist: - Maturity date is January 4th, 2030. From September 6th, 2019 (Futures contract expires) that's less than 10.5 years and clearly more than 8.5 years. - Issued by Federal Republic of Germany, checks out - Issue volume more than 9 billion, fine - Coupon is 6.25%, that's even more than 6%. Conversion factor should be even better than the 1 I'm assuming (it should be 1 at 6%)

Now the current price (as of writing) of this bond is 170.59%.

Even without the conversion factor (which should make things even better), that looks to me like an arbitrage of 1.75% (when selling a futures contract and buying the bond, holding till September).

Finding that big of an arbitrage so easily makes me skeptical, so I'm assuming I'm overlooking something. What is it?

Answer 1

Sometimes it helps writing it down, I think I figured it out:

• I forgot the interest between September and January
• At 6.25%, that's around 2.1% for four months
• That roughly matches the discrepancy I've noticed, with the conversion factor that could very well check out

So, problem solved, I guess.