## What is the Impact of Returns (Income) on the Forward Price of Bonds?

Interest income reduces the forward price vis-à-vis the cash price of bonds:

Forward price = cash index + financing costs - income

Depending on whether the financing costs or the the return is higher, the forward price will be higher or lower than the cash price.

Let's assume that you know you will receive a large sum of money in six months´ time, and want to invest it in bonds.

Now, you have the choice of either buying the bonds today with a nominal value of EUR 100,000 at a price of 100 percent, or buying them for forward delivery (on the futures market, for example).

If bought immediately, you will have to pay short-term assumed financing costs of 4 percent p.a.. However, over the next six months you are also entitled to the interest accrued (coupon) on the long-term bond of, say, 6 percent p.a. The assumed, high interest rate is for illustrative purposes only and can severely differentiate from the actual market interest rate.

### Calculation

 Cash index 100%: EUR 100,000 Financing rate 4% p.a.: EUR 2,000 Accrued interest (return) 6% p.a.: EUR 3,000 Costs: EUR 99.000

Forward price: EUR 99,000 bzw. 99.00%

In order to calculate the price for fixed income futures on Eurex Exchange (for instance Euro Bund futures), additional conversion factors of the bonds need to be considered. The theoretical price of a future is a forward rate of the cheapest to deliver (CTD) divided by the conversion factor. Assuming the forward rate of the CTD currently is at 105,804 and the conversion factor 0.765589, a price of 138,20 is calculated for the Euro Bund future.

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