## Analysis of Bond Futures

The following example demonstrates analyzing German Euro-Bund futures traded on Eurex.
However, `convfactor`

, `bndfutprice`

, and
`bndfutimprepo`

apply to bond futures in the U.S., U.K., Germany,
and Japan. The workflow for this analysis is:

Calculate bond conversion factors.

Calculate implied repo rates to find the CTD bond.

Price the bond future using the term implied repo rate.

### Calculating Bond Conversion Factors

Use conversion factors to normalize the price of a particular bond for delivery in
a futures contract. When using conversion factors, the assumption is that a bond for
delivery has a 6% coupon. Use `convfactor`

to calculate
conversion factors for all bond futures from the U.S., Germany, Japan, and
U.K.

For example, conversion factors for Euro-Bund futures on Eurex are listed at `www.eurexchange.com`

. The delivery date for Euro-Bund
futures is the 10th day of the month, as opposed to bond futures in the U.S., where
the short position has the option of choosing when to deliver the bond.

For the 4% bond, compute the conversion factor with:

CF1 = convfactor('10-Sep-2009','04-Jul-2018', .04,.06,3)

CF1 = 0.8659

This syntax for `convfactor`

works fine for bonds with standard
coupon periods. However, some deliverable bonds have long or short first coupon
periods. Compute the conversion factors for such bonds using the optional input
parameters `StartDate`

and `FirstCouponDate`

.
Specify all optional input arguments for `convfactor`

as
parameter/value pairs:

CF2 = convfactor(datetime(2009,9,10),datetime(2019,1,4), .0375,'Convention',3,'startdate',... datetime(2008,11,14))

CF2 = 0.8426

### Calculating Implied Repo Rates to Find the CTD Bond

To determine the availability of the cheapest bond for deliverable bonds against a
futures contract, compute the implied repo rate for each bond. The bond with the
highest repo rate is the cheapest because it has the lowest initial value, thus
yielding a higher return, provided you deliver it with the stated futures price. Use
`bndfutimprepo`

to calculate repo
rates:

% Bond Properties CouponRate = [.0425;.0375;.035]; Maturity = [datenum('04-Jul-2018');datenum('04-Jan-2019');datenum('04-Jul-2019')]; CF = [0.882668;0.842556;0.818193]; Price = [105.00;100.89;98.69]; % Futures Properties FutSettle = '09-Jun-2009'; FutPrice = 118.54; Delivery = '10-Sep-2009'; % Note that the default for BNDFUTIMPREPO is for the bonds to be % semi-annual with a day count basis of 0. Since these are German % bonds, we need to have a Basis of 8 and a Period of 1 ImpRepo = bndfutimprepo(Price, FutPrice, FutSettle, Delivery, CF, ... CouponRate, Maturity,'Basis',8,'Period',1)

ImpRepo = 0.0261 -0.0022 -0.0315

### Pricing Bond Futures Using the Term Implied Repo Rate

Use `bndfutprice`

to perform price
calculations for all bond futures from the U.S., Germany, Japan, and U.K. To price
the bond, given a term repo rate:

% Assume a term repo rate of .0091; RepoRate = .0091; [FutPrice,AccrInt] = bndfutprice(RepoRate, Price(1), FutSettle,... Delivery, CF(1), CouponRate(1), Maturity(1),... 'Basis',8,'Period',1)

FutPrice = 118.0126 AccrInt = 0.7918

## See Also

`convfactor`

| `bndfutprice`

| `bndfutimprepo`

| `tfutbyprice`

| `tfutbyyield`

| `tfutimprepo`

| `tfutpricebyrepo`

| `tfutyieldbyrepo`

| `bnddurp`

| `bnddury`

## Related Examples

- Managing Present Value with Bond Futures
- Fitting the Diebold Li Model
- Managing Interest-Rate Risk with Bond Futures