# FAQs

How do you find the indexation coefficient of an index-linked OAT?
The indexation coefficient calculated by the Agence France Trésor is available on its website. The coefficient will vary depending on the individual index-linked OAT and on the day. For each OATi or OAT€i, the indexation coefficient represents the cumulative inflation since the settlement date when the OATi was first issued.

Suppose a OATi is issued on 1 January 2000 and inflation has since remained constant at a rate of 1.8% per year. The index ratio on 1 January 2005 will be (1 + 0.018)5 = 1.09330.

A concrete example:  What was the value of the last coupon paid by an OATi paying 3% with a maturity date of July 25, 2009?  On July 25, 2005, the indexation coefficient for this OATi was 1.10984.  An investor who owned 10,000 OATs at a par value of €1 on 25 July 2005, received a coupon for:  3% x 10 000 x 1.10984 = €332.95

What is the yield curve?
As a creditor, a bondholder requires a return on his investment. The amount of the return will vary depending on the length of the bondholder's commitment and any changes in interest rates. This variability creates a hierarchy of rates based on maturities. This hierarchy is called the yield curve.

Investors demand higher rates for tying up their money for a longer period. This  phenomenon is reinforced if they are expecting a rise in interest rates which would diminish the value of the money they have invested. This explains why the yield curve is usually "sloping," (i.e. ascending) in line with maturities.  However, when investors anticipate a fall in future interest rates, the yield curve may invert and result short-term rates that are higher than long-term rates.

What is an actuarial rate?
The actuarial rate of a bond enables an investor to calculate the price of a bond today, knowing its redemption value, the rate at which coupons will be reinvested and its maturity.

The actuarial rate is the only reference tool that allows investors to compare bonds with one another at any given moment.

The actuarial rate after the payment of an installment due is calculated as follows:

where L = the bond’s list price

Coupon = the coupon paid annually
r = the actuarial rate
n = the bond’s repayment date (maturity)

A concrete example: An OAT paying 4% interest with an April 2009 maturity was worth 104.95% on the secondary market on 25 April 2005.

The actuarial rate (r) on April 25, 2005 after detaching the coupon can be determined using the following equation:

4 4 4 4 100
= 104.95 + -------- --------- + --------- + --------- + ------- -
(1 + r) (1 + r)2    (1 + r)3    (1 + r)4    (1 + r)4

Which gives: r = 2.68%

One can see that over the period of initial capital investment, the greater the effect of "snowball" related to the composition of interest will be. This theoretical calculation is made assuming that coupons are reinvested each intermediate year initial interest rate.

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