A zero-coupon bond is a special kind of bond. Normally, the
holder of a bond has two rights: the right to be periodically paid
interest and the right to be paid back the amount of money borrowed, the
principal. These interest payments are called coupons. The
historical reason for this is that on paper bonds,
these coupons where physical pieces of paper that would have to be cut off
and turned in to collect the interest

A zero-coupon bond is different in that it does not pay a

periodic
interest. The interest is in fact all paid at the

maturity of the bond,
together with the principal. For a one-year bond with a time to maturity of
1 year, an interest percentage of 5% and "principal" of 100

euro, we hence
receive 105 euros at the end. One important thing to remember here is that
it is common that zero-coupon bonds have a "round" final payoff; hence, it
is more probable that we would have a payoff of 100 euros, and need to pay
95.24 for this

bond.

For longer-dated bonds, the initial payment *I* depends as follows
on the final payout:

*I=M/(1+r)*^{t}

with *M* the value of the bond at maturity, *r* the interest
rate percentage, and *t* the time to maturity. As an example, consider
a bond with a time to maturity of 15 years, an interest rate of 7% (or
0.07), and a value at maturity of 1000 euro. For this, we would need to pay
362 euro initially.

Zero-coupon bonds are used for three main reasons: as an aid in doing
calculations, for short-dated bonds, and for very long-dated bonds. Below,
these three uses will be briefly discussed.

Conceptually, zero-coupon bonds are the fundamental building block of
bond mathematics. Any future payment can be seen as a zero-coupon bond and
hence be discounted to its present value. In particular, a "normal" bond
consists of a strip of small zero-coupon bonds (the coupon payments) and one
big zero-coupon bond (the principal). Note that it is entirely possible for
the present value of the principal to be smaller than that of a coupon,
especially if the bond has a very long time to maturity and/or the interest
rate is high.

Short-dated government bonds (for instance T-bills) are often zero-coupon
bonds. Having just one simple payment to track makes things considerably
easier. Furthermore, time deposits in which the interest is automatically
reinvested in the deposit are also a form of zero-coupon bond

Very long-dated bonds also may be zero-coupon bonds. The reason for this
is that in a normal bond, the present value of the coupons would be high
compared to the present value of the principal. This would mean that the
effective duration of the bond isn't very long at all, as the investor
already gets most of his investment out in a decade or so. To avoid this,
extremely long-dated zero-coupon bonds are used; these have only one
payment, at the end, avoiding this problem.

In terms of risk, short-dated zero-coupon government
bonds are about the most riskless in existence. Longer dated zero-coupon
bonds can be very risky, though. The reason is that the effective duration
is so long. If a company were to issue a normal bond and it were to
default on it, the investor would still have received the accrued interest
up to that point, which could be substantial, especially given the fact that
companies often have to pay (a lot) more interest than a government due to
the fact they may default. However, for a zero-coupon bond, this isn't the
case - it is either all or nothing.

Zero-coupon bonds, in summary, are bonds in which the accrued interest
and principal are all paid back together at maturity. This single payment
structure makes them easy to do math on. Hence, they are
an important theoretical concept in finance. The single payback also means
that the time to maturity is very well-defined, and this means they can be
used to get exactly the bond duration an investor wants