# Chapter 20

INVESTORS AND MARKETS : Bonds

A debt security is a financial instrument representing the borrower's obligation to the lender from whom he has received funds. This obligation provides for a schedule of financial flows defining the terms of repayment of the funds and the lender's remuneration in the interval.

The price of a bond does not reflect its actual cost. The yield to maturity (which cancels out the bond's NPV – that is the difference between the issue price and the present value of future flows) is the only criterion allowing investors to evaluate the various investment opportunities (according to risk and length of investment). On the secondary market, the yield to maturity is merely an opportunity cost for the issuer, i.e. the cost of re-funding today.

The basic parameters for bonds are as follows:

- Nominal or face value.
- Issue price, with a possible premium on the nominal value.
- Redemption: redemption at maturity (known as a bullet repayment), constant amortisation or fixed instalments. The terms of the issue may also include provisions for early redemption (call options) or retraction (put options).
- Average life of bond: where the bond is redeemed in several instalments, the average life of the bond corresponds to the average of each of the repayment periods.
- Nominal rate: also known as the coupon rate and used to calculate interest payable.
- Issue/redemption premium/discount: the difference between the issue premium/ discount and the nominal value and the difference between the redemption premium/discount and the nominal value.
- Periodic coupon payments: frequency at which coupon payments are made. We talk of zero-coupon bonds when total compounded interest earned is paid only upon redemption.

The diversity of these parameters explains why the yield to maturity may differ from the coupon rate.

Fixed-rate debt securities are exposed to the risk of interest rate fluctuations: the value of a fixed-rate debt security increases when interest rates fall, and vice versa. This fluctuation is measured by:

- the modified duration, which measures the percentage change in the price of a bond for a small change in interest rates. Modified duration is a function of the maturity date, the nominal rate and the market rate;
- convexity, the second derivative of price with respect to interest rates, which expresses the speed of appreciation or the sluggishness of depreciation in the price of the bond if interest rates decline or rise;
- coupon reinvestment risk. There is a time period over which the portfolio is said to be immunised, i.e. it is protected against the risk of fluctuations in interest rates (capital risk and coupon reinvestment risk). This period is known as the duration of the bond, and is equal to the ratio of the discounted cash flows weighted by the number of years to maturity and the present value of the debt.

Floating-rate securities have a coupon that is not fixed but indexed to an observable market rate (with a fixed margin that is added to the variable rate when the coupon is calculated). Variable-rate bonds are not very volatile securities, even though their value is not always exactly 100% of the nominal.

All debt securities are exposed to default risk which is assessed by rating agencies on the basis of ratings (AAA, AA, A, BBB, etc.) which depend on the volatility of the economic assets and the financial structure of the issuer. The result is a spread which is the difference between the bond's yield to maturity and that of a no-risk loan over an identical period. Obviously, the better the perceived solvency of the issuer, the lower the spread.