The yield curve

The interest rate that lenders require of any borrower will depend on the term of the borrowing. The yield curve depicts the various rates at which the same borrower is able to borrow for different periods of time. The most closely watched yield curve in any country is that of the national government, which is the closest approximation to a risk-free yield. Other yield curves, such as the one for corporate borrowers, are best understood in comparison with the risk-free yield. The yield curve is drawn against two axes, the vertical showing yield (expressed in percentage points) and the horizontal giving the term in years. Most of the time the yield curve is positively sloped, going from the lower left corner of the chart to the upper right. In this case, very short-term borrowings would have the lowest yield, with the yield increasing as the term lengthens. The reasons for this shape are readily understandable, as lenders and investors wish to be compensated for the greater risk that i…

Properties of bonds

Every bond, irrespective of issuer or type, has a set of basic properties.

Maturity
This is the date on which the bond issuer will have repaid all of the principal and will redeem the bond. The number of years to maturity is the term. In practice, term and maturity are often used interchangeably. Bonds with maturities of 1–5 years are usually categorised as short-term, those with maturities of 5–12 years as medium-term and those with maturities exceeding 12 years as long-term. Few bonds are issued with maturities beyond 30 years, and in many countries the longest maturity is only 10 or 20 years.

Coupon
This is the stated annual interest rate as a percentage of the price at issuance. Once a bond has been issued, its coupon never changes. Thus a bond that was issued for $1,000 and pays $60 of interest each year would be said to have a 6% coupon. Bonds are often identified by their maturity and coupon, for example, “the 6.25s of ’18”.

Current yield Current yield is the effective interest rate for a bond at its current market price. This is calculated by a simple formula:If the price has fallen since the bond was issued, the current yield will be greater than the coupon; if the price has risen, the yield will be less than the coupon. Suppose a bond was issued with a par value of €100 and a 6% coupon. Interest rates have fallen, and the bond now trades at €105.

Yield to maturity
This is the annual rate the bondholder will receive if the bond is held to maturity. Unlike current yield, yield to maturity includes the value of any capital gain or loss the bondholder will enjoy when the bond is redeemed. This is the most widely used figure for comparing returns on
different bonds.
Duration
Duration is a number expressing how quickly the investor will receive half of the total payment due over the bond’s remaining life, with an adjustment for the fact that payments in the distant future are worth less than payments due soon. This complicated concept can be grasped by looking at two extremes. A zero-coupon bond offers payments only at maturity, so its duration is precisely equal to its term.

A hypothetical ten-year bond yielding 100% annually lets the owner collect a great deal of money in the early years of ownership, so its duration is much 1shorter than its term. Most bonds fall in between. If two bonds have identical terms, the one with the higher yield will have the shorter duration, because the holder is receiving more money sooner. The duration of any bond changes from one day to the next. The actual calculation can be complicated, and can be done in several different ways. Different investors may have different views of a bond’s duration: one of the critical numbers in the calculation, the discount rate that should be used to attach a current value to future payments, is strictly a matter of opinion; and another, the amounts that will be paid at specific dates, is not always certain. Traders and investors pay close attention to duration, as it is the most basic measure of a bond’s riskiness. The longer the duration, the more the price of the bond is likely to fluctuate before maturity. Divergent estimates of duration are an important reason that investors differ about bond prices: if there is a ten-year bond with a 6% coupon and semi-annual interest payments, an investor who estimates the duration to be 7.6 years would be willing to pay a higher price than one who estimates it to be 7.7 years.

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