Bonds: Lending, and everything that comes with it

A bond is a loan. You lend money to a state or a company. In exchange, a promise.

The promise has two parts: regular interest, and repayment on a date set in advance.

This interest is called the coupon. Say a bond of one thousand euros, at three per cent, over ten years.

Every year, thirty euros of coupon. After ten years, your thousand euros come back. As long as the borrower keeps its promise.

But in the meantime, the bond trades on a market. And its price moves, because of one thing: rates.

If tomorrow new bonds pay four per cent, who will want yours at three? Nobody, at the same price.

Its price falls, until it pays as much as the new ones. Rates go up, prices go down.

By how much? That is what duration measures. Here, it is about eight and a half.

That means: if rates rise by one point, the price falls by about eight and a half per cent. Eighty-five euros.

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The longer a bond, the bigger its duration. And the more its price shakes when rates move.

The exact calculation gives a little less: nine hundred and eighteen euros. A fall of only eight point one per cent.

And if rates fall by one point, the price rises by almost nine per cent. More than duration says.

This gap is called convexity. Duration draws a straight line. Reality follows a curve, rather in the holder's favour.

Now the families. First, high yield. In English, it is also called junk.

These are companies rated fragile by the rating agencies. To lend to them, you demand a higher coupon.

For the example, say seven per cent promised. If four issuers in a hundred default each year, and you recover forty per cent…

… the loss swallows about two point four points. Four point six per cent is left. High yield is mostly the price of risk.

Next, the convertible: a bond with an option attached. You can exchange it for shares in the company.

If the share soars, you convert. Otherwise, you keep the bond. In exchange for this choice, the coupon is lower.

There is also the perpetual bond: the capital is never repaid. Only the coupons fall, forever.

The United Kingdom issued them as early as the eighteenth century. The last ones were only repaid in two thousand fifteen.

Its price is very sensitive to rates. Thirty euros a year are worth one thousand euros at three per cent. Seven hundred and fifty at four per cent.

Finally, the inflation-linked bond. Its capital follows rising prices. What it guarantees is a real return.

One thousand euros at one per cent real. Inflation is five per cent: capital rises to one thousand and fifty, the coupon to ten euros fifty.

Coupon, duration, convexity, and a family for every need. A bond is never risk-free. It just has different risks from a share.