4. Duration: how a safe bond loses two thirds

Macro 1: The price of money

This level closes with the concept that turns everything above into a number you can work out in your head. If you understand duration, you can estimate in five seconds how far a bond will fall when rates rise, and you will understand why in 2023 an entire bank went under without a single one of its bonds missing a payment.

A bond is not a safe product: its payments are fixed and its value is not

When you buy a bond, you lend money in exchange for a series of agreed payments. Those payments never change. What does change constantly is what others are willing to pay you today for the right to receive them.

The mechanism is crushingly logical: if you bought a bond paying 2% and identical bonds paying 5% are issued the next day, nobody will buy yours at the same price. They will only buy it if you let it go cheaply enough that, at that knock-down price, they too earn 5% to maturity. The price of the bond falls until its yield matches the market's. Price and yield always move in opposite directions, and not by convention but by arithmetic.

The interesting question is not whether it falls, but by how much. That is where duration comes in.

What duration is, without heavy formulas

Duration is, intuitively, the average waiting time for your money, weighting each payment by its share of the total. A bond that returns almost everything at the end has a duration close to its maturity; one paying high coupons along the way has a shorter duration, because you get part of it back sooner.

Its practical use is this rule, which is worth memorizing:

• Approximate fall in price ≈ duration × rise in the rate (in percentage points).

With examples:

• A bond with duration 2 and rates rising 1 point: it falls roughly 2%. You barely notice.
• A bond with duration 8 and rates rising 1 point: it falls roughly 8%.
• A 30-year bond with a low coupon has a duration of around 22. Rates rise 1 point and you lose around 22% on an asset that was sold to you as conservative.

Two qualifications to hold on to:

• The lower the coupon, the longer the duration. If the bond pays almost nothing along the way, all your money sits at the end, and is therefore maximally exposed. The bonds issued in the zero-rate era were, by construction, the most fragile ever issued.
• The relationship is not exactly a straight line, and that deviation is called convexity. It works in your favor: the price rises when rates fall are somewhat larger than the falls when rates rise by the same amount. But it is a second-order correction; it will not save you from a big move.

Austria at a hundred years: the extreme case

In 2020, with rates on the floor, Austria issued a bond maturing in 2120, that is, at a hundred years, with a coupon below 1%. It was placed without difficulty: investors needed yield and this offered something more than zero.

A bond like that has an enormous duration, of the order of 65 to 70. At these maturities the linear rule overstates the effect, because convexity is enormous: redoing the exact calculation, a one-point rise in rates takes away around 45% of the price. And between 2020 and the end of 2022 European rates did not rise by one point: they rose a good deal more. The bond went on to lose around two thirds of its value.

The important thing about the case: Austria never missed a single payment. That bond was, in the technical sense of module 1, practically free of default risk. And it still ruined anyone who had to sell. The risk was not in the issuer; it was in the duration.

Silicon Valley Bank: when duration brings down a bank

March 2023. Silicon Valley Bank held a mountain of deposits from technology companies and had invested them in long-dated US government debt and mortgage-backed securities, bought when rates were at zero. United States government debt: zero default risk.

As rates rose 425 basis points, that portfolio piled up enormous unrealized losses. In the accounts they did not appear, because a portfolio classified as 'held to maturity' is not marked to market: if you hold on to the end, you are paid what was agreed and the loss never materializes.

The problem is that a bank does not control whether it can hold on to the end. Its depositors began pulling money out, and to repay them those bonds had to be sold before maturity, turning the unrealized loss into a real one. Once the hole became known, the withdrawals accelerated: around 42 billion dollars left in a single day. The bank did not survive the weekend.

Not one of those bonds missed a payment. The collapse was caused by the combination of long duration with liabilities that could be demanded overnight.

What you take away from this level

• The interest rate is the price of time, and it is the bar that any investment has to clear.
• Discounting is dividing by (1+rate) raised to the years; the further away the money sits, the harder a rise punishes it.
• Nominal figures deceive: inflation erodes, and on top of that you pay tax on the part inflation takes.
• Duration tells you, with a single multiplication, how much you will lose if rates rise.
• 'Safe' and 'free of default risk' are not synonyms: Austria always paid, and its bonds lost two thirds.