What Waiting Costs

Would you rather have $100 today, or $100 in ten years? Almost nobody hes­i­tates. The more inter­est­ing ques­tion is how much less than $100 you would accept today instead of waiting, because the answer is a price, and it sits inside nearly every other price in this issue.

There are three reasons to prefer money now. You might want to spend it now. Prices might rise in the mean­time, so $100 later buys less. And a promise to pay later might not be kept. Put numbers on those three reasons and you have an inter­est rate: the price of time.

Discounting, without the jargon

If you could lend money safely at 4% a year, $100 in ten years is worth what you would need to lend today to end up with $100: $67.56. At 2% it is worth $82.03. At 8% it is worth $46.32. The future payment has not changed. Its value today has, because the price of time has.

That cal­cu­la­tion is called dis­count­ing, and the value it pro­duces is called present value. The rate used starts from some­thing close to risk­less, con­ven­tion­ally the yield on gov­ern­ment debt of the right matu­rity, and adds a premium for what­ever makes the par­tic­u­lar payment less certain.

Why dis­tance matters

The further away a payment is, the more its value today depends on the rate. A payment of $100 due in one year is worth $96.15 at 4% and $95.24 at 5%: a dif­fer­ence of less than one per cent. A payment of $100 due in thirty years is worth $30.83 at 4% and $23.14 at 5%, a fall of 25%. One per­cent­age point, applied over thirty years, takes a quarter off the value.

Bond traders call that sen­si­tiv­ity dura­tion. It explains why long-dated bonds lose more than short ones when rates rise. It also explains some­thing that seems unre­lated: why the prices of com­pa­nies whose profits are mostly expected far in the future, young tech­nol­ogy firms for instance, tend to fall harder when rates rise than com­pa­nies earning steady cash today.

The same clock, in other markets

Property is valued by dis­count­ing rents. When the rates investors demand rise, the value of the same build­ing with the same tenants falls, even though nothing about the build­ing has changed. A pension promise is a stream of future pay­ments, and the amount a fund must hold to meet it depends on the rate used to dis­count them, which is why pension deficits can swing by large sums with no change in the number of pen­sion­ers.

Assets that pay nothing are affected by the same clock from the other side. Gold pays no inter­est, so holding it means giving up what­ever inter­est the money could have earned. When safe rates are high, that sac­ri­fice is larger. The same logic applies, con­tested and loosely, to bitcoin.

A price of time you can watch

Crypto markets built an unusu­ally visible price of time. A per­pet­ual future is a con­tract with no expiry that is meant to track the spot price. To keep it close, the exchange makes one side pay the other every few hours: when the per­pet­ual trades above the index, holders of long posi­tions pay holders of short posi­tions, and the reverse when it trades below. That payment is called the funding rate.

In effect it is an inter­est rate on bor­rowed expo­sure, set by the market every few hours, and it is pub­lished openly. When many traders want lever­aged long posi­tions, funding rises and the price of bor­row­ing bitcoin expo­sure goes up. When the enthu­si­asm fades, it falls and can turn neg­a­tive. A cash-and-carry trader who buys spot and sells the per­pet­ual col­lects it, which pulls it back toward the cost of money else­where.

It is the same mech­a­nism as a bank deposit rate or a Treasury yield, com­pressed into hours and stripped of most of its insti­tu­tions. Central banks do not hand down the price of time on their own. Wherever someone wants some­thing now and someone else can wait, a rate appears.

The restraint

This is the point where arti­cles about inter­est rates usually over­reach, and it is worth being careful. Rates are an input to almost every price. They do not cause every price move­ment. Plenty of assets have risen while rates rose and fallen while they fell, because the other inputs, expected cash flows, risk, supply and demand for the asset itself, moved more. A central bank sets one short-term rate. Markets set the rest, and the pre­mi­ums added on top of them move for reasons of their own.

What can be said without over­reach­ing is this. Any price that describes a claim on the future con­tains a rate, whether the screen shows it or not. When the rate changes and nothing else does, the price must change. Most of the time plenty of other things change as well.

One prac­ti­cal habit follows. When a price moves, before explain­ing it with a story about the asset, check what hap­pened to the price of time on the same day. If long-dated rates jumped, a good part of the move in any­thing whose value lies far in the future may simply be the clock being re-set. If rates were still, the story has to come from some­where else.

Two iden­ti­cal claims to $100, one due today and one due in 2036. Put them side by side, and the gap between them is the price of ten years.