Interest rates as the master price

Trace a rate change through discount rates, asset prices, and real activity, and say which channel bites first.

In 2022 the Federal Reserve moved its target range from 0 to 0.25% in March to 4.25 to 4.5% in December. Over that same year the Bloomberg US Aggregate Index lost about 13%, the worst calendar year in its history, and Treasury bonds maturing in twenty years or more lost roughly a third of their value. Nothing about those bonds changed. The government that issued them was as good for the money in December as it had been in March, and every arrived on schedule. One number moved, and it repriced everything.

Why one rate sets every other price

An interest rate is the exchange rate between money now and money later. That is the whole idea, and everything else in this lesson is arithmetic performed on it.

The of a dollar arriving in year n is 1 / (1 + r)^n. Look at where r sits in that expression. It is inside a power. Change it a little and a dollar arriving next year barely moves, because the exponent is 1. Change it by the same amount and a dollar arriving in year 30 moves a great deal, because the small change has been compounded thirty times.

That single line explains the 2022 table. It explains why an unprofitable software company can fall 70% in a year when nothing about its product changed. And it explains why a savings account, a two year bond, a thirty year bond, and a growth stock respond to identical news with wildly different magnitudes. They hold cash at different distances.

Move the rate and watch

Four assets, one slider. Every number below comes from discounting the actual cash each one pays.

Risk-free rate4.50%

Starting from 4.5%

Cash in a deposit account0.0%
All of it available today
2 year government bond0.0%
Almost all of it back within two years · about 1.9% per point
30 year government bond0.0%
The principal arrives in 2056 · about 16.3% per point
A company growing at 3.5% forever0.0%
Most of the value is cash flow after 2040 · about 18.2% per point

Push the rate down toward zero and the ordering holds, running the other way. Push it far enough and the growth company stops having a finite value at all, which is the model telling you it has left the range where it means anything.

Worked example

One point, four assets

Start at 4.5% and raise the rate to 5.5%. That is one point, the sort of move a central bank can deliver in two meetings.

Cash. No change. It is already here, so there is nothing to discount.
Two year bond. Down 1.85%. Almost all of the money comes back inside two years, and you reinvest it at the new higher rate soon enough that the loss is small.
Thirty year bond. Down 14.5%. The principal arrives in 2056. You are locked into 4.5% for three decades while the world now pays 5.5%, and the price falls until the two are equivalent.
Growth company. Down 15.4%. Its cash flow grows at 3.5% a year forever, so most of its value sits beyond 2040, which puts it further out in time than the thirty year bond.

The same news. Zero, two, fifteen. A portfolio is not exposed to interest rates as a single thing. It is exposed one holding at a time, in proportion to how far away that holding's money is.

Target rate moves are in the Federal Reserve's published FOMC statements and in the FRED series DFEDTARU. The 2022 index returns are in the Bloomberg US Aggregate factsheet and in any long Treasury fund's annual report. The four numbers above come from the pricing model on this page, which you can check by moving the slider to 5.5%.

ConventionBond people describe this sensitivity as and quote it in years, which is confusing the first time you meet it. A duration of 15 does not mean fifteen years to maturity. It means the price falls about 15% for each point the yield rises. It is a measure of exposure wearing the units of time.

Three channels, and which one bites first

A rate change reaches the economy by three separate routes that run at three very different speeds. Most confusion about rates comes from mixing them up.

. Same day. Every asset with a future cash flow reprices immediately, because repricing takes nothing more than a trade. This is the channel the slider above shows.
The cost of new borrowing. Months. Mortgages reset, corporate debt matures and refinances, credit lines reprice. A company that locked in 3% for seven years feels nothing until year seven, then feels all of it at once. The pain arrives on a schedule set by whoever wrote the debt.
Real activity. A year to eighteen months. Hiring slows, projects get shelved, houses take longer to sell. This is the channel the central bank actually wants, and it is the one that arrives last.

The order matters more than the list. Markets have finished responding before the economy has started, so a reader who waits for the employment data to confirm a rate story is reading about something that was priced eleven months ago.

Nominal rates and real ones

The rate on the screen is nominal. The rate that governs decisions is real, which is roughly the nominal rate less expected .

A 12% mortgage in 1980 sounds punishing and a 6% mortgage in 2024 sounds reasonable. With inflation near 13% in 1980, the real cost of that mortgage was negative: the borrower repaid in money worth less than the money they borrowed. With inflation near 3% in 2024, the real cost of the 6% loan is about 3%. The cheaper-looking loan is the expensive one.

This is why the level of rates tells you almost nothing on its own. Money was tight at 2% in 2019 by some measures and loose at 5% in 2023 by others, and the difference is entirely what inflation was doing underneath.

What breaks

The level is not the news. The change against what was expected is. If the market has priced four cuts and the central bank delivers three, that is a tightening, and prices fall on a day the headline says rates were cut. Everything already expected is already in the price. Only the surprise moves anything.

Rate exposure hides in things that are not bonds. A company with no debt at all still carries it, because its value is a stream of future cash and future cash is what rates price. Long-dated exposure sits in growth stocks, in venture portfolios, in pension liabilities, and in the terminal value that makes up most of any discounted cash flow model. Screening a portfolio for bonds finds a fraction of it.

A forecast is worth checking against the curve before you act on it.The market already publishes what it expects rates to do, in the forward curve. Acting on "rates will fall next year" only pays if rates fall faster than that curve already says. Being right about the direction and wrong about the pace loses money.

What to do with this

When a rate move shows up in the news, ask one question before any other: how far away is the money in the thing you are looking at? A one year certificate of deposit and a thirty year bond respond to the same announcement by factors that differ tenfold, and knowing which end you are standing at tells you most of what you need.

Then check whether the move was a surprise. Compare what happened against what the curve had priced, and only the gap between them counts as news. Then work out which channel you are watching, because a repricing that finished in an afternoon and a slowdown that takes eighteen months are the same cause arriving on very different clocks, and confusing them is how people conclude that rates do not work when the second one has yet to show up.

Test yourself

01Two companies earn the same profit this year. One is a utility with flat earnings forever. The other doubles every four years for a decade before settling down. Rates rise by one point. Which falls further, and why?

The fast-growing one, and the reason has nothing to do with how good either business is. The utility's value is spread evenly across every future year, so a large share of it arrives soon. The growth company earns little now and a great deal later, which puts most of its value far out in time where the discounting compounds hardest.

The same one point of rate applied to cash arriving in year 20 does roughly seven times the damage it does to cash arriving in year 2, because the discount factor carries an exponent. Distance to the cash is what sets the sensitivity.

02The central bank cuts rates and the stock market falls. Explain that.

Two things are moving at once and they point in opposite directions. A lower discount rate raises the value of a given stream of cash. A cut also tells you the committee sees the stream itself shrinking, because that is usually why they cut.

When the cut is smaller than the news that prompted it, the second effect wins. This is also why the market often falls on a cut it had already priced in: the rate change was in the price weeks earlier, so the only new information left in the announcement is what it says about the economy.

03Your savings account pays 5% and inflation runs at 6%. You are earning interest. Are you getting richer?

No, you are losing about 1% of purchasing power a year while a statement tells you your balance is rising. The nominal rate is what the bank pays. The real rate is what the money buys, which is roughly the nominal rate less inflation. Every discounting decision in this lesson runs on real rates, which is why a period of 5% nominal rates can be loose money and a period of 2% nominal rates can be tight.

A tutor that knows this lesson. It asks before it explains, and it will not tell you what to do with your own money.

Educational material, not investment or policy advice. Figures are cited where they come from a filing or a statistical series, and labelled as illustrative where they do not.