The term structure of interest rates

The term structure of interest rates is the relationship between the interest rate and the length of time money is lent for. Plot the spot rates against their maturities and the line through them is the yield curve.

There is no such thing as “the interest rate”. There is a rate for every maturity, they are different, and the pattern of the differences carries information the individual rates do not.

The curve matters to a company in three practical ways: it sets the cost of borrowing at each term, it is what implied forward rates are calculated from, and its shape is the market’s collective forecast of where short-term rates are going.

Three theories explain why the curve takes the shape it does. They are not rivals so much as three effects operating at once, and a full answer names all three.

Expectations theory says the expected return over a given holding period is the same whatever the maturity of the security used. Lending for five years, or for one year five times over, should come to the same thing.

If it did not, arbitrage would close the gap. Investors would abandon the maturity offering less and crowd into the one offering more, and the prices of the two would move until the advantage disappeared. That is the same no-free-lunch argument the forward rate formulas in the last step rest on.

So the shape of the curve is entirely a statement about expected future short-term rates.

• An upward-sloping curve means the market expects short-term rates to rise. Longer maturities pay more because they include the higher rates expected later.
• A downward-sloping curve means the market expects rates to fall — the four maturities in the last step, running 15%, 13.5%, 11.6%, 11.2%, say exactly that.
• A flat curve means rates are expected to stay where they are.

Under this theory the implied forward rate is the market’s unbiased forecast of the future spot rate: ₁f₂ of 7.51% is what the market genuinely expects the one-year rate to be in a year’s time.

Liquidity preference says investors require a premium for holding longer-maturity investments, over and above whatever they expect rates to do. Money committed for ten years cannot be used for anything else, and the longer the commitment, the more has to be paid to obtain it.

The premium grows with maturity, so it pushes the curve upwards and steepens it. That gives the theory its main claim: the yield curve should normally slope upwards, and it does, most of the time, in most markets — which pure expectations theory cannot explain, since rates are not always expected to rise.

It also carries a warning about forward rates. If part of a long rate is a liquidity premium rather than an expectation, then an implied forward rate is a biased predictor of the future spot rate — biased upwards, by the size of the premium.

The practical consequence for a treasurer is that long-term borrowing normally costs more than short-term borrowing even when nobody expects rates to rise. Rolling over short-term debt looks cheaper — and is, until the day it cannot be rolled over, which is what the premium is compensating the lender for.

Market segmentation, also called the preferred habitat theory, says participants have a maturity range they prefer to operate in and do not move out of it readily. Rates at each maturity are therefore set by the supply and demand within that segment rather than by any relationship across the whole curve.

The habitats are real and they come from the nature of the institutions.

• A pension fund with obligations decades away is a natural lender at the long end, and has little interest in one-year paper.
• A commercial bank funding itself from deposits repayable on demand cannot lend for thirty years, whatever the rate.
• A company financing a season’s working capital wants three months and has no use for a ten-year facility.

Behaviour shifts with the rate cycle too. When rates are rising, borrowers try to lock in long maturities while investors want to stay short and reinvest at the better rates coming — so demand at the long end rises and supply falls, and long rates rise further. When rates are falling the pressures reverse.

This is the theory that explains kinks. A curve that is smooth except for a bulge at seven years is hard to reconcile with expectations or with a premium that grows steadily — but easy to explain as an imbalance in one segment, which is often exactly what a heavy government issuance programme at one maturity produces.

Three shapes, and each one is telling a treasurer something about what to do next.

The downward-sloping case is the interesting one, because it means long money is available more cheaply than short money — an unusual position, and one that is usually short-lived. The spot rates in the last step, falling from 15% to 11.2%, describe exactly that.

A caution to carry into any recommendation. The curve is what the market expects, and the market can be wrong — an inverted curve is a forecast, not a promise. Borrowing short on the strength of an expected fall in rates is a position, and a company that takes it should know it is taking one.

The safer principle is matching the maturity of the borrowing to the life of what it is funding. Fund a five-year asset with five-year money and the curve becomes a fact about the cost rather than a bet on the direction — and where a company would rather not take the rate it is offered, there are instruments designed to change it.