Interest rates, the yield curve and inflation

Key takeaways

• The real rate is the nominal rate adjusted for inflation: (1 + nominal) = (1 + real) x (1 + expected inflation).
• The Federal Reserve sets the overnight policy rate; longer rates are set by the market as expected future short rates plus a term premium.
• Spot rates price single cash flows; forward rates are the future rates locked in by today's spot curve, computed so that no maturity offers a free gain.
• An inverted curve (short rates above long rates) signals that the market expects policy rates to fall, often because it expects slower growth.
• A corporate yield equals the Treasury yield plus a credit spread that pays for expected default losses, plus compensation for risk and illiquidity.
• Higher discount rates cut the value of every asset, and cut most the value of assets whose cash arrives far in the future.

Nominal rates, real rates and the Fisher equation

A nominal interest rate is the rate quoted in dollars: a deposit paying 5 percent turns $100 into $105. But if prices rise 3 percent over the year, the $105 buys only about 2 percent more goods than the $100 did. The real interest rate measures that gain in purchasing power. Investors care about real returns, because what matters in the end is what the money will buy.

Irving Fisher's equation links the two: one plus the nominal rate equals one plus the real rate times one plus expected inflation. The popular shortcut, nominal minus inflation, is close enough when rates are low but drifts as they rise. Nominal rates therefore contain a forecast: lenders demand compensation for the inflation they expect over the life of the loan, so a rise in expected inflation pushes nominal rates up even if real rates do not change.

In the US the market reveals both pieces. Ordinary Treasury notes pay a nominal yield. Treasury Inflation-Protected Securities (TIPS) have their principal indexed to the Consumer Price Index, so their yield is a real yield. The difference between the two at the same maturity is the breakeven inflation rate, the market's rough estimate of average inflation over that horizon (rough because it also contains risk and liquidity premiums).

The policy rate and market rates

The Federal Reserve sets a target range for the federal funds rate, the overnight rate at which banks lend reserves to each other. It steers actual overnight rates into that range mainly through the interest it pays on bank reserves and through its overnight reverse repurchase facility. The Secured Overnight Financing Rate (SOFR), based on overnight Treasury repo trades, is now the main floating benchmark for US loans and derivatives, and it moves closely with the policy rate.

The Fed directly controls only the very front of the curve. A two-year or ten-year Treasury yield is set by investors trading in the market, and it reflects what they expect the overnight rate to average over that period, plus compensation for locking money up for longer. That is why long yields can rise while the Fed is cutting, or fall before it has moved at all: the market trades the expected path, not today's setting.

For a buyside investor the chain matters directly. Floating rate leveraged loans and private credit facilities are priced at SOFR plus a spread, so their coupons reset with the policy rate. Fixed rate bonds, mortgages and the discount rates used in valuations follow longer market yields. A change in the Fed's stance therefore hits a leveraged buyout's interest bill through SOFR and its exit multiple through long yields.

Spot rates and forward rates

A spot rate is the yield today on a single cash flow due at one future date, the rate on a zero coupon bond of that maturity. The set of spot rates by maturity is the zero curve, and it is the correct curve for discounting: each cash flow of a bond or project is discounted at the spot rate for its own date. A coupon bond's yield to maturity is a blend of the spot rates for all of its cash flows.

A forward rate is a rate for a future period that today's spot rates imply. If the one-year spot rate is 4.00 percent and the two-year spot rate is 4.50 percent, an investor can either lock in two years at 4.50 percent, or invest for one year at 4.00 percent and roll over. For both to be fair, the second year must be expected to earn a rate that makes the two routes end with the same money. That rate, the one-year rate one year forward, is the forward rate.

Forward rates are not forecasts in a strict sense: they contain term premium as well as expectations. But they are the rates a borrower or lender can lock in today through forward rate agreements, futures and swaps, and they show what path of short rates the curve is pricing. A rising spot curve always implies forward rates above the spot rates.

Curve shapes, what they signal, and the term premium

The yield curve normally slopes upward: lenders want more to tie money up for longer, and long bonds carry more price risk. Its shape changes with the cycle, and investors read it closely. The difference between the 10-year and 2-year Treasury yields, or the 10-year and 3-month yields, is the usual measure of slope.

An inverted curve, with short yields above long yields, says the market expects the Fed to cut rates in future, typically because it expects growth and inflation to slow. Inversions have preceded most US recessions in the past half century, though the lag has been long and variable, and the signal has not been perfect. A steepening curve after an inversion often comes as the Fed actually begins cutting.

Long yields can be split into two parts: the average short rate the market expects over the life of the bond, and a term premium, the extra return demanded for holding a long bond instead of rolling short ones. The term premium cannot be observed directly; it is estimated with models, and estimates differ. It rises when investors are less sure about future inflation, government borrowing or policy, and it can be near zero or even negative when long bonds are prized as a hedge.

Credit spreads

A corporate borrower pays more than the US Treasury because it might default. The credit spread is the gap between a corporate bond's yield and the Treasury yield at the same maturity, usually quoted in basis points (one basis point is 0.01 percent). Floating rate loans quote the spread directly over SOFR.

The spread pays for more than expected losses. Expected loss is roughly the annual probability of default times the loss given default (one minus the recovery rate). The rest of the spread compensates for the risk that defaults cluster in a recession, for the bond being harder to sell than a Treasury, and in some cases for tax differences. Historically, for investment grade bonds expected losses explain only a small part of the spread, which is why credit has paid a premium over time.

Spreads widen when investors fear recession or need liquidity, and tighten when risk appetite is strong. For leveraged buyouts this is a direct input: the same company can borrow at very different all-in costs a year apart, which changes how much debt a deal can carry and therefore what a sponsor can pay.

Why rates drive asset valuations

Every asset is worth the present value of its cash flows, and the discount rate is the risk-free rate plus a risk premium. When the risk-free rate rises and the premium does not fall to offset it, the discount rate rises and the value of every asset falls. That is why equities, real estate, private company valuations and bonds can all fall together when long yields jump.

The damage is not even. An asset whose cash arrives soon, like a short bond or a mature business paying out most of its earnings, loses little when rates rise. An asset whose value sits mostly in distant cash flows, such as a long bond, a fast growing company or a development property, loses much more. In the growing perpetuity, value equals C / (r - g), and the higher g is, the smaller the gap r - g and the bigger the proportional effect of any change in r.

For a buyout fund this works on both ends of the deal. Higher rates raise the cost of the debt that funds the purchase, and they tend to lower the exit multiple at which the asset will be sold. A deal underwritten when rates were low and exited when they are high can lose much of its return to multiple compression alone, even if the business performed to plan.