Real Interest Rate

The Fisher Equation

The relationship between the real interest rate, the nominal interest rate, and inflation was formalised by American economist Irving Fisher in his 1930 work The Theory of Interest, producing what is universally known as the Fisher equation.

The approximation form of the Fisher equation states that the real interest rate equals the nominal interest rate minus the inflation rate. If a bond pays a nominal coupon of five percent and inflation runs at two percent, the approximate real interest rate is three percent — the lender earns five dollars per one hundred dollars of principal but two dollars of that is consumed by rising prices, leaving only three dollars of genuine purchasing power gain.

The precise form of the Fisher equation states that one plus the real interest rate equals one plus the nominal interest rate divided by one plus the inflation rate. This precise formulation, rearranged to solve for the real rate, produces: real interest rate equals the quantity one plus the nominal rate divided by one plus the inflation rate, minus one. For small interest rates and inflation levels the approximation and the precise formula produce nearly identical results. For high nominal rates or high inflation — as in hyperinflationary environments — the precise formula diverges meaningfully from the approximation and must be used.

The Fisher equation also works in the forward-looking direction. When lenders and borrowers negotiate the interest rate on a new loan, they set the contracted nominal rate equal to the real rate they require plus the expected inflation rate over the loan period. If both parties expect two percent inflation and require a three percent real return, the contracted nominal rate is approximately five percent. If actual inflation proves higher than expected — say four percent rather than two percent — the realised real return to the lender is only approximately one percent despite the five percent nominal rate, while the borrower effectively paid only one percent in real terms. Unexpected inflation systematically transfers wealth from creditors to debtors.

Why the Real Rate Matters More Than the Nominal Rate

The nominal interest rate is visible and observable — it appears in the loan agreement, on the bond coupon, and in the savings account disclosure. The real interest rate is calculated rather than quoted, yet it is the real rate that governs actual economic behaviour.

For borrowers, the real interest rate determines the true cost of debt. A business investing in a project that generates a real return of four percent will rationally borrow at a real rate of three percent — earning a one percent real spread — but will decline to borrow at a real rate of five percent. The nominal rate of the loan is irrelevant without knowing what inflation will do to the real cost over the borrowing period.

For savers and investors, the real interest rate determines whether savings are genuinely growing in purchasing power or merely keeping pace with — or falling behind — inflation. A savings account offering three percent nominal interest in a two percent inflation environment provides a positive one percent real return. The same account in a four percent inflation environment provides a negative one percent real return — the saver is losing purchasing power despite receiving positive nominal interest income.

For monetary policy, the Federal Reserve monitors the real federal funds rate — the nominal federal funds rate target minus the current or expected inflation rate — as the true measure of how restrictive or accommodative its policy stance is. A nominal federal funds rate of five percent in a two percent inflation environment implies a three percent real rate — genuinely restrictive monetary conditions. The same nominal rate in a five percent inflation environment implies approximately zero real rate — neutral to mildly accommodative conditions despite an apparently high nominal rate.

The TIPS Market — Observing Real Rates Directly

Treasury Inflation-Protected Securities — governed by 31 CFR Part 356 — are the only financial instrument that quotes a real interest rate directly rather than a nominal rate. The stated yield on a TIPS is a real yield — the guaranteed increase in purchasing power the investor receives above and beyond the inflation adjustment applied to the TIPS principal each month based on changes in the Consumer Price Index for All Urban Consumers.

When a five-year TIPS is issued at a real yield of one and a half percent, the investor is guaranteed one and a half percent per year of real return regardless of what inflation proves to be over the holding period. The nominal return will be higher or lower depending on actual inflation — but the real return of one and a half percent is fixed. This direct observation of real yields through the TIPS market, combined with the nominal yield on conventional Treasuries of the same maturity, produces the breakeven inflation rate — the difference between the two yields that represents the market's consensus forecast of average annual inflation over the period.

If the five-year nominal Treasury yields three and a half percent and the five-year TIPS yields one and a half percent, the breakeven inflation rate is two percent. Investors who expect inflation to exceed two percent over the next five years prefer TIPS. Investors who expect inflation below two percent prefer the nominal Treasury. The Federal Reserve monitors breakeven inflation rates derived from the TIPS market as a real-time indicator of whether long-term inflation expectations remain anchored near the two percent target established under the dual mandate of 12 U.S.C. 225a.

Negative Real Interest Rates

When the nominal interest rate falls below the inflation rate, the real interest rate becomes negative — meaning savers and lenders are losing purchasing power in real terms even while receiving positive nominal interest. Negative real rates occurred extensively in the United States during 2021 and 2022, when inflation rose sharply above the near-zero federal funds rate that the FOMC maintained to support the post-COVID recovery. With CPI inflation reaching nine point one percent in June 2022 and the federal funds rate remaining below one percent until March 2022, the real federal funds rate was deeply negative for an extended period — representing the most accommodative monetary conditions in terms of real rates in decades.

Negative real interest rates have several economic consequences. They incentivise borrowing and discourage saving, since the real cost of debt is negative and the real return to saving is negative. They push investors into riskier assets in search of positive real returns — a phenomenon called the search for yield. They support asset price inflation by reducing the discount rate applied to future cash flows. The Federal Reserve's aggressive rate-hiking cycle of 2022 and 2023 — raising the nominal federal funds rate by five hundred and twenty-five basis points — was explicitly designed to restore positive real interest rates and bring inflation back toward the two percent target.

Investment Implications

Under the fiduciary standard of the Investment Advisers Act of 1940 and the care obligation of Regulation Best Interest at 17 CFR 240.15l-1, investment advisers and broker-dealers must account for real interest rates — not merely nominal rates — when constructing and recommending fixed income portfolios. A bond yielding three percent nominally in a two percent inflation environment provides a one percent real return. The same bond in a four percent inflation environment provides a negative real return. The advice to hold fixed income securities without considering the inflation environment may fail the care obligation if it results in portfolios that systematically lose purchasing power over the investment horizon.

Examination Relevance and Key Takeaways

The real interest rate is tested on the Series 65 examination in the context of the Fisher equation, the distinction from the nominal rate, TIPS pricing, monetary policy analysis, and investment return calculations adjusted for inflation.

The key points to retain are these.

The real interest rate equals the nominal interest rate minus the inflation rate — the approximation form of the Fisher equation developed by Irving Fisher in The Theory of Interest (1930). The precise form states that one plus the real rate equals one plus the nominal rate divided by one plus the inflation rate. When setting loan rates, borrowers and lenders set the contracted nominal rate equal to the required real rate plus expected inflation — unexpected inflation transfers wealth from creditors to debtors by reducing the real cost of debt below the contracted level. The real federal funds rate — nominal rate minus inflation — is the Federal Reserve's actual policy measure, with positive real rates being restrictive and negative real rates being accommodative regardless of the nominal rate level. TIPS under 31 CFR Part 356 are the only instruments quoting a direct real yield — the difference between the nominal Treasury yield and the TIPS real yield of the same maturity is the breakeven inflation rate representing the market's consensus inflation forecast monitored by the Federal Reserve under the dual mandate of 12 U.S.C. 225a. Negative real interest rates occur when inflation exceeds the nominal rate — incentivising borrowing, discouraging saving, and pushing investors into riskier assets in search of positive real returns.