WSU Lexicon: Quantitative Methods

Real Interest Rate

A real interest rate is an interest rate measured in purchasing power: the nominal rate with expected inflation stripped out. Exactly, real rate = (1 + nominal rate) / (1 + inf) − 1, where inf is expected inflation. The real risk-free rate is the pure reward for delaying consumption.

Its money-terms counterpart is the nominal interest rate.

The entry

Measuring Interest in Goods, Not Currency

A real interest rate asks how much more an investor can buy after a period, not how much more currency the investor holds. It removes expected inflation from the nominal rate, leaving the growth in purchasing power that lending is expected to deliver. A saver who earns 5% in a year with 3% inflation can buy about 1.9% more goods, not 5% more.

Economists read the real risk-free rate as a gauge of how strongly people prefer consumption today over consumption tomorrow. When households and firms are eager to spend, or when investment opportunities are plentiful, the real rate tends to be higher; when saving is abundant relative to the demand for investment, it tends to be lower.

The entry

From Nominal to Real: Exact and Approximate

The conversion divides rather than subtracts: real rate = (1 + nominal rate) / (1 + inf) − 1. With a nominal rate of 12% and expected inflation of 4%, the real rate is 7.69%, below the 8% that simple subtraction suggests. The shortcut is acceptable for quick estimates when rates are low, and it is exact for continuously compounded rates, but its error grows with the level of rates and compounds over long horizons.

The same formula turns a realized nominal return into a realized real return, with actual inflation in place of expected inflation. Comparing the expected real return at the start of a period with the realized real return at the end shows how much of an outcome came from inflation surprises.

The entry

Real Rates in Markets and Policy

Most real rates are inferred, but inflation-linked government bonds let investors observe them. Their yields are quoted in real terms because inflation is paid on top, through adjustments to principal or coupons. Central banks watch real rates closely: a policy rate increase that lags behind rising inflation leaves the real rate lower, and policy looser, than the headline suggests.

Real rates also drive asset values. Equities, real estate and long-term bonds are all sensitive to the real discount rate, so a sharp rise in real yields, such as the one in 2022 and 2023, tends to weigh on the prices of long-duration assets even when nominal cash flow forecasts are unchanged.

The entry

Exam Focus: Consistency and Components

Candidates should convert between nominal and real rates exactly, explain when the subtraction shortcut is acceptable, and place the real risk-free rate at the base of the building-block view of interest rates, with expected inflation and risk premiums added on top. They should also be able to compute real after-tax returns in the right order.

The central discipline is consistency. Real cash flows belong with real discount rates, and nominal cash flows with nominal rates. A forecast built in today's prices but discounted at a nominal market rate understates value, and the error grows the further out the cash flows lie.

Common trap

“To get a real rate, simply subtract inflation from the nominal rate.”

For discrete rates, subtraction is only an approximation. The exact real rate divides: (1 + nominal) / (1 + inf) − 1. At 9% nominal and 3% inflation the exact real rate is 5.83%, not 6%, and the error compounds over long horizons.

In practice

TIPS real yields from below zero to above 2%

Yields on 10-year US Treasury Inflation-Protected Securities, which are quoted in real terms, stayed below zero for much of 2020 and 2021 and rose above 2% by late 2023 as the Federal Reserve tightened policy.

Candidates ask

Questions on this term

Can a real interest rate be negative?Yes. Whenever expected inflation exceeds the nominal rate, the real rate is below zero: lenders are paid less than the loss in purchasing power. Real yields on inflation-linked government bonds were negative in several major markets in 2020 and 2021.
How do I compute a realized real return?Use the same exact formula with realized numbers: real return = (1 + R) / (1 + inf) − 1, where R is the nominal return and inf the inflation over the period. A portfolio that earned 9% in a year when prices rose 6% gained 2.83% in real terms, not 3%. For after-tax figures, deduct taxes from the nominal return first, then remove inflation.
Where can investors observe real rates directly?In the yields on inflation-linked bonds, such as US TIPS or UK index-linked gilts. Because their principal or payments are adjusted for realized inflation, their yields are quoted in real terms. The gap between a nominal government bond yield and the real yield on a linked bond of the same maturity, called the breakeven inflation rate, is a market-based gauge of expected inflation.

Related entries

Fisher EffectThe Fisher effect is the proposition that the nominal interest rate reflects the real interest rate plus expected inflation, so that (1 + nominal) = (1 + real) × (1 + expected inflation).
InflationInflation is a sustained increase in the general price level of goods and services in an economy, which erodes the purchasing power of a unit of currency.
Inflation PremiumThe inflation premium is the part of a nominal interest rate that compensates lenders for the loss of purchasing power they expect over the life of a loan.
Nominal Interest RateA nominal interest rate is a rate stated in money terms, before any adjustment for inflation.

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Real Interest Rate

Its money-terms counterpart is the nominal interest rate.