Real interest rate
Also written Real rate · Inflation-adjusted interest rate
The nominal rate adjusted for inflation — what the lender actually gains in purchasing power, and a number that turns negative whenever inflation runs above the coupon.
In plain language
A bond paying 9% looks like a 9% gain. If prices rose 6% over the same year, it is not. The rupees grew by 9% and what a rupee buys shrank by 6%, so the investor is roughly 3% better off in anything that matters.
The nominal rate is the stated coupon, the number printed on the instrument. The real rate is what survives inflation. Only the second one tells you whether wealth actually increased.
The uncomfortable corollary is that the real rate can be negative. When inflation exceeds the coupon, a bondholder's balance grows every year while his purchasing power falls — and no amount of credit quality protects against it, because this is not a default risk.
How it works
The exact relationship is multiplicative, not additive. Nominal growth is real growth compounded with price growth:
(1 + r) × (1 + i) = (1 + R)
At the rates India typically sees, the cross-term is small enough that the workbook's approximation r = R − i is close, and it is the form the exam uses. At high inflation the approximation drifts and the exact form should be used.
Two consequences run through the rest of the paper.
Inflation risk is the household sector's biggest macroeconomic exposure, and it is an interest rate exposure in disguise — which is why the workbook argues that interest rate derivatives, not equity or currency products, are the primary instruments available to hedge it.
Expected inflation feeds back into nominal rates. That is the Fisher effect: other things equal, a rise in expected inflation raises the nominal interest rate, so a bondholder who sees inflation coming should expect yields to rise and prices to fall.
The formula
Exact: (1 + r) × (1 + i) = (1 + R)
1 + R
r = ─────────── − 1
1 + i
Approximate: r = R − i (valid at low rates)
R = nominal rate i = inflation rate r = real rate
A worked example
The workbook's two cases, exact and approximate side by side.
| Nominal | Inflation | Approximate real | Exact real | |
|---|---|---|---|---|
| Positive | 9% | 6% | 3.00% | 1.09/1.06 − 1 = 2.830% |
| Negative | 7% | 9% | −2.00% | 1.07/1.09 − 1 = −1.835% |
The approximation is 17 basis points out in the first case and 16 in the second — close enough for an exam, material on a portfolio.
What negative real rates do to a retirement corpus. A retiree holds Rs 1 crore in a bond paying 7% while inflation runs at 9%, and spends the coupon each year.
After 1 year : corpus Rs 1,00,00,000, purchasing power Rs 91,74,312
After 5 years: corpus Rs 1,00,00,000, purchasing power Rs 64,99,314
The bank statement never moves. Over a third of the real wealth is gone in five years, and the instrument performed exactly as promised throughout. This is why the workbook treats inflation as the household sector's single most important macroeconomic risk.
And on the other side of the trade. A bank funds a Rs 500 crore 10-year loan book at a nominal 7.50% when inflation is 6.00%:
Real rate = 1.075 / 1.06 − 1 = 1.415%
Real return on the book = Rs 7.08 crore a year
Nominal interest = Rs 37.50 crore a year
Four-fifths of the interest income is compensation for inflation, not a return.
Why NISM asks about it
Chapter 1, section 1.1.2 (Nominal and Real Interest Rate), gives the exact equation, the low-rate approximation and both worked cases including the negative one. Chapter 3, section 3.5, connects it to the rationale for exchange-traded interest rate derivatives: because of the Fisher effect, interest rate derivatives are the primary instruments available to households for hedging inflation risk.
Questions are computational and almost always use the approximation — given a nominal rate and an inflation rate, find the real rate, including the case where the answer is negative.
Common exam traps
- The exact relationship is multiplicative.
(1+r)(1+i) = (1+R), notr + i = R; the subtraction is an approximation and the workbook says so. - A negative real rate is a normal outcome, not an error. Inflation above the coupon produces one, and the workbook works that case deliberately.
- Nominal is the coupon; real is what you keep. The bond still pays exactly what it promised — the erosion happens outside the instrument.
- Inflation risk is not credit risk. A AAA rating is no protection at all; only an inflation-linked or interest rate hedge is.
- The approximation drifts as rates rise. At Indian levels it is within twenty basis points; at high inflation use the exact form.
- Do not confuse the real rate with the Fisher effect. The real rate is an adjustment applied today; the Fisher effect is the causal claim that expected inflation pushes nominal rates up.
Check yourself
1.A bond carries a nominal interest rate of 7% while the rate of inflation is 9%. Using the approximation the workbook gives for low-level rates, what is the real interest rate?
- a)Approximately −2%
- b)Approximately +2%
- c)Approximately +16%
- d)Approximately +0.63%
Show the answer
Answer: (a) Approximately −2%
The exact relationship is (1 + r) × (1 + i) = (1 + R), where r is real, i is inflation and R is nominal. For low-level rates this approximates to real = nominal − inflation = 7% − 9% = −2%. The workbook uses this exact example to make its point: if the rate of inflation exceeds the coupon rate of a bond, the real interest rate is negative. The investor's balance grows on paper while their purchasing power shrinks — which is exactly what Indian FD holders experienced in 2020–2022.
Where this is taught
Free preparation for NISM Series V-DRelated terms
- InflationA sustained general rise in the price level, which erodes what a rupee buys — and the reason a nominal return has to be deflated before it means anything.
- Inflation riskThe risk that the money an investment pays out will be worth less in goods and services than expected, because prices have risen — highest in fixed-return products and most damaging to retirees.
- Yield to MaturityThe single discount rate at which a bond's future coupons and redemption amount add up to exactly its market price today — the return you actually earn if you hold it to maturity.
- Effective interest rateThe rate actually earned over a year once compounding within the year is counted — always at or above the quoted nominal rate, and equal to it only when interest is paid once a year.
- Fisher effectThe proposition that, other things equal, a rise in expected inflation raises the nominal interest rate — which is why interest rate derivatives are the household sector's instrument for hedging inflation.
- Risk-free rateThe rate on a sovereign borrowing in its own currency, where credit risk is absent because the government can print the money — the benchmark every other valuation is measured against.
- Term structure of interest ratesInterest rate plotted against term — one curve per credit quality, with the risk-free curve as the base and every other borrower quoted as a spread over it.