Fisher effect

Lenders are not indifferent to inflation. If they expect prices to rise 6% over the coming year, a 7% loan leaves them barely ahead, and they will ask for more. Borrowers, expecting to repay in cheaper rupees, will pay more. The two sides meet at a higher nominal rate.

That is the Fisher effect in the form the workbook states it: ceteris paribus, an increase in the expected inflation rate leads to an increase in the nominal interest rate. It is a statement about expected inflation, and about the nominal rate, and about the direction only.

Its practical importance in this paper is a chain of three steps. Inflation expectations move nominal rates. Nominal rates move bond prices. Bond prices are what interest rate derivatives are written on — so an inflation exposure can be hedged in the interest rate market.

Start from the real-rate identity, (1 + r)(1 + i) = (1 + R), and hold the real rate constant. Any increase in expected inflation i must then come through as an increase in the nominal rate R. The real rate is the anchor; the nominal rate is what moves.

The consequence for a bondholder is immediate and unpleasant. A bond already issued has a fixed coupon. If inflation expectations rise, market yields rise, and the existing bond must fall in price until its yield matches. So an inflation shock arrives at a bond portfolio as a capital loss, not as a slow erosion.

This is what makes the household exposure hedgeable. The workbook's argument in Chapter 3 runs: households carry large financial savings on the asset side and growing housing loans on the liability side; inflation is their single most important macroeconomic risk; because of the Fisher effect, that risk shows up in interest rates; and therefore interest rate derivatives are the primary instruments available to hedge it. It is one of the stated public-policy reasons for introducing exchange-traded interest rate derivatives in India at all.

The long end of the yield curve carries the same logic. The workbook attributes the upward slope of a normal curve to the inflation-risk premium investors demand for lending long.

Nominal rate  ≈  Real rate + Expected inflation

Exactly:   (1 + R) = (1 + r) × (1 + i)

   R rises with i when r is held constant.

And the transmission into a bond price:

Δ Price ≈ − Modified duration × Δ Nominal yield
        ≈ − Modified duration × Δ Expected inflation   (real rate constant)

The chain, priced out. A provident fund holds Rs 300 crore of a 10-year G-Sec with a modified duration of 7.2, yielding 6.50% against expected inflation of 4.50% — a real rate of about 2.00%.

The monthly inflation print comes in high and the market revises expected inflation to 5.75%. The real rate has not changed; by the Fisher effect the nominal yield moves with the expectation:

New nominal yield ≈ 2.00% + 5.75% = 7.75%
Yield change                      = +125 basis points

Price change = − 7.2 × 1.25% = − 9.00%
Loss         = 9.00% × Rs 300 crore = Rs 27 crore

Rs 27 crore on an inflation forecast, with no default, no downgrade and no change in the coupon.

Hedging it. Bond futures with a modified duration of 4.7 trade at Rs 98.50. The duration-based hedge ratio sizes the short:

Lots = (3,00,00,00,000 × 7.2) ÷ (98.50 × 4.7 × 2,000)
     = 21,60,00,00,000 ÷ 9,25,900
     = 2,333 lots

Sell 2,333 lots and the same 125 bp move produces a futures gain of roughly 4.7 × 1.25% × 2,333 × 2,000 × 98.50 ÷ 100 = Rs 27 crore, offsetting the portfolio loss. The inflation exposure was never traded directly — it was hedged in the interest rate market, which is precisely the workbook's argument for why these contracts exist.

The household version. A borrower with a Rs 60 lakh floating-rate home loan sees the same 125 bp pass through to his loan rate: Rs 75,000 a year of extra interest, arriving through exactly the same channel.

Chapter 3, section 3.5 (Rationale for Introducing Exchange Traded Interest Rate Derivatives in India), invokes the Fisher effect and defines it in a footnote: "ceteris paribus, increase in expected inflation rate leads to an increase in the nominal interest rate." It is the link in the argument that interest rate derivatives are the primary instruments available to the household sector for hedging inflation risk. Chapter 1, section 1.1.2, supplies the underlying real-versus-nominal relationship, and section 1.6 attributes the normal yield curve's slope to an inflation-risk premium.

Questions are conceptual and directional: what happens to nominal rates when expected inflation rises, and why interest rate derivatives are described as inflation-hedging instruments for households.

• It concerns expected inflation, not realised inflation. Rates move when the expectation moves, which is usually before the print.
• It is the nominal rate that adjusts. The real rate is held constant in the statement; a question that has the real rate moving has inverted the proposition.
• "Ceteris paribus" is load-bearing. Policy, liquidity and global flows move rates too, and in practice can swamp the inflation channel.
• A bond investor is hurt, not helped, by higher inflation expectations. Yields rise and existing prices fall; the higher nominal rate benefits new money only.
• Fisher effect is not the same as the real interest rate calculation. One is a causal proposition about direction, the other an arithmetic adjustment made today.
• The Fisher of the Fisher effect is Irving Fisher. The Black-Scholes model in Chapter 4 is co-authored by Fisher Black — a different person, and the two names sit only twenty pages apart in the workbook.