Bond price and interest rate inverse relation

Topic: Financial Markets, Instruments, Insurance and Pensions · NCERT: Class 12, Ch 3 "Money and Banking"

Meaning

Bond price and interest rate inverse relation means that when the market rate of interest rises, the price of an existing bond falls, and when the rate falls, the price rises. This happens because the bond's coupon and principal are fixed in rupees, so a higher rate lowers the present value (PV) of those future payments.

The rule matters because it decides who gains and who loses when interest rates change. It explains capital gains and losses for bondholders, mark-to-market (MTM) losses at banks, and the speculative demand for money.

Formula. Bond price = PV of its future cash flows, with market rate r and payment C in year t:

P = C₁/(1+r) + C₂/(1+r)² + … + Cₙ/(1+r)ⁿ

Because r is in the denominator, a bigger r gives a smaller P.

Explanation

How it works: fixed payments, changing discount rate

• Bond = a tradable paper that a government or company issues to borrow money. It promises fixed payments until its maturity (the end date).
• Face value (par value) = the amount printed on the bond and repaid at the end.

• Coupon rate = the fixed yearly payment, shown as a % of face value. Coupon amount = Coupon rate × Face value.

• Present value (PV) = the amount you would need today, at the market interest rate, to get a given sum in the future.

• Why price = PV (arbitrage logic):
• If the price is below PV, the bond is cheap. Buyers rush in and push the price up.
• If the price is above PV, holders sell. The price falls back.

• So in a competitive market, price = PV.

• The chain when rates rise:

• The market rate goes up.
• Each future rupee is discounted more heavily.
• The PV of the fixed coupon and principal falls.
• The bond's price falls.

Worked example (NCERT bond)

A firm issues a bond with face value Rs 100, a 2-year maturity and a 10% coupon. It pays Rs 10 at the end of year 1 and Rs 110 at the end of year 2.

Market rate	Bond price (= PV)	How it sells
5%	10/1.05 + 110/(1.05)² ≈ Rs 109.29	Premium (above face value)
6%	10/1.06 + 110/(1.06)² ≈ Rs 107.33	Premium
10% (= coupon)	10/1.10 + 110/(1.10)² = Rs 100.00 (illustration)	At par
12%	10/1.12 + 110/(1.12)² ≈ Rs 96.62 (illustration)	Discount (below face value)

• As the rate climbs from 5% to 12%, the price falls from Rs 109.29 to Rs 96.62.
• Market rate < coupon → price > face value → bond sells at a premium.
• Market rate = coupon → price = face value → bond sells at par.
• Market rate > coupon → price < face value → bond sells at a discount.

Longer bonds swing more (interest-rate risk)

• Take two zero-coupon bonds, each with face value Rs 100, and let the rate move from 5% to 6% (illustration):
• 1-year bond: Rs 95.24 → Rs 94.34, a fall of about 0.9%.

• 10-year bond: Rs 61.39 → Rs 55.84, a fall of about 9%.

• Interest-rate risk = the risk that a bond's price falls because rates rise. It is much larger for long bonds, because their payments are discounted over more years.

• Floating Rate Bonds (FRBs) reset their coupon in line with a benchmark. Because the coupon follows market rates, their price swings much less than a fixed-coupon bond's price.

Yield: the same relation seen from the other side

• Yield = the return an investor actually earns on a bond. It is not the same as the coupon rate.
• Current yield = (Annual coupon ÷ Market price) × 100 [2]
• NCERT bond at Rs 109.29: 10/109.29 ≈ 9.15%.

• It ignores capital gains or losses at maturity and the return from reinvesting coupons [2].

• Yield to maturity (YTM) = the single discount rate that makes the PV of all future cash flows equal to today's price. It is the bond's internal rate of return (the yearly return you earn if you hold the bond to maturity) [2].

• In the NCERT example, a price of Rs 109.29 gives a YTM of 5%.

• So a rise in bond yields is the same thing as a fall in bond prices. News headlines use "yields up" and "prices down" to mean the same event.

• How price, coupon and YTM are linked [2]:
• Price < face value → YTM > coupon rate
• Price > face value → coupon rate > YTM
• Price = face value → YTM = coupon rate

Capital gains, capital losses and the demand for money

• Capital gain = gain from a rise in an asset's price. Capital loss = loss from a fall.
• Rates rise → bond prices fall → holders suffer a capital loss.

• Rates fall → bond prices rise → holders make a capital gain.

• This is why people hold money for speculation. If they expect rates to rise, they hold cash, not bonds, to avoid a capital loss.

• Liquidity trap = when rates are very low, everyone expects them to rise (and bond prices to fall). So people hold cash instead of bonds.

In India

• Government securities (G-secs) = tradable papers issued by the Central or a State Government. Each one records the government's debt [2].
• Treasury Bills (T-bills) are short-term, zero-coupon G-secs in 91-day, 182-day and 364-day tenors [2]. They are issued at a discount and repaid at face value. Example: a 91-day T-bill with face value Rs 100 is issued at Rs 98.20, so the investor earns Rs 1.80 [2].

• Dated securities usually mature in 5 to 40 years and pay interest every half-year [2]. Because they are long, their prices react most to rate changes.

• GoI FRB: the coupon can be set as the average of the implied yields at the cut-off prices of the last three 182-day T-bill auctions, plus a fixed spread [2]. This keeps its price more stable.

• Benchmark: the 10-year G-sec yield is the reference rate for pricing corporate bonds and long-term loans. When it rises, G-sec prices fall and borrowing becomes costlier across the economy.
• Banks and MTM losses:
• Mark-to-market (MTM) = valuing an asset at its current market price, not at the price paid for it.

• When yields rise, the prices of bonds banks already hold fall. For example, if the rate rises from 5% to 6%, the NCERT bond falls from Rs 109.29 to Rs 107.33, a loss of about 1.8%.

• RBI's investment norms (in force from 1 April 2024): the RBI (Classification, Valuation and Operation of Investment Portfolio of Commercial Banks) Directions, 2023, issued on 12 September 2023 [3].

• HTM (Held to Maturity): carried at amortised cost (the purchase price, adjusted step by step towards face value) and not marked to market [3].
• AFS (Available for Sale): net gains or losses go to an AFS-Reserve, not the profit and loss account (P&L), until the security is sold [3].
• FVTPL (Fair Value Through Profit and Loss): changes in value go straight to the P&L [3]. HFT (Held for Trading) sits inside FVTPL and must be valued daily [3].

• The old norms (Master Direction, 2021) used HTM / AFS / HFT, and HTM was capped at 25% of total investments [4].

• Global lesson: Silicon Valley Bank (US) collapsed in March 2023. It held long bonds bought when rates were low. When rates rose, it had large unrealised losses. Depositors panicked and withdrew their money, so the bank had to sell bonds at a loss.

Don't confuse with

• Coupon rate: fixed at issue as a % of face value and never changes for a fixed-coupon bond. The market rate / yield changes every day, and that is what moves the price.
• Current yield vs YTM: current yield uses only coupon ÷ price [2]. YTM is the full internal rate of return and includes the capital gain or loss up to maturity [2].
• Interest-rate risk vs credit risk: interest-rate risk means the price falls because market rates rise, even for a safe G-sec. Credit risk is the risk that the borrower does not repay. That risk shows up in the credit spread over a G-sec of the same maturity.
• Face value vs market price: face value is fixed and repaid at maturity. The market price moves above or below it depending on the market rate.

Prelims Hooks

• Bond price and market interest rate (yield) move in opposite directions. A rise in rates causes a capital loss for bondholders.
• Market rate > coupon rate → bond sells at a discount. If the price is below face value, YTM > coupon rate [2].
• Current yield = (Annual coupon ÷ Market price) × 100 [2]. Trap: it is not the same as YTM.
• For the same change in rates, longer bonds fall more in price than short bonds (interest-rate risk). Floating Rate Bonds swing the least.
• T-bills (91/182/364-day) are zero-coupon, issued at a discount [2]. Trap: they do not pay a coupon.
• From 1 April 2024, banks classify investments as HTM / AFS / FVTPL. HTM is not marked to market, and AFS gains and losses go to the AFS-Reserve [3].

Mains Points

• Monetary policy and bank stability: when the RBI raises rates, bond yields rise, bond prices fall and banks face MTM losses.
• The 2023 framework keeps HTM at amortised cost and sends AFS losses to a reserve. This reduces swings in reported profits [3].

• But SVB (2023) shows that unrealised losses can still trigger a deposit run. So RBI supervision must track interest-rate risk, not just credit risk.

• Government borrowing and crowding out:

• When the government borrows heavily, it sells more G-secs.
• Bond prices fall and yields, including the 10-year benchmark, rise.

• Companies then find it costlier to borrow and invest ("crowding out"). Fiscal consolidation (cutting the deficit step by step) works the other way and lowers borrowing costs.

• Investor protection and product design: retail investors in long, fixed-coupon bonds can suffer capital losses when rates rise. Instruments like Floating Rate Bonds, whose coupon resets with the market, and inflation-indexed bonds help spread this risk more fairly.

Related concepts

• Bonds
• Coupon rate
• Present value
• Capital gain
• Zero-coupon bond
• Floating rate bond
• Mark-to-market
• Yield curve
• Inverted yield curve
• Credit rating

Read more

• Bond basics: present value, coupon, yield and the yield curve