Introduction to Interest Rates, Interest Rate Instruments and the Fixed Income Market

1Interest rates and what drives them

An interest rate is the price of money: what a borrower pays a lender for the use of money over time, usually quoted as a percentage per year. It compensates the lender for time (giving up current use), inflation (lost purchasing power) and risk (the chance of not being repaid).

• The nominal rate is the quoted rate. The real rate is roughly the nominal rate minus inflation: a 7% deposit with 5% inflation earns a real return of about 2%.
• The risk-free rate is the return on a borrower with no default risk. In India this is taken from Government of India securities, because the government can always pay in its own currency. Treasury bill yields are used for short periods and dated G-sec yields for longer periods.
• Other borrowers pay a spread (credit spread) over the risk-free rate for the extra risk they carry.

Rates are driven by the central bank's policy (the RBI's repo rate is the anchor for short-term rates), inflation and inflation expectations, government borrowing, credit demand, liquidity in the banking system and global rates.

Example If the RBI raises the repo rate, short-term money market rates usually rise first; bond yields across maturities then adjust to the new expectations.

Remember

• Interest = reward for time, inflation and risk.
• Real rate ≈ nominal rate − inflation.
• Risk-free benchmark in India = Government of India securities.

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2Fixed income securities and how they are classified

A bond (or debenture) is a loan in tradable form: the issuer borrows money and promises coupon (interest) payments and repayment of the face (par) value on the maturity date. Key features: face value, coupon rate, coupon frequency, maturity, and any call or put option.

Ways to classify bonds:

• By issuer: central government (G-secs, Treasury bills), state governments (State Development Loans, SDLs), public sector undertakings, banks and financial institutions, and companies (corporate bonds, commercial paper).
• By maturity: money market instruments (up to one year, such as T-bills, commercial paper and certificates of deposit) and longer-term bonds.
• By coupon:
  • Fixed-rate bonds pay the same coupon throughout.
  • Floating-rate bonds reset the coupon to a benchmark plus a spread, so their price stays close to par.
  • Zero-coupon bonds pay no coupon; they are issued at a discount and repaid at par. Treasury bills work this way.
  • Inflation-indexed bonds link the principal or coupon to an inflation index.
• By embedded option:
  • A callable bond lets the issuer repay early, usually when rates fall, which hurts the investor.
  • A putable bond lets the investor demand early repayment.
• STRIPS (Separate Trading of Registered Interest and Principal of Securities) split a G-sec into separate zero-coupon pieces for each coupon and for the principal.

Exam trap A Treasury bill pays no coupon. The investor's return is the difference between the discounted issue price and the face value received at maturity.

Remember

• Coupon is paid on face value, not on the market price.
• Zero-coupon = issued at a discount, redeemed at par.
• Floaters carry little interest rate risk because the coupon resets.

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3Equity versus debt

A company's cost of debt is usually lower than its cost of equity because lenders take less risk. Interest is also tax-deductible for the company.

Remember

• Bondholders rank ahead of shareholders.
• Debt return is contractual; equity return is residual.

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4Yield curve and the term structure of interest rates

The term structure of interest rates is the relationship between yields and maturity for bonds of the same credit quality (normally government bonds). Drawn as a graph, it is the yield curve.

• Normal (upward-sloping): longer maturities yield more. This is the usual shape.
• Inverted (downward-sloping): short rates are above long rates, often when markets expect rates to fall, for example ahead of a slowdown.
• Flat: yields are similar across maturities.
• Humped: medium maturities yield the most.

Three theories explain the shape:

1. Expectations theory: long-term rates reflect the market's expectation of future short-term rates. An upward slope means rates are expected to rise.
2. Liquidity preference theory: investors want a premium for locking money away longer, so the curve tends to slope upwards even if rates are not expected to rise.
3. Market segmentation theory: different investors keep to different maturity segments (banks short, insurers and pension funds long), so each segment's yield is set by its own demand and supply.

Spot rates are yields on zero-coupon bonds for each maturity. They can be derived from coupon bond prices step by step, a method called bootstrapping. Forward rates are the rates for a future period implied by today's spot rates.

Example If the 1-year spot rate is 6% and the 2-year spot rate is 7% (annual compounding), the implied 1-year rate starting in one year is (1.07² ÷ 1.06) − 1 ≈ 8.0%.

Remember

• Same credit quality, different maturities.
• Normal curve slopes up; inverted slopes down.
• Expectations, liquidity preference and segmentation are the three theories.

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5Compounding, day counts and accrued interest

Compounding frequency changes the effective return. A rate of r% compounded n times a year gives an effective annual rate of (1 + r/n)ⁿ − 1. More frequent compounding means a higher effective rate. With continuous compounding, it is eᴿ − 1.

Example 8% a year paid half-yearly gives (1.04)² − 1 = 8.16% effective. Indian G-secs pay coupons half-yearly.

Day count conventions decide how many days of interest have built up:

• 30/360: every month counts as 30 days and the year as 360 days. It is used for Government of India dated securities.
• Actual/365 or Actual/Actual: actual days elapsed. SEBI has standardised Actual/Actual for corporate bonds.
• Treasury bill yields are calculated on a 364-day year: Yield = (Face − Price) ÷ Price × 364 ÷ days to maturity.

Bonds trade between coupon dates, so the buyer pays the seller the interest earned since the last coupon: the accrued interest.

• Clean price: the quoted price, without accrued interest.
• Dirty (full, invoice) price = clean price + accrued interest. This is the amount the buyer actually pays.

Example A G-sec with a 7.2% coupon and ₹100 face value last paid interest 60 days ago (30/360). Accrued interest = 7.2 × 60 ÷ 360 = ₹1.20 per ₹100. If the clean price is ₹99.50, the buyer pays ₹100.70.

Remember

• Dirty price = clean price + accrued interest.
• G-secs: half-yearly coupons, 30/360.
• T-bill yield uses a 364-day year.

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6Bond pricing and yield measures

A bond's price is the present value of all its future cash flows (coupons and principal), discounted at the market's required yield:

Price = C ÷ (1+y) + C ÷ (1+y)² + … + (C + Face) ÷ (1+y)ⁿ

This gives the most important rule in the module: bond prices move opposite to yields. If market yields rise, the fixed coupons are worth less, so the price falls.

• If the coupon rate equals the yield, the bond trades at par.
• If the coupon is above the yield, it trades at a premium (above par).
• If the coupon is below the yield, it trades at a discount (below par).

Yield measures:

• Coupon rate: coupon ÷ face value.
• Current yield: annual coupon ÷ current market price. It ignores the gain or loss to maturity.
• Yield to maturity (YTM): the single discount rate that makes the present value of all cash flows equal to the price. It is the bond's internal rate of return if held to maturity, and it assumes coupons are reinvested at the YTM.
• Yield to call: the same calculation assuming the issuer calls the bond at the first call date.

Example A ₹100 bond with an 8% annual coupon trades at ₹95. Current yield = 8 ÷ 95 = 8.42%. Its YTM is higher still, because the investor also gains ₹5 when the bond is repaid at par.

Remember

• Price and yield move in opposite directions.
• Premium bond: coupon > YTM. Discount bond: coupon < YTM.
• YTM assumes reinvestment at the same yield and holding to maturity.

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7Duration, convexity and PVBP

Interest rate risk is the risk that bond prices fall when rates rise. Its size depends on maturity and coupon: longer maturity and lower coupon mean higher sensitivity. A zero-coupon bond is the most sensitive for its maturity.

Macaulay duration is the weighted average time (in years) to receive the bond's cash flows, weighted by the present value of each cash flow.

• A zero-coupon bond's duration equals its maturity.
• A coupon bond's duration is less than its maturity.
• Duration rises with maturity and falls as the coupon or the yield rises.

Modified duration = Macaulay duration ÷ (1 + y/n), where n is the number of coupon payments a year. It gives the approximate percentage price change for a 1 percentage point change in yield:

% change in price ≈ − Modified duration × change in yield

Example A bond with a modified duration of 6 falls by about 6 × 0.5 = 3% if yields rise by 0.50 percentage points (50 basis points).

Convexity measures the curvature of the price-yield relationship. Duration gives a straight-line estimate. For an ordinary (option-free) bond, convexity means the price rises more when yields fall than it drops when yields rise by the same amount. Higher convexity is good for the holder. Duration alone underestimates the price after a large yield change either way.

PVBP (price value of a basis point, also called DV01) is the change in a bond's price for a 1 basis point (0.01%) change in yield:

PVBP ≈ Modified duration × Price × 0.0001

Example A ₹1 crore position in bonds with a modified duration of 5 has a PVBP of 5 × 1,00,00,000 × 0.0001 = ₹5,000 per basis point.

Remember

• Longer maturity, lower coupon, lower yield → higher duration.
• Modified duration → % price change for a 1% yield change.
• PVBP = rupee change per 1 basis point.
• Convexity: the gain from a fall in yield exceeds the loss from an equal rise.

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8India's debt market: primary and secondary

The Reserve Bank of India manages the borrowing of the central and state governments.

• Primary market: G-secs and T-bills are sold through auctions on the RBI's E-Kuber platform. In a uniform price (Dutch) auction, all successful bidders pay the same cut-off price. In a multiple price (French) auction, each pays its own bid price. Small investors can bid non-competitively and receive the cut-off price, including through RBI Retail Direct.
• Primary dealers are RBI-registered entities that underwrite government auctions and make markets in G-secs.
• Treasury bills are issued for 91, 182 and 364 days. Cash management bills are very short-term bills that meet temporary government cash needs.
• Secondary market: G-secs trade mainly on the RBI's anonymous electronic order-matching platform, NDS-OM, and over the counter. Trades are cleared and settled through the Clearing Corporation of India (CCIL), which acts as the central counterparty. Normal settlement is T+1.
• Corporate bonds are issued through public issues or private placements on the exchanges' electronic bidding platforms. OTC trades must be reported and settled through the exchange clearing corporations.
• Main investors include banks (for statutory liquidity ratio holdings), insurers, provident and pension funds, mutual funds, primary dealers, foreign portfolio investors and, increasingly, retail investors.

Exam trap NDS-OM is the RBI's trading platform for government securities. CCIL is the clearing corporation that guarantees settlement. Don't mix up the two.

Remember

• RBI runs G-sec and T-bill auctions; primary dealers underwrite them.
• Secondary G-sec trading: NDS-OM, cleared by CCIL.
• T-bills: 91, 182 and 364 days.

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