X-A chapters / Module 3: Investment Products
Chapter 9. Investing in Fixed Income Securities
How bonds are priced and measured, the money market, government and corporate debt markets, and India's small saving instruments.
Chapter 9 – Part A · 46 min
Chapter 9 – Part B · 13 min
Total watch time 59 min · Hindi audio
Key topics
- Bond features and risks
- Bond pricing and yield measures (CY, YTM, clean/dirty price)
- Yield curve and duration
- Money market, G-Secs and corporate debt
- Small savings schemes: FRSB, SCSS, SSA, KVP
Chapter test
25 multiple-choice questions with explanations. Score 60% or more to complete this chapter.
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Take the testFormulas in this chapter (8)
Full formula sheet →Bond price (discounted cash flow)
Ch 9.4Price = Σ Coupon ÷ (1 + y)ᵗ + Face value ÷ (1 + y)ⁿ
Excel: PV(ytm, n, −coupon, −face)
- Example →
- 10% annual coupon, face ₹100, 5 years, YTM 8% → 10 × 3.9927 + 100 × 0.6806 = ₹107.99 (premium, since coupon > YTM).
- Trap →
- With semi-annual coupons use n = 10, y = 4%, coupon ₹5 → ₹108.11. Questions forget to halve the rate and coupon.
Coupon (nominal) yield
Ch 9.5Coupon yield = Annual coupon ÷ Face value
- Example →
- Coupon ₹8.24 on face ₹100 → 8.24%.
- Trap →
- Using the market price in the denominator gives the current yield, not the coupon yield.
Current yield
Ch 9.5Current yield = Annual coupon ÷ Current market price
- Example →
- Coupon ₹8.24, price ₹103 → 8.00%.
- Trap →
- Current yield ignores the capital gain or loss to maturity; that's why YTM differs from it.
Yield to maturity (YTM)
Ch 9.5Solve Price = Σ CFₜ ÷ (1 + YTM)ᵗ
Excel: RATE(n, coupon, −price, face) · YIELD(settle, maturity, rate, price, redemption, freq, basis)
- Example →
- G-Secs pay semi-annually: freq = 2. YTM is the bond's IRR.
- Trap →
- YTM assumes every coupon is reinvested at the YTM, which rarely happens. Don't use annual frequency for a semi-annual bond.
Price, yield and coupon relationship
Ch 9.4Par: Coupon = CY = YTM · Discount: Coupon < CY < YTM · Premium: Coupon > CY > YTM
- Example →
- Market rate 9%, coupon 8% → bond sells at a discount, with YTM 9% > current yield > 8% coupon.
- Trap →
- Questions reverse the ordering. Remember: price and yield move in opposite directions.
Macaulay duration
Ch 9.7Macaulay duration = Σ [t × PV(CFₜ)] ÷ Bond price
- Example →
- A 5-year zero-coupon bond has a Macaulay duration of exactly 5 years.
- Trap →
- 'Duration equals maturity for all bonds' is wrong; only for zero-coupon bonds. Coupon bonds have duration below maturity.
Modified duration
Ch 9.7Modified duration = Macaulay duration ÷ (1 + periodic yield) · % price change ≈ −ModDur × Δy
- Example →
- Macaulay duration 6.50, YTM 8% → 6.50 ÷ 1.08 = 6.02, so the price falls about 6.02% if yield rises 1%.
- Trap →
- With semi-annual compounding divide by (1 + y/2), not (1 + y).
Clean vs dirty price
Ch 9.5Dirty (invoice) price = Clean price + Accrued interest
- Example →
- Clean price ₹102 + accrued interest ₹1.50 → dirty price ₹103.50. Markets quote clean; trades settle at dirty.
- Trap →
- Yield formulas use the clean price, not the dirty price.