Chapter 4: Investing in Fixed Income Securities

Anatomy of Fixed Income Instruments

Fixed income securities represent contractual borrowing arrangements where the issuer promises to pay the investor periodic interest payments (coupons) over a specified duration and repay the principal amount (par value) at maturity:

Debt Instrument Building Blocks:
┌─────────────────────────────────────────────────────────────────────────────────┐
│ • Par (Face) Value: Nominal redemption value, standard ₹1,000 or ₹100,000       │
│ • Coupon Rate: Contractual annual interest percentage paid periodically         │
│ • Maturity Date: Date on which the principal borrowing is redeemed in full      │
│ • Frequency of Payment: Annual, semi-annual, quarterly, or cumulative           │
│ • Call / Put Options: Issuer early redemption right (Call) or investor put right│
└─────────────────────────────────────────────────────────────────────────────────┘

Determinants of Bond Safety: Credit Rating Framework

Unlike sovereign government debt which carries zero credit/default risk in domestic currency, corporate debentures carry credit risk—the probability that the corporate borrower fails to service timely coupon or principal commitments.

SEBI-registered Credit Rating Agencies (CRISIL, ICRA, CARE, India Ratings) assign standardized ratings:

Pricing and Valuation of Debt Instruments

The intrinsic value (fair market price $P_0$) of a fixed-rate bond is the sum of the discounted present values of all future cash flows (periodic coupon payments $C$ and terminal par value $M$), discounted at the investor's required rate of return ($r$):

$$P_0 = \sum_{t=1}^{n} \frac{C}{(1 + r)^t} + \frac{M}{(1 + r)^n}$$

Bond Price - Yield Inverse Seesaw:
   BOND PRICE (P)  ▲                  ▼  MARKET INTEREST RATE / YIELD (r)
                   │                  │
                   └───────[/\───────┘
  • When market interest rates RISE, existing bond prices FALL (trade at a DISCOUNT).
  • When market interest rates FALL, existing bond prices RISE (trade at a PREMIUM).

Yield Measures in Fixed Income Analysis

1. Coupon Rate: The stated annual nominal interest rate printed on the bond certificate:

$$\text{Coupon Rate} = \frac{\text{Annual Coupon Payment}}{\text{Face Value}}$$

2. Current Yield: Relates the annual coupon payment to the prevailing current market price of the bond:

$$\text{Current Yield} = \frac{\text{Annual Coupon Payment}}{\text{Current Market Price } (P_0)}$$

3. Yield to Maturity (YTM):
   • The internal rate of return (IRR) earned by an investor who purchases the bond at its current market price and holds it until final maturity, assuming all intermediate coupon cash flows are reinvested at an identical interest rate equal to the YTM.
   • It represents the single discount rate $y$ that equates the bond’s market price to the present value of its future cash flows:

$$P_0 = \sum_{t=1}^{n} \frac{C}{(1 + y)^t} + \frac{M}{(1 + y)^n}$$

Quantitative Measurement of Bond Price Volatility

When interest rates change, bond prices adjust. The magnitude of this price change depends on the bond’s term to maturity, coupon rate, and prevailing yield level.

                         ┌────────────────────────────────────────┐
                         │      Bond Volatility Measurement       │
                         └───────────────────┬────────────────────┘
                                             │
                    ┌────────────────────────┴────────────────────────┐
                    ▼                                                 ▼
┌───────────────────────────────────────┐         ┌───────────────────────────────────────┐
│           MACAULAY DURATION           │         │               CONVEXITY               │
│ Weighted average time until bond cash │         │ Measures the curvature of the price-  │
│ flows are received (measured in years)│         │ yield curve; corrects duration error  │
└───────────────────────────────────────┘         └───────────────────────────────────────┘

1. Macaulay Duration ($D_{\text{mac}}$)

Formulated by Frederick Macaulay in 1938, it measures the weighted average time (in years) an investor must wait to recover the bond's economic value:

$$D_{\text{mac}} = \frac{\sum_{t=1}^{n} \frac{t \times C_t}{(1 + y)^t}}{P_0}$$

• For a Zero-Coupon Bond, Macaulay Duration equals its exact time to maturity ($D_{\text{mac}} = n$).
• For a Coupon-Paying Bond, Macaulay Duration is always strictly less than its term to maturity ($D_{\text{mac}} < n$) because cash coupons are received prior to maturity.

2. Modified Duration ($D_{\text{mod}}$)

Measures the percentage change in bond price for a 100-basis-point (1%) change in Yield to Maturity:

$$D_{\text{mod}} = \frac{D_{\text{mac}}}{1 + y}$$

$$\frac{\Delta P}{P_0} \approx - D_{\text{mod}} \times \Delta y$$

Example: A corporate bond with a Modified Duration of 5.0 years will experience an approximate 5% decline in price if market interest rates rise by 100 bps (+1.0%), and an approximate 5% increase in price if interest rates drop by 100 bps (-1.0%).

3. Bond Convexity

Modified Duration provides a linear approximation of a non-linear (convex) price-yield curve. For large interest-rate shifts, Convexity ($CX$) provides the second-order adjustment:

$$\frac{\Delta P}{P_0} \approx - D_{\text{mod}} \times \Delta y + \frac{1}{2} CX (\Delta y)^2$$

Bonds with higher positive convexity exhibit greater price appreciation when interest rates drop, and smaller price depreciation when interest rates rise.