Immunization

An investor who must pay a fixed sum on a known future date faces two opposing interest-rate risks:

• Price risk — if rates rise, bonds held fall in value.
• Reinvestment risk — if rates fall, coupons received are reinvested at lower yields.

Immunization uses one to cancel the other. When rates fall, bond prices rise but coupons earn less on reinvestment. When rates rise, bond prices fall but coupons earn more. If the portfolio's Macaulay duration equals the time to the liability, the two effects roughly offset, and the value at that date is locked in.

The simplest version is a zero coupon bond maturing on the liability date.

The workbook's illustration needs ₹10,00,000 in 10 years, with rates at 10%.

• Zero coupon route: ₹10,00,000 ÷ 1.10¹⁰ = ₹3,85,543.30 today.
• Portfolio route: a bond portfolio with 7% annual coupon, face value ₹5,18,000, 20-year maturity and 10-year duration, costing ₹3,85,699.

Value at the end of year 10 under three rate scenarios:

In every scenario the target of ₹10 lakh is met. The fall in bond price is compensated by coupon reinvestment, and vice versa. The final value is somewhat higher when rates move, which the workbook attributes to duration overstating losses and understating gains.

Immunization condition:  Macaulay duration of portfolio = time horizon of liability

Zero coupon route:       Cost = Liability ÷ (1 + r)^n

Duration gap = Duration of assets − Duration of liabilities  (target: close to zero)

Illustrative figures, following the workbook's method. A family office has promised a ₹2 crore endowment to a medical college, payable in 10 years. Ten-year rates are 10%.

Option 1 — the zero. Buy a 10-year zero coupon bond: 2,00,00,000 ÷ 1.10¹⁰ ≈ ₹77.1 lakh today. No coupons, no reinvestment risk, duration exactly 10. If such a zero is available in the required size, this is theoretically perfect.

Option 2 — the portfolio. Long zeros are rarely available, so the manager builds a portfolio of coupon bonds whose weighted average Macaulay duration is 10 years — scaled up from the workbook's portfolio, roughly 20 times its ₹3.86 lakh cost. Every coupon received is reinvested at the prevailing rate.

Two years later rates fall to 8%. The portfolio's bonds have risen in price, but coupons are now being reinvested at 8%, not 10%. Its remaining duration has also drifted away from the remaining 8-year horizon. The manager must re-immunize: sell and buy bonds so duration once again matches the time left. That rebalancing is why the workbook says immunization involves some active management.

Chapter 19 (Fixed Income Portfolio Management Strategies), section 19.2.3, presents immunization with the zero coupon route and the three-scenario portfolio in Illustration 19.2 and Table 19.1; section 19.6 applies the idea to insurers and pension funds with 20–40-year liabilities through minimising the duration gap. The Chapter 19 caselet asks for the number of two bonds that give a 10-year duration for a ₹50 lakh fund.

• Match duration, not maturity — except with a zero coupon bond, where they are the same. The workbook's portfolio has a 20-year maturity and a 10-year duration.
• The workbook calls immunization passive and then says it is not. Section 19.2 lists it as one of three passive strategies (with buy and hold and indexing); the end of section 19.2.3 says it "is not a passive strategy like Buy and Hold" because duration must be readjusted whenever rates change. Both statements are in Chapter 19 — expect it grouped with passive strategies, and know why it needs rebalancing.
• Immunization offsets two risks against each other: price risk and reinvestment risk. It does not remove credit risk.
• Re-immunize when rates change, because duration and the remaining horizon drift apart.
• The Illustration 19.2 price (₹3,85,699) differs slightly from the zero's ₹3,85,543.30 — the workbook says this is only for ease of calculation.