Liability-driven and active fixed-income
In this chapter: Single liability immunisation · Multiple liability matching · Cash-flow matching · Active strategies — duration, curve, sector, selection
For pension/insurance/structured products, fixed income must match liabilities. For active managers, FI offers multiple alpha sources beyond duration.
**Single liability immunisation**: - Match Macaulay duration of bond portfolio to liability horizon. - Match present value of assets to PV of liability. - Convexity should be slightly higher than liability for protection. - Rebalance as duration drifts (passage of time + yield changes). **Multiple liability matching**: - Bullet (concentrated maturity) vs barbell (long + short, no middle). - Cash-flow matching: explicit dedication of bonds to each liability. - Combination: immunisation + cash-flow. **Active strategies**: 1. **Duration**: take duration view ahead/behind benchmark. 2. **Curve**: bullet/barbell shifts based on curve view. 3. **Sector rotation**: corporate vs sovereign vs MBS. 4. **Security selection**: undervalued issues within sector. 5. **Credit**: spread tightening expected. 6. **Currency**: international FI hedge decisions.
Convexity matters because: - Duration-matched portfolio loses if rates change (positive convexity protects). - Liability convexity ≈ 0 if cash-flow lump sum, much higher if multi-period payouts. - Insurance: GMxB obligations have negative convexity in equity drops. Key rate duration: - Decompose duration into sensitivity to changes at specific points on curve. - 1Y, 5Y, 10Y, 30Y rate exposures. - Allows curve-shape immunisation, not just parallel shifts. Butterfly trade: long wing maturities, short body. Profits from curve curvature change. Or reverse. Corporate vs sovereign: - Spread = corp yield – sovereign yield same maturity. - Drives credit-spread risk + default risk. - Spread duration: sensitivity of price to spread change.
L3 essay: "Pension fund has ₹1,000 cr liability in 10 years. Recommend immunisation strategy." 1. Calculate liability PV and duration. PV = 1,000/(1+r)^10. Duration = 10 years. 2. Build asset portfolio with same duration + PV. 3. Bullet 10y bonds easiest; barbell (5y + 30y) higher convexity. 4. Rebalance when duration mismatch >0.5y or yield changes materially. 5. Monitor reinvestment risk — coupon income may not earn assumed rate. 6. Stress test: rate shocks, credit events.
- IRDAI ALM Regulations
- CFA Institute FI curriculum
- RBI Bond Market Regulations
- Duration matching without convexity check.
- Ignoring twist risk — barbell underperforms bullet if curve flattens.
- Reinvestment risk on coupon-paying immunisation.
Frequently asked
Why barbell over bullet?
Can immunisation fully eliminate risk?
Practice questions
Click each question to reveal the answer and explanation.
Q 1Single-liability immunisation requires matching:- (a)Maturity only
- (b)Duration and PV
- (c)Coupon rate
- (d)Yield only
- (a)Maturity only
- (b)Duration and PV
- (c)Coupon rate
- (d)Yield only
Q 2Higher convexity is preferred because:- (a)Increases yield
- (b)Protects against rate shocks
- (c)Reduces duration
- (d)Eliminates risk
- (a)Increases yield
- (b)Protects against rate shocks
- (c)Reduces duration
- (d)Eliminates risk
Q 3Barbell vs bullet:- (a)Barbell has lower duration
- (b)Barbell higher convexity
- (c)Both equal
- (d)Bullet has higher convexity
- (a)Barbell has lower duration
- (b)Barbell higher convexity
- (c)Both equal
- (d)Bullet has higher convexity
Q 4Spread duration measures sensitivity to:- (a)Rate change
- (b)Credit spread change
- (c)Currency
- (d)Inflation
- (a)Rate change
- (b)Credit spread change
- (c)Currency
- (d)Inflation
Q 5Cash-flow matching is:- (a)Probabilistic
- (b)Explicit dedication of bonds to liability dates
- (c)Index-based
- (d)Active
- (a)Probabilistic
- (b)Explicit dedication of bonds to liability dates
- (c)Index-based
- (d)Active