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Reading 1CFA L3 FIFull chapter

Liability-driven and active fixed-income

In this chapter: Single liability immunisation · Multiple liability matching · Cash-flow matching · Active strategies — duration, curve, sector, selection

~3 min readLayer 4 · Professional CertificationsFree

For pension/insurance/structured products, fixed income must match liabilities. For active managers, FI offers multiple alpha sources beyond duration.

Foundation

**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.

Deep Dive

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.

Advanced

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.

Regulatory references
  • IRDAI ALM Regulations
  • CFA Institute FI curriculum
  • RBI Bond Market Regulations
Common mistakes & pitfalls
  • 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?
Higher convexity protects against parallel shifts. Trade-off: more vulnerable to curve twists.
Can immunisation fully eliminate risk?
No. Risks remain: yield curve shape changes, credit risk, reinvestment risk for coupon bonds.

Practice questions

Click each question to reveal the answer and explanation.

Q 1
Single-liability immunisation requires matching:
  1. (a)Maturity only
  2. (b)Duration and PV
  3. (c)Coupon rate
  4. (d)Yield only
Correct: (b) Duration and PV
Match duration (interest-rate sensitivity) and PV (amount).
Q 2
Higher convexity is preferred because:
  1. (a)Increases yield
  2. (b)Protects against rate shocks
  3. (c)Reduces duration
  4. (d)Eliminates risk
Correct: (b) Protects against rate shocks
Positive convexity provides asymmetric protection against parallel rate shocks.
Q 3
Barbell vs bullet:
  1. (a)Barbell has lower duration
  2. (b)Barbell higher convexity
  3. (c)Both equal
  4. (d)Bullet has higher convexity
Correct: (b) Barbell higher convexity
Barbell (long + short maturities) has higher convexity than bullet (concentrated middle).
Q 4
Spread duration measures sensitivity to:
  1. (a)Rate change
  2. (b)Credit spread change
  3. (c)Currency
  4. (d)Inflation
Correct: (b) Credit spread change
Spread duration = price sensitivity to credit-spread change. Important for corporate bonds.
Q 5
Cash-flow matching is:
  1. (a)Probabilistic
  2. (b)Explicit dedication of bonds to liability dates
  3. (c)Index-based
  4. (d)Active
Correct: (b) Explicit dedication of bonds to liability dates
CFM: bonds chosen to mature exactly when liability due. Eliminates timing risk.
Educational purposes only. The numbers, returns, and examples used in this lesson are illustrative. Past performance does not guarantee future results. Mutual fund and securities investments are subject to market risks. This lesson is not investment advice; for advice tailored to your circumstances, consult a SEBI-registered Investment Adviser. Read our full disclaimer.