Introduction to Fixed income portfolio management Convexity strategies

1. Introduction to Fixed income portfolio management Convexity strategies Asset/Liability management (e.g., banks) Passive strategies: indexing immunization Finance 30233 Fall 2006 Associate Professor S. Mann The Neeley School at TCU

5. Example: The BillyBob Bank Simplified balance sheet risk analysis: Amount Duration PVBP Assets $100 mm 6.0 100,000,000 x 6.0 x 0.0001 = $60,000 Liabilities 90 mm 2.0 90,000,000 x 2.0 x 0.0001 = 18,000 Equity 10 mm ??? PVBP(E) = PVBP(A) – PVBP(L) = 60,000 – 18,000 = $42,000 Q: What is effective duration of equity? PVBP(E) = DE x VE x 0.0001 $42,000 = DE x ($10,000,000) x 0.0001 DE = $42,000/$1000 = 42.0

6. The BillyBob Bank, continued Simplified balance sheet risk analysis: Amount Duration PVBP Assets $100 mm 6.0 100,000,000 x 6.0 x 0.0001 = $60,000 Liabilities 90 mm 2.0 90,000,000 x 2.0 x 0.0001 = 18,000 Equity 10 mm 42.0 PVBP(E) = PVBP(A) – PVBP(L) = 60,000 – 18,000 = $42,000 Assume that the bank has minimum capital requirements of 8% of assets (bank equity must be at least 8% of assets) Q: What is the largest increase in rates that the bank can survive with the current asset/liability mix? A: Set 8% = E / A = ($10mm - $42,000 Dy) / (100mm – 60,000 Dy) and solve for Dy: 0.08 (100mm – 60,000 Dy ) = 10mm - 42,000 Dy $8 mm – 4800 Dy = 10mm - 42,000 Dy (42,000 – 4800) Dy = $2,000,000 Dy = $2,000,000/$37,200 = 53.76 basis points

7. Callability and Convexity - Callable bonds - Mortgages Negative Convexity Call Price Positive Convexity rates

8. Passive Bond portfolio management strategies - Assume market prices are correct (efficient market) - management is essentially risk management Indexing - track performance of benchmark index - Identify target risk (amount/type) - difficulties due to: index composition bond market liquidity Immunization - attempt to essentially eliminate risk - “immunize” against changes in interest rates

9. Guaranteed Investment Contract Liability Immunization