Introduction to Fixed income portfolio management Convexity strategies

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

Example: The Billy. Bob Bank Simplified balance sheet risk analysis: Assets Amount $100 mm Duration 6. 0 Liabilities 90 mm 2. 0 Equity 10 mm ? ? ? PVBP 100, 000 x 6. 0 x 0. 0001 = $60, 000 90, 000 x 2. 0 x 0. 0001 = 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) x 0. 0001 DE = $42, 000/$1000 = 42. 0 18, 000

The Billy. Bob Bank, continued Simplified balance sheet risk analysis: Amount Assets $100 mm Liabilities 90 mm Equity 10 mm Duration 6. 0 2. 0 42. 0 PVBP 100, 000 x 6. 0 x 0. 0001 = $60, 000 90, 000 x 2. 0 x 0. 0001 = 18, 000 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 = ($10 mm - $42, 000 Dy) / (100 mm – 60, 000 Dy) and solve for Dy: 0. 08 (100 mm – 60, 000 Dy ) $8 mm – 4800 Dy (42, 000 – 4800) Dy Dy = 10 mm - 42, 000 Dy = $2, 000, 000/$37, 200 = 53. 76 basis points

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

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

Guaranteed Investment Contract Liability Immunization