FFIEC Capital Markets Conference

1. FFIEC Capital Markets Conference Portfolio Management and Theory Steve Mandel May 18-19, 2004

2. Portfolio Management Tools Nominal Yield/Risk Measures Effective Yield/Risk Measures Return Attribution Security Level Portfolio Level Portfolio vs. Liabilities Optimization Scenario Analysis

3. Nominal Yield/Risk Measures • Nominal Yield Measures • Current Yield • Yield (to Maturity, to Worst) • Spread to Benchmark • Spread to Yield Curve • Nominal Risk Measures • Years to Maturity (Average Life) • Nominal Duration (Macaulay, Modified) • Nominal Convexity

5. Nominal Yield Measures • Current Yield FHLB 4.25 11/15/2010 Price (2/29/2004) = 103.369 Current Yield = 4.111%

6. Nominal Yield Measures • Yield to Maturity – The discount rate at which the present value of the cash flows equals the full price of the bond.

7. Yield to Maturity

8. Nominal Yield Measures • Spread to Benchmark - The difference between the yield of a security and the yield of a corresponding benchmark security stated in basis points (1 bp=.01%) The benchmark is typically an On-the-Run Treasury closest to the maturity of the security (or average life for an amortizing security)

9. Nominal Yield Measures • Spread to Benchmark (Continued) Benchmark Security: US 5 2/15/2011 Yield of Bond:3.68 Yield of Benchmark Security: 3.47 Spread to Benchmark: 0.21 (21basis points)

10. Nominal Yield Measures • Spread to Yield Curve - The difference between a security’s yield and the interpolated point on the yield curve corresponding to the security’s average life, stated in basis points (1 bp=.01%) • On-The-Run Treasury Curve • Off-The-Run Treasury Model Curve • Swap Curve

12. Nominal Yield Measures • Spread to On-the-Run Treasury Yield Curve • Yield Curve: On-The-Run Tsy (2/27/2004) • Average Life of Security: 6.71 • Interpolated Point on Yield Curve: 3.302 • Yield of Security: 3.678 • Spread to Yield Curve:100x(3.68-3.30)=38bp

14. Yield Curves (2/27/2004)A -Treasury On-the-Run, B - Treasury Off-the-Run

15. Nominal Yield Measures • Spread to Off-the-Run Treasury Yield Curve • Yield Curve: Off-The-Run Tsy (2/27/2004) • Average Life of Security: 6.71 • Interpolated Point on Yield Curve: 3.442 • Yield of Security: 3.678 • Spread to Yield Curve:100x(3.68-3.44)=24bp

16. Yield Curves (2/27/2004)A -Tsy On-the-Run, B - Tsy Off-the-Run, C - Swap

17. Nominal Yield Measures • Spread to Swap Yield Curve • Yield Curve: Swap (2/27/2004) • Average Life of Security: 6.71 • Interpolated Point on Yield Curve: 3.820 • Yield of Security: 3.678 • Spread to Yield Curve:100x(3.68-3.82)= -14bp

18. Nominal Risk Measures • Years to Maturity (Average Life): 6.71 • Macaulay Duration - Percentage change in Price for a percentage change in Yield. (Average life of PV of Cash Flows)

19. Macaulay Duration

20. Nominal Risk Measures • Years to Maturity • Macaulay Duration • Modified Duration - Percentage change in Price for a 100 basis point change in Yield. The tangent (first derivative) of the price/yield curve for a given yield. Modified Duration = 5.851/(1+3.678/200) = 5.746

21. Modified Duration

22. Nominal Risk Measures • Years to Maturity • Macaulay Duration • Modified Duration • Nominal Convexity - measures the degree to which the price/yield curve of a security differs from the tangent at the current yield.

23. Portfolio Management Tools Nominal Yield/Risk Measures Effective Yield/Risk Measures Return Attribution Security Level Portfolio Level Portfolio vs. Liabilities Optimization Scenario Analysis

24. Effective Yield/Risk Measures • Effective Yield Measures • OAS • Yield Curve Margin* • Effective Risk Measures • Effective Duration • Partial Durations • Effective Convexity • Spread Duration • Volatility Duration • Prepay Duration

25. Effective Yield Measures • Option Adjusted Spread OAS • A security’s spread (in basis points) over the yield curve, after adjusting for the probability of any optional calls, puts, or prepayments and assuming a volatility (or set of volatilities) of future yields. • The spread over the yield curve’s forward rates (multiple rate paths are considered) that makes the present value of the cash flows equal to the full price.

26. Option Adjusted Spread (OAS) • Bonds Without Embedded Options – OAS is not dependent on volatility and will be close to nominal spread (small difference due to the shape of the yield curve). OAS depends on Price and Yield Curve • Bonds With Embedded Options – OAS will depend on Price, Yield Curve and the volatility assumption. For callable bonds and mortgages the higher the volatility assumption the lower the OAS.

29. Effective Yield Measures • Yield Curve Margin – OAS assuming a zero volatility. The spread over the yield curve’s forward rates that makes the present value of the cash flows equal to the full price. • Option Cost = Yield Curve Margin – OAS

30. Effective Risk Measures • Effective Duration • A measure of the sensitivity (percent change) of the Full Price of a security to a (100 bp) parallel shift of the Yield Curve. • Utilized to measure a security’s price sensitivity to a change in the general level of interest rates.

33. Effective Duration Calculation

34. Effective Risk Measures • Effective Duration • Partial Duration - A measure of the sensitivity (percent change) of the full price of a security to a move in a single “key rate” point of the Yield Curve. Utilized to measure a security’s sensitivity to a particular reshaping of the Yield Curve

37. Partial Duration Calculation • Partial Duration (5Year)

38. Effective Risk Measures • Effective Duration • Partial Duration • Effective Convexity - measures the degree to which the price/parallel-shift curve of a security differs from the tangent at the current curve. A measure of the sensitivity of the Effective Duration of a security to a parallel shift of the Yield Curve so as to measure the sensitivity of price to “large” rate moves.

39. Effective Convexity • Positive Convexity implies P/Y curve is above tangent. • Effective Duration goes up as rates come down. • P/Y curve gets steeper as rates come down. • Negative convexity implies P/Y curve falls below tangent. • Effective Duration goes down as rates come down. • P/Y curve flattens as rates come down.

40. Effective Convexity Calculation

42. Effective Risk Measures • Effective Duration • Partial Duration • Effective Convexity • Volatility Duration - A measure of the sensitivity (percent change) of the full price of a security to changes in Volatility.

44. Term Structure of Volatilities

45. Volatility Durations

46. Effective Risk Measures • Effective Duration • Partial Duration • Effective Convexity • Volatility Duration • Pre Pay Duration - The sensitivity of a (mortgage) security’s full price to changes in Prepayment Rates

47. Prepay Durations

48. Portfolio Management Tools Nominal Yield/Risk Measures Effective Yield/Risk Measures Return Attribution Security Level Portfolio Level Portfolio vs. Liabilities Optimization Scenario Analysis

49. Portfolio Risk Measures • The Portfolio Risk Measures are analogous to the Security Measures in that they are measures of the sensitivity (percent change) of a Portfolio’s Market Value to various market changes. • They are calculated by taking a Market Weighted Average of the Individual Security Risk Measures.

50. Portfolio Risk Measures • Effective Duration - A measure of the sensitivity (percent change) of the Market Value of a Portfolio to a parallel shift in the Yield Curve. • The Market Weighted Average of the individual securities Effective Durations