Chapter 5 Bond Management.

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Presentation transcript:

Chapter 5 Bond Management

A. The term structure of interest rates ---Term to Maturity vs. YTM (A) The expectation theory, Fisher 1896 If  Arbitrage buy long-term bond yield  P    Arbitrage sell long-term bond yield  P  

(B) The Liquidity Preference Theory,Hicks 1946 YTM Yield with liquidity premium Yield without liquidity premium N

(C) Market Segmentation Theory, Gulberson 1957

(D) CIR Theory, 1979 Cox, Ingersoll and Ross

B. Fixed-Income Portfolio Management 1. Duration the weighted average of the times to each coupon or principal payment made by the bond

B. Fixed-Income Portfolio Management (1) Macaulay's Duration, 1938 Macaulay (MD) MD=1{[C1/(1+Y)]/P0}+2{[C2/(1+Y)2]/P0} +...+T{[(CT+F)/(1+Y) ]/P0} = {[tCT/(1+Y) ]+[FT/(1+Y) ]}/P0

B. Fixed-Income Portfolio Management (2) Duration vs. Interest rate sensitivity MD= ―(ΔP/P)/[ΔYTM/(1+YTM)]

B. Fixed-Income Portfolio Management (3) Bond Rules a. The duration of a zero-coupon bond equals its time to maturity < Proof >: MD = / P0 = T(P0/ P0) =T

B. Fixed-Income Portfolio Management b. Holding time to maturity and YTM constant, a bond's duration and interest rate sensitivity are higher when the coupon rate is lower i.e. MD/i<0

B. Fixed-Income Portfolio Management c. Holding the coupon rate constant, a bond's duration and interest rate sensitivity generally increase with its time to maturity i.e. MD/t >0

B. Fixed-Income Portfolio Management d. Holding other factors constant,the duration and interest rate sensitivity of a coupon bond are higher when the bond's yield to maturity is lower i.e. MD/YTM < 0 e. The duration of a level perpetuity is (1+YTM)/YTM

B. Fixed-Income Portfolio Management 2. Immunization: strategies used by investors to shield their overall financial status from exposure to interest rate fluctuations  Rebalancing portfolio As interest rates and asset durations change, a manager must rebalance the portfolio of fixed income assets continually to realign its duration with the duration of the obligation

B. Fixed-Income Portfolio Management Single bond, Single payment [Immunization rule] MD of the bond = MD of the liability Bond portfolio, Single payment [Immunization rule] Weighted Average MD of the bond portfolio = MD of the liability