Bond Portfolio Management. Term Structure Yield Curve Expected return versus forward rate Term structure theories Managing bond portfolios Duration Convexity Immunization and trading strategy. Overview of Term Structure. The relationship between yield to maturity and maturity.
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1). Pure yield curve; 2). on-the-run yield curve (page 485)
1-year rate is 5%, 2-year rate is 6%, 3-year rate is 7%, 4-year rate is 8%. Compute the yield to maturity of a 3-year coupon bond with a coupon rate of 10%.
fn = one-year forward rate for period n
yn = yield for a security with a maturity of n
4 yr = 8.00% 3yr = 7.00% f4 = ?
Zero-Coupon RatesBond Maturity
1yr Forward Rates
1yr= = 0.115006
2yrs= = 0.102567
3yrs= = 0.063336
4yrs= = 0.063008
See page 516-517.
Price change is proportional to duration and not to maturity.
P/P = -D x [(1+y) / (1+y)
D* = modified duration
D* = D / (1+y)
P/P = - D* x y
Rule 1 The duration of a zero-coupon bond equals its time to maturity.
Rule 2 Holding maturity constant, a bond’s duration is higher when the coupon rate is lower.
Rule 3 Holding the coupon rate constant, a bond’s duration generally increases with its time to maturity.
Rule 4 Holding other factors constant, the duration of a coupon bond is higher when the bond’s yield to maturity is lower.
Rules 5 The duration of a level perpetuity is equal to: (1+y) / y
Correction for Convexity:
Which bond does you prefer?
Negative convexity: page 526; mortgage has the similar feature (page 526, 528)
Duration of assets = Duration of liabilities
Holding Period matches Duration
Yield to Maturity %
1.5 1.25 .75
3 mon 6 mon 9 mon