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Relationship btwn bd price & yield
- bd price & yield are inversly related
- incr in y leads to smaller chg in P than same size decr
- as term inc, price more sensitive to chg in y
- sensitivity of price incr at decr rate as maturity incr
- lower coupon bds are more sensitive to chg in y
- sensitivity of bd price to yield inversly related to y
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Duration
- measures avg maturity of financial instrument's CF
- used to (1) summarize avg maturity (2) immunize pf (3) measure int rate sensitivity
 - D* = D / (1 + y/k)
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Properties of Duration
- duration of zero-coupon bd = time to maturity
- D decr as coupon rate incr
- D generally incr as maturity incr
- D incr as ytm decr
- D perpetuity = (1 + y) / y
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Convexity of a callable bond
- As value approaches call price, negative convexity
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Immunization
- passive mgt strategy
- create pf w duration = investment horizon
- due to convexity, this produces a surplus
- (-) once duration changes, requires rebalancing
- (-) based on D -> assumes flat yield curve
- (-) only effective for parallel shifts in yield curve
- (-) inappropriate in inflationary environment
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Cash Flow Matching / Dedication
- Passive mgt strategy
- CF matching: buy zero-coupon which matches future obligations
- Dedication: CF matching over multiple periods
- (+) automatically immunizes pf from chg in int rate
- (+) no rebalancing
- (-) hard to implement -> strong constraints on selectable bds
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Contingent immunization
- mix of active and passive mgt strategies
- start w active until reaches trigger point
- if active threatens ability to meet obligations, switch to passive
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Tools to modify pf duration
- Mortgage Backed Securities: diff tranches have diff durations
- Swaps: can transform fix into floating or vice versa
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