B.02.BKM 16/Hull 7

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B.02.BKM 16/Hull 7
2012-05-09 18:55:35
bond duration convexity immunization

Managing Interest Rate Risk
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  1. 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
  2. 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)
  3. 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
  4. Convexity
    • D approximation always understates bd value
    • as C incr, bd appreciates more when y falls, depr less when yield rise
  5. Convexity of a callable bond
    • As value approaches call price, negative convexity
  6. 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
  7. 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
  8. 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
  9. 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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