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first a note on yield curve implications for coupon bond valuation
- suppose zeroes of term [.5,1.1.5,2] years yield [5%,5.5%,5.6%,6%].
What the equilibrium price of a 2 year 10% coupon bond that makes
semi-annual payments?
- half year yields:
k6 = (1+k12)^(6/12) - 1
- = [2.44948974, 2.54950976, 2.56904652, 2.64575131]
- cash flows per 6 month period = 5,5,5,105
- PV of these cash flows at these discount rates
- = [4.88045379, 4.75447784, 4.63362677, 94.5856794]
- bond price today is the sum of these present values
= 108.854238
- moral: present values computed at yield curve rates and not at constant rate
the repo dealer
- active bond managers make use of repo dealers because these dealers
stand to lend and borrow treasuries
- in each roundtrip transaction with the repo dealer you will incur
his spread as a transaction cost. the spread is referred to as the dealer's
"hair cut" because it is very thin.
- a typical bond strategy of long A and short B goes like this:
- 1. borrow cash from the repo dealer and buy A in the market
- 2. lend A to the repo dealer for the term of the strategy to offset
the cash borrowed ("hair cut" cost)
- 3. post margin cash with dealer and borrow B
- 4. sell B in the market
- to close out the strategy
- collect A from the dealer and sell in the market paying the dealer
cash plus haircut
- buy B in the market and deliver to the repo dealer
- receive cash (less haircut) for B from the dealer
yield curve strategy- currently the spread between 30-year and 2-year treasuries is 100 bp and stephanie expects that the yield curve will become steeper in the coming months.
- she wishes to profit from this forecast without taking interest rate risk
- the strategy will gain if the curve steepens and lose if it flattens but should have no response to changes in interest rate levels without a slope change
- her strategy is to long the short and short the long
- to protect herself from interest rate risk she makes these trades in amounts that are inversely proportional to the dP value of these bonds
- the dP value is derived from the P/k elasticity of the bonds:
- recall: D = (dP/P)/((dk/(1+k)), so dP = D*P*dk/(1+k)
- example: P2 = 91, P30 = 100, D2 = 2, D30 = 15, k2=5%, k30=6%
- dP2 = 2*91*.01/1.05 = 1.73, dP30 = 15*100*.01/1.06 = 14.15
- the ratio = 14.15/1.73 = 8.16
- so if she goes long $1 million in 30-year bonds she should short about $8 million in 2-year notes
- now she can profit from yield curve steepening but is immunzied against parallel shifts in the yield curve
- stephanie is "exposed" because a flattening of the yield curve could wipe her out. this is the nature of active strategies.
using strips to leverage price appreciation- consider the 30-year 6% bonds with P = 100 and D = 14 years
- brian is sure that the yield curve will make a downward parallel shift and wishes to profit from this projection
- his strategy is to go long $1 million in 30 year treasury strips which he buys for 17.40 each
- if rates fall by 1%, the value of his treasury strip rises by dP = DP/(1+k)
- the strips have D = 30, so dP/P = 30*.01/1.06 = 28%
- with the coupons, D = 14, and dP/P = 14*.01/1.06 = 13%
- so brian is able to double his price appreciation by using strips
- of course if the rates move against him he will lose
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