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20-1 yield curve strategies (5 inter-market curve strateties (two…
20-1 yield curve strategies
1 introduciton
active yield curve: designed to capitalized on expectations regarding the level, slope or shape (curvature) of yield curve
2 foundational
concepts
for active
management
of yield curve
strategies
a review
of yield
curve
dynamics
three basic movement
level - parallel shift
slope - flattening ro steepening
curvature
new reality - bond issued with negative coupon rates - modified duration larger than muturity
yield
curve
slope
the spread between yield on long-maturity and on shorter-maturity
spread increases / widens - steepen
narrow - flatten
turn negative - inverted
yield curve
curvatue
relationship between yields at short, midpoint and long end of curve
a common measure - butterfly spread
= -short + 2&midium - long
correlated with
one another
level with shape
upwar shift level - flatten and less curved
short rates tend to be more volatile
duration
and
convexity
duration
measures
Macaulay duration:
weighted average of time to receive promised payments
assume cash flow not change when yields change
modified duration:
percentage price change for a given 1% change in yield to maturity
assume cash flow not change when yields change
effective duration:
sensitivity of price to a change in benchmark yield curve
key rate duration:
sensitivity to a change in benchmark yield curve at specific maturity point or segment - identify shaping risk
money duration:
price change in units of currency denominated
price value of a basis point PVBP:
change in bond price given 1bp change in yield to maturity
duration - first-order effect - linear relationship bw bond price and YTM
convexity
second-order - for larger movement
postive-price increase more if interest rates decrease
higher convexity - expected to have lower yield
valuable when interest rates expected to change
even more valuable when interest rate volatility expected to increase
nominal convexity
assume cash flow not change when yields change
a helpful
heuristic
MD increas linearly with maturity
convexity approximately proportional to duration squared
coupon-paying →more widely dispersed cash flows → more convexity than zero-coupon
convexity's effect may be large for bonds with short option positions embedded in structures or portfolio
adding convexity not free: higher convexity most often with lower yields
altered by
shifting maturity/duration distribution of bonds
adding physical bonds with desired convexity properties
using derivatives
a yield curve:
a stylized representation of yields avaiable at various maturities within a market
3 major
types of
yield curve
strategies
4 formulating a portfoio
positoning strategy given
a market view
duraition positioning in anticipation
of a parallel upward shift in the yield curve
any bond with an implied forward yield change greater than forecasted increase in yield expected to have higher return
the best bond determined by a combination of the basis point difference in forward yield versus forecast yield translated through the duration of the bond at horizon
Total return ≈ −1 × Ending effective duration × (Ending yield to maturity − Beginning yield to maturity) + Beginning yield to maturity
portfolio positioning in
antcipation of a change in
interest rates direction uncertain
increase convexity -
gain more in decline and losse less in rising
increase convexity -
willing to give up yield to imporve return
performance
bullets
and
barbells
in an instantaneous downward parallel shift -
higher-convexity barbell outprform bullet slightly
barbell outperm bullet if yield curve flatten
bullet outperform barbell if yield curve steepens
the predicted change using partial:
= portfolio par amount
partial PVBP
( - curve shift)
butterflies
a combination of a barbell and a bullet
portfolio weight selected so that position is money duration neutral
→change in value offset in parallel yield curve shift
long wings and short body - positive convexity - benefit from flatttening / interest rates more volatile than currently market pricing
short wings and long body - predicated stable interest rates /
yield curve steepening
ways to
structure
duration-neutral weighting - also money duration neutral
50 /50 weighting
regression weighting
*of duration-neutral bullets barbells and butterflies given a change in the yield curve
using
options
much simpler to extend duration and add convexity
using securities with
embedded options - MBS
to reduce convexity
with negtive convexity - more sensitive to increase in rates
work well if interest rates not move much
sell
option
drag on performce created by owning convexity when interest rates not move up or down in a meaningful fashion
to reduce convexity
5 inter-market
curve
strateties
involve more than one yield curve and
require to either accept or somehow hedge currency risk
any significant spread changes will dominate the carry and riding the curve components of relative return
two markets
share a yield curve
perfect capital mobility
exchange rate credibly fixed forever
all asset hedged into a common currency - base currency become irrelevant for inter-market decisions
currency exposure decisions based on projected appreciation or depreciation relative to forward FX rates
currency hedged forerign bonds and domestic bonds not perfect substitutes
imposing the duration-neutrality and cash-neutrality conditions across all markets - to capture the best opportunities at each maturity and best maturities on each curve
6 comparing
the performance
the baseline portfolio
extreme barbell vs
laddered portfolio
extreme barbell - max convexity - penalized for give-up yield over longer horizon
the reward of barbell more significant for
changes in slope and curvature
extreme
bullet
perfrom well - yield curve steepens
perform pool - yield curve adds curvature
a less exteme barbell portfolio
vs laddered portfolio
minimizes the magnitude of potential shorfall
also reduces opportunity to add value
comparing
must willing to add meaningful degree of convexity
change in convexity often accomplished by changing portfolio structure
*the extreme and less extreme barbell portfolios
the yield curve scenarios
reduction / addition of curvature -
the changes in the butterfly spread
*of various duraion-meutral protfolios in multiple curve enviroments
7 a framework
for evaluating
yield curve trades
E(R) ≈ Yield income +Rolldown return
+E(Change in price based on investor's views of yields and yield spreads)
−E(Credit losses) +E(Currency gains or losses)
the effect of trader's interest rate view on total expected return of portfolio:
[−MD × ∆Yield] + [½ × Convexity × (∆Yield)^2]
risk is about deviations from the expected
structured notes
used in fixed-income portfolio
types
deleveraged floaters - a multiplier less than one
range accrual notes - specify a daily accrual rate
extinguishing accrual notes - cancel all future accruals if reference rate outside specified range
interest rate differential notes - pay a coupon based on difference between rates from two different points on the yield curve
ratchet floaters - a provision preventing coupon from ever declining
inverse floaters - coupons rise as index rate linked declines
dual-currency notes - denominated in one currency but pay interest in a different currency
can offer
significantly lower all-in costs
allow packaging of certain risk or bets