Emerging Market Sentiment: Evaluating Pricing Signals from the Bond Markets

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Emerging Market Sentiment Evaluating Pricing
Signals from the Bond Markets

• John J. Merrick, Jr.
• Zicklin School of Business
• Baruch College

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Understanding Sovereign Bond Yields

• What determines emerging market sovereign bond
  yields?
• How does perceived default probability affect
  bond yields?
• How does perceived default-state recovery value
  affect yields?

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Plan of the paper

• Brief review of literature on sovereign yield
  spreads
• Develop a step-by-step approach to incorporating
  default probability and recovery value into yield
  spread analysis
• Relate to the 1998 Russian Eurobond meltdown
• Apply the model to Republic of Argentina
  Eurobonds during Argentinas 2001 crisis

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Define the yield spread vs. benchmark
default-free issue

•  
• 1 Y (1 y)(1 s)
•  
• Y yield to maturity on emerging market bond
• y yield to maturity on benchmark default-free
  bond
• s sovereign yield spread

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Selected literature on emerging market sovereign
yield spreads

• Eichengreen and Mody (1998) What explains
  changing spreads on emerging-market debt?
• Kamin and von Kleist (1999) The evolution and
  determinants of emerging market credit spreads in
  the 1990s
• Becker, Richards and Thaicharoen (2001) and
  Eichengreen and Mody (1998) Collective action
  clauses
• Merrick (2001) Crisis dynamics of implied
  default recovery rates evidence from Russia and
  Argentina

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Yield on a 1-year, 0-coupon bond(Computed as
internal rate of return on promised cash flows)

•  
• 100
• V
• (1 Y)  
• V market value
• C coupon per 100 par value
• Y yield to maturity

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Risk-neutral bond valuation given default
recovery value R

•  
• 100 R
• V p (1 p)
  (1 y) (1 y)  
• V market value
• p per-period payment probability
• R assumed default-state recovery value per 100
  par value
• Y yield to maturity on benchmark default-free
  bond

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R-N valuation under R0 recovery

•   p (100)
• V
• 1 y  
• V market value
• p per-period payment probability
• y yield to maturity on benchmark default-free
  bond

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Sovereign yield under 0 recovery

•  
• 1 y
• 1 Y
• p
• Y yield to maturity on emerging market bond
• y yield to maturity on benchmark default-free
  bond
• p per-period payment probability
• (Combine yield R-N under R0slides to
  generate this solution.)

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Yield spread (s) under 0 recovery

•  
• 1 y
• 1 Y (1 y)(1 s)
• p
• Y yield to maturity on emerging market bond
• y yield to maturity on benchmark default-free
  bond
• s sovereign yield spread
• p per-period payment probability

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Yield spread and payment probability (for 0
recovery)

•  
• s (1 p)/p
• Implied p 1/(1 s)
•  
• s sovereign yield spread
• p per-period payment probability

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Yield on a 2-year bond(Computed as internal rate
of return on promised cash flows)

•  
• C (C 100)
• V
• (1 Y) (1 Y)2
•  
• V market value
• C coupon per 100 par value
• Y yield to maturity

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Risk-neutral bond valuation assuming 0 default
recovery value

•  
• V p2 C/(1y) (C 100)/(1 y)2
• p(1-p) C/(1y)
• V market value
• C coupon per 100 par value
• p per-period payment probability
• y yield to maturity on benchmark default-free
  bond

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R-N valuation under 0 recovery

•  
• p C p2 (C 100)
• V 1 y
  (1 y)2
•  
• V market value
• C coupon per 100 par value
• p per-period payment probability
• y yield to maturity on benchmark default-free
  bond

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Recall the IRR definition of yield

•  
• C (C 100)
• V
• (1 Y) (1 Y)2
•  
• V market value
• C coupon per 100 par value
• Y yield to maturity

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Sovereign yield under 0 recovery

•  
• 1 y
• 1 Y
• p
• Y yield to maturity on emerging market bond
• y yield to maturity on benchmark default-free
  bond
• p per-period payment probability
• (Combine last two slides to generate this
  solution.)

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Yield spread (s) under 0 recovery(same result
as in the 1-period model)

•  
• 1 y
• 1 Y (1 y)(1 s)
• p
• Y yield to maturity on emerging market bond
• y yield to maturity on benchmark default-free
  bond
• s sovereign yield spread
• p per-period payment probability

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Example assuming R 0 recovery
Maturity 2 years Par Value 100 Coupon rate
10 Compounding annual Also given V 93.21
Solve for Y Y .1413 93.21 10/(1.1413)
(10 100)/(1.1413)2
Assumed benchmark yield y .05
Solve for spread s (1Y)/(1y) 1 s
(1.1413/1.05) 1 .0870 ( 1-p/p .08/.92).
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R-N valuation under 0 recovery(C 10 y .05
p .92)

•  
• .92 (10) (.92)2 (10 100)
• V 93.21 1.05
  (1.05)2
•  
• V market value
• C coupon per 100 par value
• p per-period payment probability
• y yield to maturity on benchmark default-free
  bond

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Brady bonds

• Brady bonds were created in the 1990s
• Part of the debt restructurings of defaulted
  emerging market sovereign loans
• Each Brady is partially collateralized by
  zero-coupon US Treasuries
• Collateral complicates the interpretation of the
  yield spread each cash flow does not carry an
  equivalent exposure to default loss

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Calculating Stripped spreads

• Practitioners adjust the spread for Brady bonds
• Strip out the collateralized cash flow (and use
  risk-free rates to discount this collateral)
• Apply the standard spread calculation only to the
  uncollateralized cash flow stream
• The answer is the stripped sovereign spread

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Different risk and discount rates(2-year Brady
only principal of 100 is collateralized)

•   V V 100/(1y)2
• C C
• V
• 1 Ys (1 Ys)2
• V total bond market value
• V value of uncollateralized cash flows
• C coupon per 100 par value
• Ys stripped sovereign yield to maturity
• y yield on benchmark default-free bond

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Brady bond discounting _at_ y Ys
Maturity 2 years Par Value 100 Coupon rate
10 Compounding annual Yields assumed
benchmark y .05 stripped sovereign Ys .1413
Value of Treasury collateral 100/(1.05)2
90.703 V 90.703 V
10 10 V
16.439 1.1413
(1.1413)2 V 90.703 16.439 107.142
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Risk-neutral Brady bond valuation(assuming 0
recovery of coupons in default)
Maturity 2 years Par Value 100 Coupon rate
10 Compounding annual Assumptions benchmark
y .05 p .92
V 90.703 V
p C (1 p) 0 p2 C p(1 p) 0
V (1 y)
(1 y)2 .92 (10) (.08) 0
(.92)2 10 .92(.08) 0 V
16.439. (1.05)
(1.05)2
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Blended yield on a Brady bond(IRR at fair
market value of 107.142)

• C (C 100)
• V
• 1 Y (1 Y)2
•  
• Solve for Y .06099
• 10 (10 100)
• 107.142 1.06099
  (1.06099)2

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Stripped spread vs. Blended spread(only the
Stripped spread 1 p/p .08/.92 .087)
Solve for stripped spread s (1Ys)/(1y) 1
s (1.1413/1.05) 1 .0870 (or 8.70).
Solve for blended spread s (1Y)/(1y) 1
s (1.06099/1.05) 1 .0105 (or 1.05).
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Risk-neutral bond valuation assuming default
recovery value R

•  
• p C (1 p) R/(1 y) p2 (C 100)
  p(1 p) R V (1
  y) (1 y)2
• If 0 lt R lt 100, this formula does not reduce to
  any simple relationship between yield spread and
  payment probability.

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Risk-neutral bond valuation R 50

•   92 (10) (1 .92) 50/1.05
  (.92)2 (10 100) .92(1 .92) 50
• V
• 1.05
  (1.05)2
•  
• V 100.18
• At V 100.18, yield-to-maturity Y .0990, and
  so
• s (1.0990/1.05) 1 .0466 (not 1 p/p
  .087)
• Can no longer infer p directly from s!

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Normal yield curves for different recovery
values (R)
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Crisis yield curves for different recovery
values (R)
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R-N valuation of N-period bond
Bond value V0 via the expected discounted cash
flow relation   N N V0
S Pt ft Ct PN fN FN S dt ft R
t1 t1 Pt payment probability
of date t cash flow dt default probability
between dates t-1 and t Pt-1 Pt ft
risk-free discount factor for date t cash flow R
recovery value C coupon F principal value
of bond
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Term default rate curve (use standard yield
curve formulations for default rate curve)
  Pt exp(-dt t) Pt payment probability
of date t cash flow dt term default
rate Assume that the term default rate curve
takes the following functional form   dt a0
a11 exp(-t)/t   a0 asymptotic
(long run) value of the instantaneous forward
interest rate a1 current deviation of the
instantaneous interest rate from its long-run
value  
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Estimation of model parameters

• The model incorporates three unknown parameters
• R, a0 and a1
• The risk-free discount factors (ft) are known
• The bonds notional cash flows are known, but
  involve a lot of work to program accurately
• For any day (date 0), solve for the R, a0 and a1
  that minimize the sum of squared bond pricing
  residuals (while constraining the average bond
  residual 0)

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Interpret the default curve results

• dt 0.3108 0.3097 1 exp(-t)/t
• Apply for the t 1 year term
•   d1 0.3108 0.3097 1 exp(-1)/1 .507
• P1 exp(-d1 1) exp(-.507)(1) .603
• Apply for the t 2 year term
• d2 0.3108 0.3097 1 exp(-2)/2 .445
• P2 exp(-d 2 2) exp(-.445)(2) .411  

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An inverted default rate curve

• dt 0.3108 0.3097 1 exp(-t)/t
• For t 1-year term d1 .507
• For t 2-year term d2 .445
• Implicit 1-year Forward 1-year rate d1,1
  .383
• exp(-d1 1) exp(-d1,1 1) P2 exp(-d 2 2)
•  

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Summary

• Yield spreads produce important signals regarding
  the markets consensus of issuer default
  probabilities.
• However, these market-based signals are sometimes
  confusing and need to be interpreted with care.
• This paper has developed a step-by-step
  analytical framework to highlight the importance
  of assumptions regarding default-state recovery
  value on attempts to interpret yield spreads as
  signals of issuer default probability.

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Conclusions (1)

• Sovereign yield and yield spread curves can be
  upward sloping or downward sloping (inverted)
  depending upon the assumed recovery value even
  for a constant per-period default rate.

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Conclusions (2)

• A stripped of recovery value spread concept for
  Eurobonds akin to stripped of collateral spread
  analysis for Brady bonds is needed to close the
  measured spread gap between these two sectors.

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Conclusions (3)

• Default probability signals from a standard
  yield-based sovereign spread analysis (based on
  0 recovery value) tend to be overly optimistic
  with regard to implied issuer prospects of
  avoiding default.

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Conclusions (4)

• Discounted expected cash flow models can be used
  to jointly estimate both implied recovery value
  and (risk-neutral) default probabilities from a
  cross-section of bond prices.

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Conclusions (5)

• An estimate for the Argentine Eurobond markets
  implied recovery value (34 per 100 of par on
  October 3, 2001) during the recent crisis was
  lower than that from 1998 (50 per 100).