International%20Fixed%20Income

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International Fixed Income

• Topic IVA
• International Fixed Income Pricing -
• Hedging

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Outline

• Review of foreign bond investments
• Hedging and its consequences
• Empirical evidence
• Concluding remarks

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I. Review Rates of Return on Bonds
Consider a a foreign government bond. What is
its US rate of return?
Taking logs of the above and rearranging gives us
This is approximately equal to yield - dur
x (Dr) - DS(Fn/)
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Rates of Return Summary

• The return on a foreign bond has three
  components
• Its yield (e.g., coupon, or imputed yield) in
  the foreign currency.
• Its duration component in the foreign currency.
• Its exchange rate exposure.
• The first two components are always true, while
  the second is unique to international fixed
  income.

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Rates of Return Summary Continued...

• The risk associated with this return can be
  broken up into two pieces
• interest rate risk (i.e., duration and maybe
  convexity) as the first component (i.e., the
  coupon) is fixed.
• exchange rate risk.

Of course, if there is no exchange rate risk, we
just get the usual result that the volatility of
a bond is its duration times the volatility of
rates.
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Intuition

• Positive covariance between FN/ exchange rate
  and FN interest rates
• Interest rates FN/ - the investor
  loses money on the bond, and loses money in the
  currency market (i.e., minus the exchange rate).
• Why? Suppose inflation in the foreign country
  goes up, then (I) interest rates rise, leading to
  a bond price fall, and (II) the currency
  depreciates.
• Negative covariance between FN/ exchange rate
  and FN interest rates
• Interest rates FN/ - the investor
  loses money on the bond, but makes money in the
  currency market (i.e., minus the exchange rate).
• Why? Suppose monetary policy is tightened,
  raising interest rates (with corresponding bond
  market losses), but attracts foreign capital
  (with appreciation in the foreign currency).

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II. Hedged Returns

• The previous slides showed unhedged returns, that
  is, -adjusted returns on foreign bonds, without
  any hedging of currency risk.
• In practice, it may be worthwhile hedging the
  currency risk using forwards, futures, or
  options. Here, we will concentrate on forwards.

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Hedging Mathematics
Recall the unhedged return on -adjusted foreign
bonds
Two strategies (I) Buy foreign bond at price P,
and sell all future coupon and principal payments
in exchange for . (This is like a currency swap,
and transforms the foreign bond into a bond via
interest rate parity). We will see that next
class. (II) Alternatively, sell a one-period
forward currency contract equal to next periods
estimated value of the bond (plus interest if
any).
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Hedging continued
If the investor guesses right, and the estimate
of next periods bond price, , is close to
the true price, , then the hedge will be
perfect
The value of his foreign bond will be
The new, hedged return has two components (I)
the return on the bond in foreign currency terms,
just like before, which includes the yield and
capital gain component. (II) the one-period
forward premium weve talked about before.
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Hedging continued.

• Since the forward premium is known today, the
  volatility of the hedged -adjusted return just
  reflects the volatility of the bond, i.e., its
  duration times foreign interest rate volatility
  (at least for small changes).
• What are we assuming here?

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Hedging continued.

• We are assuming that the investor perfectly
  predicts the price next period. Suppose this does
  not occur. Then what?
• Define the prediction error as

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Hedging continued.

• If e was too large, then our hedge amount was too
  small and the unexpected excess value of the bond
  is valued at St1. If e was too small, then our
  hedge was too large and we need to buy additional
  funds at at St1.
• We can therefore measure the return on the
  foreign bond in , hedged but not perfectly.

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Hedging formula.
Three components (I) the return from the
investors predicted price change in the foreign
bond (II) the forward premium (III) the
unpredicted price change of the foreign bond that
is valued at the FUTURE uncertain exchange rate.
The volatility now involves two parts (I) the
component from before, and (II) the new
unpredictable component which depends on the
volatility of the error, as well as the
exchange rate.
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III. Empirical Evidence

• Two cases
• Monthly data 10 year-period during 1980s G7
  countries, plus global portfolio.
• Weekly data 1996-1999 G7 countries, as previous
  lectures.
• Comparison of unhedged and hedged returns.

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Mean -adjusted Annualized Return on Foreign Bond
Portfolios (1980s)
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Volatility of -adjusted Annualized Return on
Foreign Bond Portfolios (1980s)
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Mean -adjusted Annualized Return on Foreign Bond
Portfolios (1996-99)
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Vol. -adjusted Annualized Return on Foreign Bond
Portfolios (1996-99)
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Recall of Volatility of -adjusted Foreign
Bond Due to Currency Risk
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Concluding Remarks.

• Is hedging having your cake and eating it too?
• As a long-run matter, the interest rate
  differential should offset exchange rates, so
  passive strategies should produce the same level
  of returns.
• Here, most of the correlations between interest
  rates and exchange rates moved in the opposite
  direction of this theory (except Canada), so
  their were ex-post gains to hedging.
• Alternatively, what we have shown is that hedged
  -adjusted foreign bond returns subjects you to
  foreign interest rate movements.
• These foreign-based movements depend on real
  economic and central bank risk in those
  countries. By diversifying across countries in
  terms, you can reduce your overall exposure to
  country-specific risks.