International Fixed Income

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International Fixed Income

• Topic IIIA
• Stylized Facts and Their Implications

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Outline

• Explaining the Term Structure
• The Effect of Currency Movements

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I. Explaining Term Structure Movements

• What factors explain movements in the term
  structure across countries?
• Case study
• G7 countries (US,UK,JPN,CAN,GER,ITA,FR)
• 1996-1999
• Weekly movements in zeroes of 1yr-30yr maturities

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Principal Components Analysis

• Find the principal component that explains most
  of the variation in term structure movements
  across the maturities.
• How much does it explain?
• Are there additional components
• How correlated are these components across
  countries?
• How much does the U.S. explain of movements in
  foreign term structures?

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How Many Factors?
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What Do These Factors Look Like?
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What Do These Factors Look Like?
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What Do These Factors Look Like?
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What Do These Factors Look Like?
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What Do These Factors Look Like?
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What Do These Factors Look Like?
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What Do These Factors Look Like?
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Worldwide Principal Component Analysis
(US,UK,JPN,GER)
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of Worldwide Movements in Term Structure
Explained by Factors
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Implications Continued...
APPROXIMATION of CHANGE IN BONDS VALUE
Whats the exposure of the foreign bonds value
to US rates?
In other words, the change in the foreign
bond to a change in US rates is just the US bond
change times the sensitivity of foreign rates to
US rates.
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Implications of Factor Analysis

• Most of the movements in the term structure,
  e.g., 90, can be explained by one factor.
• Caution Ignoring short-term rates here and
  focusing on 1-30 yr zeroes.
• This factor looks like a parallel shift in rates.
  (The second less important factor looks like a
  steepening/flattening.)

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Sensitivities of Foreign Factor to US Interest
Rate Factor (i.e., b)
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Sensitivities of Foreign Factor to German
Interest Rate Factor (i.e., b)
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Example

• Consider from earlier in class, the 1.5-year and
  30-year zeroes with durations of 1.46 and 29.26,
  respectively.
• If these were the durations of the foreign bonds,
  and you had them in your portfolio, what does
  that say about their durations in your
  portfolio? (That is, your exposure to US rates,
  not currencies).

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Durations of Foreign Bonds
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II. Currency Movements

• Introduction about bond price variation
• Facts about currency and interest rate
  co-movements

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Rates of Return on Zeroes
Consider a T-period zero in 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 zero rate -
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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Interest Rate Currency Factoids

• Correlation between interest factor in foreign
  country and the F/ exchange rate.
• Volatility of interest rate factor.
• Volatility of change in exchange rate.

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Correlation Between Foreign Interest Rate Factor
and Exchange Rate Changes
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Volatility of Interest Rate FactorWeekly in
Basis Points
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Volatility of Change in Fn./ Exchange
Rates(Weekly Terms)
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Estimate of Volatility of US bond -adjusted
Foreign Bonds
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of Volatility of -adjusted Foreign Bond Due to
Currency Risk