International Fixed Income

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International Fixed Income

• Topic IVB
• International Fixed Income Pricing -
• Investment Strategies

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Outline

• Strategies
• Relation between international fixed income bonds
• Examples of active strategies
• An example mean-variance analysis

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I. Strategies

• Trading strategies in the international fixed
  income arena are theoretically separable
• Currency bet
• buy fn. Gvt bond - could lose money if interest
  rates rise
• buy/sell forwards/futures in currency market
• Foreign interest rate bet
• buy fn. Gvt bond - could lose money if currency
  depreciates
• buy forward-hedged, foreign gvt. bonds

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Strategies continued.

• Interesting combinations of bets
  suppose you thought US rates were going to
  decline, but the /euro was going up, i.e., Euro
  is appreciating.
  What could you do?
• Buy U.S. gvt. Bonds
• Sell U.S. forward for Euros
  Youre exposed to US rates Euros at the
  same time. You have converted future (risky)
  into Euros.

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IA Pricing International Fixed Income Bonds

• How do you price future cash flows?
• What does interest rate parity tell us about
  relative discount factors across countries?
• General pricing formula
• Example from class

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Pricing Review

• Suppose we have an asset whose cash flows are
  risk-free.
• Then, by no arbitrage, the market value of the
  asset must be

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Review of Interest Rate Parity

• Ftd/f/S0d/f (1rd)/(1rf)t
• Forward premiums and discounts are entirely
  determined by interest rate differentials.
• It holds by ARBITRAGE
• ...that is, if it didnt, you
• could make an infinite profit

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General Pricing Formula

• What these two no-arbitrage results tell us is
  that the price of a foreign bond can be described
  by the (I) domestic bond valuation, and (II) the
  forward currency curve.

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Underlying Mathematics
The forward premium/discount is just the ratio
of the discount factors in the two countries,
i.e., between their prices of future currencies.
If a countrys discount factor is higher, then
it sells at a premium.
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General Pricing Formula
Using this result, then the value of a foreign
bond in dollar terms is
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Example of U.S. Treasury Bond

• From class earlier in semester, recall that the
  6-mth, 1-yr and 1.5-yr discount factors for the
  U.S. were 0.9730, 0.9476 and 0.9222,
  respectively.
• The corresponding exchange rate for /DEM is a
  spot rate of .7095, and corresponding forward
  rates of .7158, .7214 and .7256.

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Valuing A 1.5-Year, 8.5 T-Note

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Valuing A 1.5-Year, 8.5 Bund

This gives a total value in DEM of 10,658.78.
Why?
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Intuition

• What happened if the prices of these bonds were
  different?
• Translate the German bund into a U.S. bond by
  converting future DEM cash flows into US .
• Take US and discount them at U.S. rates. If this
  value is different then the bund value times the
  /DEM exchange rate, you have arbitrage!

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IB. Popular Active Strategies

• Tactical hedging strategy
• Hedge only a percentage of the currency risk,
  depending on strength of currency forecasts
  (e.g., if you expect currency to appreciate,
  dont hedge as much)
• R()Ru(1-P)Rh(P), where P hedged
• Currency overlay strategy
• Hedged foreign currency position, plus a currency
  bet
• R()RhP(St1/Ft), where -1ltPlt1

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Comparison of Strategies

• 4 strategies (hedge, no hedge, tactical, currency
  overlay) based on forecasts
• Levich-Thomas (1993) study of 5 markets
  (DM,C,GBP,Yen,Global) over 1977-90 period.
• Sharpe Ratio measures
  (m-r)/s , i.e., excess return/risk
  During this period, it was 0.12 for US
  gvts.

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Sharpe Ratios
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Sharpe Ratios in Subperiods for Global Portfolio
of Intl. Bonds
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II. Mean-Variance Analysis

• One popular criteria for judging an investment is
  to consider its expected return (its mean) versus
  its risk (its volatility)
• Mean-variance portfolios find the weights in each
  individual security (in this case, intl. Gvt.
  Bonds) which give minimum volatility for a given
  level of expected return.

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Procedure

• Consider a portfolio of intl. Government bonds,
  each with return, Ri.
• The expected return on the portfolio is
  
• where wi is the weight in each bond.
• Find the weight wi that, for a given ER,
  minimizes the risk, i.e., the vol. Of the
  portfolio

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Example of Mean-Variance Efficient Portfolios
(unhedged and hedged), 1977-90
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Example of Mean-Variance Efficient Portfolios
(unhedged and hedged), 1977-90
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General Conclusions

• Substantial benefits in terms of risk reduction
  by diversifying across bond markets - diversify
  away idiosyncratic central bank and economy risks
  that do not get incorporated into exchange rates.
• There seem to be gains from actively managing
  international bond portfolios by using forecast
  methods for exchange rates
• these methods were discussed earlier in the
  course, and involve such techniques as
  market-based and model-based (e.g., technical and
  fundamental) methods.