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International Fixed Income

International Fixed Income. Topic IVB: International Fixed Income Pricing - Investment Strategies. Outline. Strategies Relation between international fixed income bonds Examples of active strategies An example: mean-variance analysis. I. Strategies.

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International Fixed Income

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  1. International Fixed Income Topic IVB: International Fixed Income Pricing - Investment Strategies

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

  3. 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

  4. 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 You’re exposed to US rates & Euros at the same time. You have converted future (risky) $ into Euros.

  5. 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

  6. 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:

  7. Review of Interest Rate Parity Ftd/f/S0d/f = [(1+rd)/(1+rf)]t Forward premiums and discounts are entirely determined by interest rate differentials. • It holds by ARBITRAGE ...that is, if it didn’t, you could make an infinite profit

  8. 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.

  9. 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 country’s discount factor is higher, then it sells at a premium.

  10. General Pricing Formula Using this result, then the value of a foreign bond in dollar terms is:

  11. 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.

  12. Valuing A 1.5-Year, 8.5% T-Note

  13. Valuing A 1.5-Year, 8.5% Bund This gives a total value in DEM of 10,658.78. Why?

  14. 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!

  15. 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, don’t hedge as much) • R($)=Ru(1-P)+Rh(P), where P=% hedged • Currency overlay strategy: • Hedged foreign currency position, plus a currency bet • R($)=Rh+P(St+1/Ft), where -1<P<1

  16. 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.

  17. Sharpe Ratios

  18. Sharpe Ratios in Subperiods for Global Portfolio of Intl. Bonds

  19. 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.

  20. 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 E[R], minimizes the risk, i.e., the vol. Of the portfolio:

  21. Example of Mean-Variance Efficient Portfolios (unhedged and hedged), 1977-90

  22. Example of Mean-Variance Efficient Portfolios (unhedged and hedged), 1977-90

  23. 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.

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