Outline
• Strategies– Relation between international
fixed income bonds– Examples of active strategies
• An example: mean-variance analysis
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
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.
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
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
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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
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.
Underlying Mathematics
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The forward premium/discount is just the ratio ofthe discount factors in the two countries, i.e., between their prices of future currencies. If a country’s discountfactor is higher, then it sells at a premium.
General Pricing Formula
Using this result, then the value of a foreign bond in dollarterms 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.
Valuing A 1.5-Year, 8.5% T-Note
5.115. 10425$425$425$ dddV
Time Cash Flow Discount Factor Value
0.5 $425 0.9730 $4141.0 $425 0.9476 $4031.5 $10425 0.9222 $9614
Total $10430
Valuing A 1.5-Year, 8.5% Bund
5.115. 10425425425 dDMdDMdDMV
Period CashFlow
U.S. dis.fctr
S/F for.Prem.
ValueDM
.5 DM 425 .9730 1.0089 417.20
1 DM 425 .9476 1.0168 409.48
1.5 DM10425
.9222 1.022692
9832.10
This gives a total value in DEM of 10,658.78. Why?
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 $/DEM exchange rate, you have arbitrage!
IB. Popular Active Strategies
• Tactical hedging strategy:– Hedge only a percentage of the currency
risk, depending on strength of currency forecasts (e.g., if you expect currency to appreciate, don’t hedge as much)
– R($)=Ru(1-P)+Rh(P), where P=% hedged
• Currency overlay strategy:– Hedged foreign currency position, plus a
currency bet– R($)=Rh+P(St+1/Ft), where -1<P<1
Comparison of Strategies
• 4 strategies (hedge, no hedge, tactical, currency overlay) based on forecasts
• Levich-Thomas (1993) study of 5 markets (DM,C$,GBP,Yen,Global) over 1977-90 period.
• Sharpe Ratio measures (-r)/ , i.e., excess return/risk During this period, it was 0.12 for US gvts.
Sharpe Ratios in Subperiods for Global Portfolio of Intl. Bonds
-1
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1977-90 77-78 79-81 82-84 85-87 88-90
UnhgeHdgeTacticalOverlay$ strat.
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.
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:
][i
ii REw
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iiRwvol
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.