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 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:

Review of Interest Rate Parity F t d/f /S 0 d/f = [(1+r d )/(1+r f )] 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

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 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.

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

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 , and , 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

Valuing A 1.5-Year, 8.5% Bund This gives a total value in DEM of 10, 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($)=R u (1-P)+R h (P), where P=% hedged Currency overlay strategy: –Hedged foreign currency position, plus a currency bet –R($)=R h +P(S t+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 period. Sharpe Ratio measures (  -r)/ , i.e., excess return/risk During this period, it was 0.12 for US gvts.

Sharpe Ratios

Sharpe Ratios in Subperiods for Global Portfolio of Intl. Bonds

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, R i. The expected return on the portfolio is where w i is the weight in each bond. Find the weight w i that, for a given E[R], minimizes the risk, i.e., the vol. Of the portfolio:

Example of Mean-Variance Efficient Portfolios (unhedged and hedged),

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.