Chapter 7 (Conti.)98.10.16

1. Chapter 7(Conti.)98.10.16 Global Bond Investing

2. Bond Valuation • Valuation of zero coupon bonds • There exists an inverse relationship between market yield and bond price. • Valuation of coupon bonds

3. Bond Valuation • Yield to maturity: Zero coupon bonds • Yield to maturity: Coupon Bonds

4. Coupon Bonds – example 7.4 • Question: A six-year bond has exactly three years till maturity, and the last coupon has just been paid. The coupon is annual and equal to 6 percent. The bond price is 95 percent. What is its European YTM and U.S. YTM?

5. Coupon Bonds – example 7.4 Solution:The European YTM is r, given by the formula We find r = 7.94% The U.S. YTM is r’, given by the formula Hence r’= 7.79% Note that

6. Exhibit 7.6: Example of Yield Curve

7. Duration and Interest Rate Sensitivity • Duration is a measure of interest risk for a specific bond. • Modified duration, Dmod, can be written as: • Macaulay duration, Dmac can be written as: • The bond return can be approximated as: Return = Yield – Dmod (yield)

8. Duration – Example 7.5 Question: You hold a government bond with a duration of 10. Its yield is 5 percent. You expect yields to move up by 10 basis points in the next few minutes. Calculate a rough estimate of expected return. Solution: The expected return =5% － 10 · 0.1% =4%

9. Duration – Example 7.6 Question: You hold a government bond with a duration of 10. Its yield is 5 percent, although the cash (one-year) rate is 2 percent. You expect yields to move up by 10 basis points over the year. Give a rough estimate of your expected return. What is the risk premium on this bond?

10. Duration – Example 7.6 Solution: Expected return = Yield – D · (Δyield) = 5% - 10 · 0.1% = 4% Risk premium=4%-2% = 2%

11. Credit Spreads • The risk premium reflects a credit spread, or quality spread, over the default-free yield. • International rating agencies (Moody’s, Standard & Poor’s, Fitch) provide a credit rating for most debt issues traded worldwide. • The credit spread captures three components: • An expected loss component • A credit-risk premium. • A liquidity premium.

12. Credit Spreads (Conti.) • On a specific bond market, one can draw yield curves for each credit rating; the credit spread typically increases with maturity. • The migration probability is the probability of moving from one credit rating to another. • The n-year migration table shows the percentage of issues with a given rating at the start of the year that migrated to another rating at the end of n years.

13. Credit Migration

14. Duration – Example 7.7 Question: A one year bond is issued by a corporation with a 1 percent probability of default by year end. In case of default, the investor will recover nothing. The one year yield for default free bonds is 5 percent. What yield should be required by investors on this corporate bond if they are risk-neutral? What should the credit spread be?

15. Duration – Example 7.7 Solution: Assume the corporate bond is issued at par and the yield is y%. [99%·(100+100·y%)+1%·0]∕(1+5%)=100 y%=6.06% Then the credit spread=6.06%-5%=1.06%

16. Exhibit 7.7: Yield Curves in Different Currencies in 2007

17. Return on Foreign Bond Investments • The return from investing in a foreign bond has three components: • During the investment period, the bondholder receives the foreign yield. • A change in the foreign yield (Δforeign) induces a percentage capital gain/loss on the price of the bond. • A currency movement induces a currency gain or loss on the position. i.e. Return =Foreign yield–D(foreign yield)+currency movement(%)

18. Risk on Foreign Bond Investments • The risk on a foreign bond investment has two major sources: • Interest rate risk: the risk that foreign yields will rise. • Currency risk: the risk that a foreign currency will depreciate. • Credit risk should be taken into account for nongovernmental bonds.

19. Duration – Example 7.8 Question: You are British and hold a U.S. Treasury bond with a full price of 100 and a duration of 10. Its yield is 5 percent. The next day, U.S. yields move up by 5 basis points and the dollar depreciates by 1 percent relative to the British pound. Give a rough estimate of your expected return in British pounds.

20. Duration – Example 7.8 Solution: Return = Foreign Yield – D · (Δforeign yield) + currency movement(%) = 5% - 10 · 0.05% - 1% = 3.5%

21. Currency-Hedging Strategies • Foreign investments can be hedged against currency risk by selling forward currency contracts for an amount equal to the capital invested. • If you expect the foreign exchange rate to move below the forward exchange rate, you should hedge; otherwise, you should not hedge. i.e. Hedged Return = Foreign yield–D(foreign yield)+Domestic cash rate – Foreign cash rate Note that

22. Currency-Hedging Strategies – Example 7.9 • You are British and hold a U.S. Treasury bond with a full price of 100 and duration of 10. Its yield is 5 percent. The dollar cash rate is 2 percent and the pound cash rate is 3 percent. You expect U.S. yields to move up by 10 basis points over the year. Give a rough estimate of your expected return if you decide to hedge the currency risk.

23. Currency-Hedging Strategies – Example 7.9 • Solution For British investor: Hedged Expected Return = Foreign yield – D  (foreign yield) + Domestic cash rate －Foreign cash rate = 5% – 10  (0.1%) + 3% – 2% = 5% Note that: For British investor , the risk premium = 5% – 3% = 2% For American investor: Hedged Expected Return=5%-10 0.1%=4% And the risk premium = 4% – 2% = 2%

24. International Portfolio Strategies • International portfolio management includes several steps: • Benchmark selection • Bond market selection • Sector selection/credit selection • Duration/yield management • Yield enhancement techniques