1. Copyright © 2009 Pearson Prentice Hall. All rights reserved. Chapter 7 (Conti.)98.10.16 Global Bond Investing

2. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 2 Bond Valuation  Valuation of zero coupon bonds  There exists an inverse relationship between market yield and bond price.  Valuation of coupon bonds

3. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 3 Bond Valuation  Yield to maturity: Zero coupon bonds  Yield to maturity: Coupon Bonds

4. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 6 Exhibit 7.6: Example of Yield Curve

7. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 7 Duration and Interest Rate Sensitivity  Duration is a measure of interest risk for a specific bond.  Modified duration, D mod, can be written as:  Macaulay duration, D mac can be written as:  The bond return can be approximated as: Return = Yield – D mod  (  yield)

8. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 10 Duration – Example 7.6 Solution: Expected return = Yield – D · (Δyield) = 5% - 10 · 0.1% = 4% Risk premium=4%-2% = 2%

11. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 13 Credit Migration AAAAAABBBBBBCCCD AAA92.296.960.540.140.060.00 0.000 AA0.6490.757.810.610.070.090.020.010 A0.052.0991.385.770.450.170.030.051 BBB0.030.204.2389.334.740.860.230.376 BB0.030.080.395.6883.108.121.141.464 B0.000.080.260.365.4482.334.876.663 CCC0.100.000.290.571.5210.8452.6634.030 D0.00 100

14. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 16 Exhibit 7.7: Yield Curves in Different Currencies in 2007

17. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 20 Duration – Example 7.8 Solution: Return = Foreign Yield – D · (Δforeign yield) + currency movement(%) = 5% - 10 · 0.05% - 1% = 3.5%

21. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 7 - 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