Chapter 7 (Conti.)98.10.16

Copyright © 2009 Pearson Prentice Hall. All rights reserved.

Chapter 7(Conti.)98.10.16

Global Bond Investing

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

ttr

tCP

1

nnrnC

r

C

r

CP

)1(2)21(2

1)11(1


Bond Valuation

Yield to maturity: Zero coupon bonds

Yield to maturity: Coupon Bonds

tYTMtCP

1

nYTMnC

YTM

C

YTM

CP

)1(2)1(2

1)1(1


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?


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

31

10621

611

695

rrr

62/'1

10642/'1

622/'1

695

rrr

%94.71)1( 22

%79.7


Exhibit 7.6: Example of Yield Curve


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)

rDrD

P

P PP

modmod

rr

PP

macmac Dr

rD

P

P

11


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%



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?



Solution:

Expected return = Yield – D · (Δyield)

= 5% - 10 · 0.1%

= 4%

Risk premium=4%-2% = 2%


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.


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.


Credit Migration

AAA AA A BBB BB B CCC D

AAA 92.29 6.96 0.54 0.14 0.06 0.00 0.00 0.000

AA 0.64 90.75 7.81 0.61 0.07 0.09 0.02 0.010

A 0.05 2.09 91.38 5.77 0.45 0.17 0.03 0.051

BBB 0.03 0.20 4.23 89.33 4.74 0.86 0.23 0.376

BB 0.03 0.08 0.39 5.68 83.10 8.12 1.14 1.464

B 0.00 0.08 0.26 0.36 5.44 82.33 4.87 6.663

CCC 0.10 0.00 0.29 0.57 1.52 10.84 52.66 34.030

D 0.00 0.00 0.00 0.00 0.00 0.00 0.00 100



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?



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%


Exhibit 7.7: Yield Curves in Different Currencies in 2007


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(%)


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.



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.



Solution:

Return

= Foreign Yield – D · (Δforeign yield)

+ currency movement(%)

= 5% - 10 · 0.05% - 1%

= 3.5%


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 AB

A

AB rrr

rr

S

SF

1


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.


Currency-Hedging Strategies – Example 7.9

SolutionFor 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%


International Portfolio Strategies

International portfolio management includes several steps:

Benchmark selection

Bond market selection

Sector selection/credit selection

Duration/yield management

Yield enhancement techniques

Chapter 7 (Conti.)98.10.16

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