Chapter 7 Global Bond Investing 73
30. Fuji Bank issued convertible Eurobonds in January 1989. Convertible bonds were a popular way for
Japanese banks to raise funds while the Tokyo stock market was booming in the 1980s. The lure of
capital gains from converting the bonds to equity allowed the banks to issue the securities with a very
low interest rate.
Fuji Bank Eurobond was a 500-million Swiss franc zero-coupon bond, issued at par with a maturity
of five years. A bond with a face value of 100 Swiss francs could be converted into two shares of Fuji
Bank at any time starting in 1991. At time of issue, Fuji’s stock was worth 3,590 yen, and a Swiss
franc was worth 80 yen. The bond also had a put option that could be exercised at the start of 1991
(and only at that time). Bondholders had the option of redeeming the bond at a premium of 2.625%
over its face value. In other words, bondholders could obtain 102.625 francs for each bond. On
January 14, 1991, the Tokyo stock market and the yen dropped. A stock of Fuji Bank was worth
2,400 yen, and a Swiss franc was worth 95 yen. Yields on Swiss franc bonds were around 4%. Most
bonds were presented for early redemption.
a. Why was it advantageous for a bondholder to exercise the put option?
b. What was the total yen loss for Fuji Bank?
Solution
74 Solnik/McLeavey • Global Investments, Sixth Edition
31. The current euro yield curve on the euro Eurobond market is flat at 4% for top-quality borrowers. A
French company of good standing can issue plain-vanilla straight and floating-rate dollar Eurobonds
at the following conditions:
• Bond A: Straight bond. Five-year straight dollar Eurobond with a coupon of 4%.
• Bond B: Floating rate note (FRN). Five-year dollar FRN with a semiannual coupon set at London
InterBank Offered Rate (LIBOR).
An investment banker proposes to the French company to issue bull and/or bear FRNs at the
following conditions:
• Bond C: Bull FRN. Five-year FRN with a semiannual coupon set at:
7.60% − LIBOR.
• Bond D: Bear FRN. Five-year FRN with a semiannual coupon set at:
2 LIBOR − 4.2%.
The floor on all coupons is zero. The investment bank also proposes a five-year floor option at 2.1%.
This floor will pay to the French company the difference between 2.1% and LIBOR, if it is positive,
or zero if LIBOR is above 2.1%. The cost of this floor is spread over the payment dates and set at an
annual 0.05%. The bank also proposes a five-year cap at 7.60%. The annual premium on the cap is
0.1%. The company can also enter in a five-year interest-rate swap of 4% fixed against LIBOR.
a. Assume that the French company issues Bonds C and D in equal proportions. Is it more
advantageous than issuing Bonds A and B in equal proportion and why?
b. Find out the borrowing cost reduction that can be achieved by issuing the bull Note C compared
to issuing a fixed-coupon straight Bond A at 4%.
c. Find out the borrowing cost reduction that can be achieved by issuing the bull Note C compared
to issuing a plain-vanilla FRN B at LIBOR.
d. Find out the borrowing cost reduction that can be achieved by issuing the bear Note D compared
to issuing a fixed-coupon straight Bond A at 4%.
e. Find out the borrowing cost reduction that can be achieved by issuing the bear Note D compared
to issuing a plain-vanilla FRN B at LIBOR.
Solution
Chapter 7 Global Bond Investing 75
32. An FRN is a bond that pays a quarterly or semiannual coupon indexed on a short-term interest rate
such as the LIBOR.
a. Why does it make sense to use a short-term interest rate as the index?
b. Why are banks heavy issuers of FRNs?
33. A company without default risk can issue a perpetual FRN at LIBOR. The coupon is paid and reset
semiannually. It is certain that the issuer will never have default risk and will always be able to
borrow at LIBOR. The FRN is issued on November 1, 2005, when the six-month LIBOR is at 4.5%.
On May 1, 2006, the six-month LIBOR is at 5%.
a. What is the coupon paid on May 1, 2006, per $1,000 bond?
b. What is the new value of the coupon set on the bond?
c. On May 2, 2006, the six-month LIBOR has dropped to 4.9%. What is the new value of the FRN?
76 Solnik/McLeavey • Global Investments, Sixth Edition
33. A company without default risk can issue a ten-year FRN at LIBOR. The coupon is paid and reset
semiannually. It is certain that the issuer will never have default risk and will always be able to
borrow at LIBOR. The FRN is issued on November 1, 2005, when the six-month LIBOR is at 4.5%.
Here are the dollar yield curves on two different dates:
May 1, 2006 %
August 1, 2006 %
1 Month
5.00
4.00
3 Months
5.00
4.50
6 Months
5.00
5.25
12 Months
5.00
6.00
a. What should the value of the FRN be on May 1?
b. What should the value and the clean price of the FRN be August 1, 2006?
Solution
Chapter 7 Global Bond Investing 77
35. A company without default risk can issue a five-year dollar FRN at LIBOR. The coupon is paid and
reset semiannually. It is certain that the issuer will never have default risk and will always be able to
borrow at LIBOR. The FRN is issued on November 1, 2005, when the six-month LIBOR is at 5%.
Here are the dollar yield curves on two different dates:
May 1, 2006 %
August 1, 2006 %
1 Month
6.00
5.00
3 Months
6.00
5.50
6 Months
6.00
6.25
12 Months
6.00
7.00
a. What should the value of the FRN be on May 1?
b. What should the value and the clean price of the FRN be August 1, 2006?
Solution
36. A company without default risk has issued a perpetual Eurodollar FRN at LIBOR. The coupon is paid
and reset semiannually. It is certain that the issuer will never have default risk, and will always be
able to borrow at LIBOR. The FRN is issued on March 1, 2002, when the six-month LIBOR is at 5%.
The Eurodollar yield curve on September 1, 2002, and December 1, 2002, is as follows.
September 1, 2002 %
December 1, 2002 %
1 Month
4.25
4.00
3 Months
4.50
4.25
6 Months
4.75
4.50
12 Months
5.00
4.75
a. What is the coupon paid on September 1, 2002, per $1,000 FRN?
b. What is the new value of the coupon set on the FRN on September 1, 2002?
c. What is the new value and clean price of the FRN on December 1, 2002?
Solution
78 Solnik/McLeavey • Global Investments, Sixth Edition
37. A corporation rated AA issues a five-year FRN Eurobond in euros on November 1, 2005. The coupon
is paid quarterly and is equal to euro-LIBOR plus a spread of ½ %. On November 1, the three-month
euro LIBOR is at 4%. The issuer remains rated at AA during the life of the bond.
a. Three months later (February 1, 2006), the three-month euro-LIBOR has moved to 4.5%, and the
market-required spread for AA borrowers has remained at ½ %. What should the value of the
bond on reset date be?
b. Three months later (May 1, 2006), the three-month euro-LIBOR is still at 4.5%, but the market-
required spread for AA borrowers has increased to ¾%. Give some estimation of the new value
of the FRN on the reset date.
Solution
38. A corporation rated A has issued a semiannual FRN in dollars. This is a perpetual bond, which will
pay coupons indefinitely if the corporation does not default. The coupon is set at six-month LIBOR
plus a spread of ¾%. The six-month dollar LIBOR is equal to 5%.
Six months later, the six-month dollar LIBOR has remained at 5%, but the market-required spread for
A-rated corporations on long-term FRNs has moved to 1%. Give some estimation of the new value of
the FRN on the reset date.
Chapter 7 Global Bond Investing 79
Solution
39. In March 1993, the Student Loan Marketing Association (Sallie Mae) issued five-year notes with a
coupon set at 4.5% in the first year and reset quarterly subsequently. The floating quarterly coupon
rate was set to be the higher of either 4.125% or 50% of the rate on ten-year Treasury notes plus
1.25%. At time of issue, the interest rates for all maturities were well below 4%, and investors were
attracted by the high current yield (4.5%) compared to other straight bonds available.
Assume that in March 1994, interest rates have risen dramatically and that the U.S. Treasury yield
curve is now flat at 7% for all maturities.
a. What is the new coupon rate set on the Sallie Mae bond?
b. Why is the Sallie Mae bond now trading at a hefty discount?
Solution
40. The current dollar yield curve on the Eurobond market is flat at 7% for top-quality borrowers. A
French company of good standing can issue plain-vanilla straight and floating-rate dollar Eurobonds
at the following conditions:
• Bond A: Straight bond. Five-year straight dollar Eurobond with a coupon of 7.25%.
• Bond B: FRN. Five-year dollar FRN with a semiannual coupon set at LIBOR plus ¼% and a cap
of 14%. The cap means that the coupon rate is limited at 14% even if the LIBOR passes 13.75%.
An investment banker proposes to the French company to issue bull and/or bear FRNs at the
following conditions:
• Bond C: Bull FRN. Five-year FRN with a semiannual coupon set at: 13.75% − LIBOR.
• Bond D: Bear FRN. Five-year FRN with a semiannual coupon set at: 2 LIBOR − 7%.
80 Solnik/McLeavey • Global Investments, Sixth Edition
The coupon on a bull FRN will increase when LIBOR drops. This is sometimes known as a reverse
floater. The coupon on the bull FRN cannot be negative, so it has a floor of zero. The bear FRN will
benefit from a rise in interest rates. The coupon on the bear FRN is set with a cap of 20.50%.
a. Explain why a bull FRN could be attractive to some investors.
b. Explain why a bear FRN could be attractive to some investors.
c. Explain why it would be attractive to the French company to issue these FRNs compared to
current market conditions for plain-vanilla straight Eurobonds and FRNs. The company assumes
that LIBOR can never be below 3.5% or above 13.75%.
Solution
Chapter 7 Global Bond Investing 81
41. The French luxury-goods company LVMH, Louis Vuitton−Moët Hennesy, issued a series of perpetual
floating-rate notes on the international capital market in the 1990s. These bonds have the advantage
of being quasi-equity, while benefiting from favorable tax treatment. Pioneered by state-owned
French firms that cannot sell stock to the public, and subsequently used by a number of private
European companies that were reluctant to dilute their stocks, the subordinated perpetual floating-rate
note is an instrument that remains outstanding in name only. These securities are called instantly
repackaged perpetuals, or IRPs.
After a 5-billion franc issue in 1990, LVMH sold, in March 1992, 1.5 billion francs of IRPs. The
company received 1.1 billion francs, the remaining 400 million being transferred to an offshore trust.
The trust used the proceeds to buy fifteen-year zero-coupon bonds issued by banks underwriting the
LVMH issue or by sovereign borrowers such as Denmark and Austria. The 400-million investment in
zero-coupon bonds will be redeemed for 1.5 billion in fifteen years. The IRPs have the peculiarity
that they pay interest only for the first fifteen years; the interest becomes nil thereafter. After these
fifteen years, the trust is committed to repurchase the perpetuals at their face value of 1.5 billion
francs. The trust, especially set up for this purpose, will then hold the IRPs forever, but their market
value has become zero as they are perpetuals, which pay no interest. The semiannual coupon was set
at six-month PIBOR (Paris InterBank Offer Rate) plus ½%.
From an accounting viewpoint, these IRPs are treated as new equity of LVMH, because they are
perpetual. From a tax viewpoint, the interest paid on the IRPs during fifteen years can be deducted as
interest expense (while dividend payments are not tax deductible).
a. Assume that you are an investment banker proposing such an IRP to a potential client. Explain in
detail the advantage of such a package relative to a plain-vanilla fifteen-year FRN, or relative to a
new stock issue.
b. In 1990, the French tax authorities decided to allow a write-off of interest expense for only the
net amount of capital that the issuer actually takes on its books (1.1 billion for LVMH). Why
does this decision reduce the attraction of issuing IRPs?
c. Following the 1992 LVMH issue, the tax authorities decide to introduce a new regulation for
trusts, whereby capital gains would be taxed at the normal income tax rate. In effect, the trust
would make a capital gains equal to the difference between the face value of the zero-coupon
bonds and their issue price. This basically shut the market for IRPs. Why?
82 Solnik/McLeavey • Global Investments, Sixth Edition
42. Which of the following statements about the Macaulay duration of a zero-coupon bond is true? The
Macaulay duration of a zero-coupon bond:
a. Is equal to the bond’s maturity in years.
b. Is equal to one-half the bond’s maturity in years.
c. Is equal to the bond’s maturity in years divided by its yield–to-maturity.
d. Cannot be calculated because of the lack of coupons.
Chapter 7 Global Bond Investing 83
43. Which of the following bonds has the longest duration?
a. 8-year maturity; 6% coupon.
b. 8-year maturity; 11% coupon.
c. 15-year maturity; 6% coupon.
d. 15-year maturity; 11% coupon.
44. A bond with annual coupon payments has the following characteristics:
Coupon Rate
Yield-to-Maturity
Macaulay Duration
8%
10%
9
The bond’s modified duration (in years) is:
a. 8.18 years.
b. 8.33 years.
c. 9.78 years.
d. 10.00 years.
45. A nine-year bond has a yield-to-maturity of 10% and a modified duration of 6.54 years. If the market
yield changes by 50 basis points, the bond’s expected price change is:
a. 3.27%
b. 3.66%
c. 5.00%
d. 6.54%
46. You are a U.S. investor considering purchase of one of the following securities. Assume that the
currency risk of the German government bond will be hedged, and the six-month discount on
Deutsche mark forward contracts is −0.75% versus the U.S. dollar.
Bond
Maturity
Coupon
Price
U.S. Government
June 1, 2013
6.50%
100.00
German Government
June 1, 2013
7.50%
100.00
You do not expect any price change in U.S. bond prices in the next six months. Calculate the expected
price change required in the German government bond, which would result in the two bonds having
equal total returns in U.S. dollars over a six-month horizon.
84 Solnik/McLeavey • Global Investments, Sixth Edition
47. Guaranteed note.
You are a young banker offering a client to issue a guaranteed note. The yield curve is flat at 9% for
each maturity. Options on the stock index are offered by banks. An at-the-money call with a two-year
maturity trades at 12% of the index value, whereas a three-year call is worth 15% of the index.
You wonder about the characteristics of the bond. If you offer a high coupon, the indexation will be
low. Therefore, you decide to compute the indexation levels in accordance to the current market
conditions for maturities of two and three years and coupon levels of 0%, 2%, and 5%.
Solution
The following table shows the indexation for different coupons and maturities.
Coupon
p (2 years)
p (3 years)
0%
105.55%
126.57%
2%
82.09%
98.44%
5%
46.91%
56.26%
Chapter 7 Global Bond Investing 85
48. You’re a banker. A client wishes to buy a guaranteed note with a 100% indexation to the stock
index’s growth. In other words, he does not want any coupon but requires 100% of the index growth.
You wonder about the maturity of such a note. You check the prices of various index calls traded on
the market for different maturities. Their strike is the current index level and their price is expressed
as a percentage of this level. (For instance, if the CAC is worth 3,000, the strike is 3,000, and the one-
year maturity call trades at 11% of 3,000. You also check the price of a zero-coupon in percentage for
various maturities. The following graph shows, for each a maturity, the price of the option, that of the
zero-coupon and 100%-zero.
a. What is the maturity of the guaranteed note (Coupon = 0%, indexation = 100%)? Justify.
b. If as a banker, you want to make a profit, should you lengthen or shorten the maturity of that
note? Explain why.
c. Everything remaining constant (i.e., same volatility and interest rate), should the maturity
of the guaranteed note be shorter or longer if the index pays a low dividend rather than a
high one? Why?
49. The investment fund of Lemon County of California is investing $1 billion in a leveraged-bond hedge
fund. This hedge fund has the following structure:
• $4 billion invested in a reverse-floater (also called bull FRN). This is a five-year bond with a
coupon set at: 9% minus three-month LIBOR.
• $3 billion borrowed at: three-month LIBOR.
The current yield curve is flat at 4.5%. The reverse floater is currently priced at 100%.
a. Estimate the yield-enhancement over LIBOR that the hedge fund would provide if the yield
curve drops uniformly by 10 basis points (0.1%).
86 Solnik/McLeavey • Global Investments, Sixth Edition
Actually, the whole yield curved moved up to 7% within a few days.
b. What would be the new income (coupon rate) on this $1 billion investment made by Lemon
County?
c. Can you provide some rough estimate of the new market value of this $1 billion investment?
Solution
Chapter 7 Global Bond Investing 87
50. Strumpf Ltd. decides to issue a convertible bond with a maturity of two years. Each bond is issued
with a nominal value of £100 and an annual coupon C; of course, C has to be determined. Each bond
can be redeemed for £100 or converted into one share of Strumpf at the option of the bondholder.
The current stock price of Strumpf is £90. The yield curve for an issuer like Strumpf is flat at 6%.
Barings is ready to issue long-term options on Strumpf shares. The premiums on calls with one-year
and two-year expirations are given below:
Strike
Price
European-Type
American-Type
1-Year
2-Year
1-Year
2-Year
90
11
16
12
17
100
6
8
6.5
9
a. American-type calls are more expensive than European-type calls. Is it reasonable?
b. Assume that the bond can only be converted at maturity, after payment of the second coupon.
What should be the fair coupon rate C, consistent with the above market conditions?
c. Assume that the bond is issued with the coupon rate determined above. The yield curve suddenly
moves from 6% to 6.1% and the option premiums stay the same. What should be the new market
price of the convertible bond?
d. Assume now that the bond can be converted on two dates (rather than one as above). These dates
are the first year (right after the first coupon payment) and the second year as above. It is not
possible to convert the two-year bond at any other date. Is it possible to construct an arbitrage
portfolio allowing to price the fair coupon C with the above data? Be precise in your explanation
and state what type of options you would need to price the bond.
Solution
88 Solnik/McLeavey • Global Investments, Sixth Edition
51. On April 1, 2000, a corporation rated AA has issued a semiannual FRN in dollars. This is a perpetual
bond, which will pay coupons indefinitely if the corporation does not default. The coupon is set at
six-month LIBOR plus a spread of ½ %. The six-month dollar LIBOR is equal to 5%.
a. Three months later (July 1, 2000), the corporation is still rated AA and the market-required credit
spread for AA is still at ½%. We observe the following LIBOR rates:
1-Month
3-Month
6-Month
3 3/4%
4 %
5 %
Give an estimation of the total value of the bond. What should be its quoted price?
b. Three months later (October 1, 2000), the coupon has just been paid. The six-month dollar
LIBOR is again at 5%, but the market-required spread for AA-rated corporations on long-term
FRNs has moved to 1%. Give some estimation of the new value of the FRN on reset date.
52. The Kingdom of Papou issues a very-bull bond with a coupon equal to:
14.6 − 2 LIBOR.
Of course, the coupon cannot be negative.
The Kingdom could have issued a FRN at LIBOR + ¼%, or a straight bond at 5.30%.
The current market conditions for swaps are 5% against LIBOR.
You could also trade in CAPS and FLOORS with different exercise prices (these are levels of interest
rates). The premiums are paid annually.
Exercise
Interest Rate
Annual Premium
Cap
Floor
7.3 %
0.2%
2%
14.6 %
0.1%
10%
Chapter 7 Global Bond Investing 89
a. You are a buyer of this very-bull bond. Tell us what it is equivalent to, in terms of buying/selling:
FRN, straight bonds, caps or floors?
b. Assume that the Kingdom actually wanted to issue a straight bond (fixed coupon). The bank will
put in place a “de–mining” portfolio with swaps and options so that this very-bull bond plus the
“de–mining” portfolio is equivalent to a straight bond. What is exactly the “de–mining” portfolio?
[Be very precise and tell us if the Kingdom must pay fixed, receive LIBOR or vice versa, etc. …]
c. What is the cost advantage for the Kingdom compared to issuing bonds @ 5.30 %?
d. Same question assuming that the Kingdom wanted to issue an FRN @LIBOR + ¼ %?
53. Inflation indexed bonds.
Many countries, among which the United Kingdom, the United States, and France, have issued
inflation indexed bonds. Coupons and reimbursement value depend on the price index at the time of
payment. Let’s assume that a bond has been issued for 100 at time 0, with a maturity n and a real
coupon equal to
0 . Let It be the price index at time t. The coupon paid at t will be:
Ct =
0 It/I0.
And the reimbursement value at maturity n will be:
Rn = 100 In/I0.
Since the reimbursement is also indexed on the price index, we can easily check that the actual yield
is equal to the real coupon accrued by the inflation rate.
However, the real interest rate required by the market fluctuates with time. Knowing the market price
of an inflation indexed bond and its real coupon, we can easily compute (using a discounting method)
its real yield
at any time t.
90 Solnik/McLeavey • Global Investments, Sixth Edition
If the indexed bond still has n years to maturity, we just have to use the discounting method for a real
cash-flow bond:
0 0 0
12
100 .
(1 ) (1 ) (1 )n
P
+
= + + +
+ + +
Knowing the real interest rate
we can compare it with the nominal interest rate r on classic bonds.
a. In terms of risk, what is the interest of such bonds? What kind of investors is it aimed at?
b. In terms of return, assume that yield curves r and
are flat and that we expect the inflation level
to remain constant for the coming years. You expect an annual inflation rate of
. In what case do
you prefer an inflation-indexed bond to a straight bond? [Find the relation between r,
and
]