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Exam 7: Global Bond Investing  

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Question 21

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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?

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a. FRNs issued on the international mark...

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Question 22

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There is a 0.5% probability of default by the year-end on a one-year bond issued at par by a particular corporation. If the corporation defaults, the investor will not get anything. Assuming that a default-free bond exists with identical cash flows and liquidity, and the one-year yield on this bond is 4%. a. What yield should be required by risk-neutral investors on the corporate bond? b. What should the credit spread be?

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a. Let y be the yield on the corporate b...

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Question 23

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Two bond indexes of the same market tend to give the similar total return indications even if their composition is quite different. Why?

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. $\begin{array} { l c c c } \text { Eond } & \text { Maturity } & \text { Coupon } & \text { Price } \\\hline \text { U.S. Gavernment } & \text { June 1,2013 } & 6.50 \% & 100.00 \\\text { German Government } & \text { June 1,2013 } & 7.50 \% & 100.00\end{array}$ 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.

A straight bond with an annual coupon of 9% will be reimbursed 100% in three years. The previous coupon has just been paid and this bond currently trades at 105.25%. Its European yield-to-maturity is 7%. a. What is its modified duration? b. What is its semiannual yield-to-maturity? c. What is its simple yield?

What are the potential biases of the simple yield calculation? Take the example of two straight yen Eurobonds with the same maturity of five years. Bond A has a coupon of 12% and Bond B, a coupon of 8%. The current market yield on yen bonds is 10%. These two bonds have the same yield-to-maturity of 10% and are correctly priced at 107.58% for Bond A and 92.42% for Bond B. What would be the yield-to-maturity indicated by the simple yield calculation?

Discuss the differences between a par and a discount Brady bond. a. Take the viewpoint of the emerging country. b. Take the viewpoint of the bondholder.

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: $\bullet$ Bond A: Straight bond. Five-year straight dollar Eurobond with a coupon of 7.25%. $\bullet$ 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: $\bullet$ Bond C: Bull FRN. Five-year FRN with a semiannual coupon set at: 13.75%-LIBOR. $\bullet$ Bond D: Bear FRN. Five-year FRN with a semiannual coupon set at: 2 * LIBOR - 7%. 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%.

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?

The yield curves in U.S. dollars and Swiss francs are as follows: $\begin{array} { l c c } & \text { U.E. Dollar\% } & \text { Swiss Franc\% } \\\hline 1 \text { Year } & 10 & 6 \\2 \text { Years } & 12 & 7 \\\hline\end{array}$ These are yields for zero-coupon bonds of one- and two-year maturities. The spot exchange rate is SF/$ = 1.5. a. What are the implied one-year and two-year forward exchange rates? b. You contemplate issuing a dual-currency bond. You could issue zero-coupon bonds in both currencies at the interest rates above. Instead, you wish to issue bonds of SF 150 with a coupon C in Swiss francs, paid each year for two years, and reimbursed for $100 at the end of two years. What is the interest rate c% (c = C/150) on the bond that would be consistent with the yield curves above? c. You contemplate issuing a two-year currency option bond. The bond is issued for $100 and gives the option to receive the coupons and principal payment in either dollars or Swiss francs at a fixed exchange rate of SF/$51.5. A bank gives you quotes on the premiums for SF calls with a strike price of 1/1.5 = 0.66666 US$. The premium for a one-year call is 4 U.S. cents (per Swiss franc) and for a two-year call is 7 U.S. cents. What coupon rate should you set on your currency option bond?

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%.

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:

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. 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 %?

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: $\begin{array} { c c c } & \text { May } 1,2006 \% & \text { August } 1,2006 \% \\\hline 1 \text { Month } & 5.00 & 4.00 \\3 \text { Months } & 5.00 & 4.50 \\6 \text { Manths } & 5.00 & 5.25 \\12 \text { Months } & 5.00 & 6.00\end{array}$ 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?

A bond has been issued in euros with an annual coupon rate of 10%. The previous coupon has just been paid. This bond has a sinking fund provision: Half of the issue is reimbursed in two years and half in three years. You hold €10 million of nominal value of this bond. a. Write the three future annual cash flows in euros, assuming that the previous coupon has just been paid. b. The yield curve is currently flat at 9%. What is the value of the bond, its yield-to-maturity, its duration, and its modified duration? c. How much do you stand to lose if the yield curve moves uniformly from 9% to 9.1% within one day?

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: $\bullet$ Bond A: Straight bond. Five-year straight dollar Eurobond with a coupon of 4%. $\bullet$ 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: $\bullet$ Bond C: Bull FRN. Five-year FRN with a semiannual coupon set at: 7.60% - LIBOR. $\bullet$ 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.

Why did U.S. commercial banks have an interest in the development of the Eurobond market?

Take the example of two straight yen Eurobonds with the same maturity of five years. Bond A has a coupon of 12% and Bond B a coupon of 8%. The current market interest rate on yen bonds is 9%. These two bonds have the same yield-to-maturity of 10% and are correctly priced at 111.67% for Bond A and 96.11% for Bond B. What would be the yield-to-maturity indicated by the simple yield calculation?

You purchase a Eurobond in euros, at a quoted price of 101.5%. The annual coupon on the bond is 6%, and we are exactly one month after the past coupon date. You buy €100,000 of nominal value of this bond. What is your total expense?

A young investment banker considers issuing a DM/$ currency option bond for a AAA client and wonders about its pricing. He knows that currency options are available on the market and that they could help set the conditions on the bond issue. As a first step, he decides to study a simple case: a one-year bond. The current market conditions are as follows: $\bullet$ One-year dollar interest rate: 10%. $\bullet$ One-year Deutsche mark interest rate: 7%. $\bullet$ Spot DM/$ exchange rate: $1 =DM 2. The banker could issue a bond in dollars at 10%, a bond in DM at 7%, or a currency option bond at an interest rate to be determined. One-year currency options are negotiated on the over-the-counter market. A one-year currency option to exchange one dollar for two Deutsche marks is quoted at 4%, that is, four cents per dollar. This is a European option, which can be exercised only at maturity. The one-year forward exchange rate is: $F = 2 \times \frac { 1 + 7 \% } { 1 + 10 \% } .$ a. Given these data, what should the interest rate be on a one-year DM/$ bond? b. How would you determine how to set the interest rate on an n-year currency bond?