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The following information relates to Questions 1–6 Katrina Black, portfolio manager at Coral Bond Management, Ltd

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The following information relates to Questions 1–6

Katrina Black, portfolio manager at Coral Bond Management, Ltd., is conducting a training session with Alex Sun, a junior analyst in the fixed income department. Black wants to explain to Sun the arbitrage-free valuation framework used by the firm. Black presents Sun with Exhibit 1, showing a fictitious bond being traded on three exchanges, and asks Sun to identify the arbitrage opportunity of the bond. Sun agrees to ignore transaction costs in his analysis.

EXHIBIT 1 Three-Year, €100 par, 3.00% Coupon, Annual-Pay Option-Free Bond

	Eurex	NYSE Euronext	Frankfurt
Price	€103.7956	€103.7815	€103.7565

 

Black shows Sun some exhibits that were part of a recent presentation. Exhibit 3 presents most of the data of a binomial lognormal interest rate tree fit to the yield curve shown in Exhibit 2. Exhibit 4 presents most of the data of the implied values for a four-year, option-free, annual-pay bond with a 2.5% coupon based on the information in Exhibit 3.

EXHIBIT 2 Yield to Maturity Par Rates for On-, Two-, and Three-Year Annual-Pay

Option-Free Bonds

One-Year	Two-Year	Three-Year
1.25%	1.50%	1.70%

 

EXHIBIT 3 Binomial Interest Rate Tree Fit to the Yield Curve (Volatility = 10%)

Time 0	Time 1	Time 2	Time 3	Time 4
				Node 4-1
			2.6241%
		1.8280%		4.2009%
	1.8229%		Node 3-2
1.2500%		Node 2-2		3.4394%
	1.4925%		1.7590%
		1.2254%		2.8159%
			Node 3-4
				Node 4-5

 

EXHIBIT 4 Implied Value (in Euros) for a 2.5%, Four-Year, Option-Free, Annual-Pay Bond Based on Exhibit 3

Time 0	Time 1	Time 2	Time 3	Time 4
			99,8791% 2,6241%	102.5
		100.7696 1,8280%	2.5
	101.7877 1,8229%	2.5	100.3442 2,1484%	102.5
103.4960 1,2500%	2.5	101.5168 1,4967%	2.5
	Node 1-2 1,4925%	2.5	100.7282 1,7590%	102.5
		102.1350 1.2254%	2.5
			101.0449 1.4401%	102.5

 

Black asks about the missing data in Exhibits 3 and 4 and directs Sun to complete the following tasks related to those exhibits:

Task 1 Test that the binomial interest tree has been properly calibrated to be arbitrage-free.

Task 2 Update Exhibit 3 to reflect the current volatility, which is now 15%.

1. Based on Exhibit 1, the best action that an investor should take to profit from the arbitrage opportunity is to:

A. buy on Frankfurt, sell on Eurex.

B. buy on NYSE Euronext, sell on Eurex.

C. buy on Frankfurt, sell on NYSE Euronext.

2. Based on Exhibits 1 and 2, the exchange that reflects the arbitrage-free price of the bond is:

A. Eurex.

B. Frankfurt.

C. N YSE Euronext.

3. Which of the following statements about the missing data in Exhibit 3 is correct?

A. Node 3–2 can be derived from Node 2–2.

B. Node 4–1 should be equal to Node 4–5 multiplied by e0.4

C. Node 2–2 approximates the implied one-year forward rate two years from now.

4. Based on the information in Exhibits 3 and 4, the bond price in euros at Node 1–2 in

Exhibit 4 is closest to:

A. 102.7917.

B. 104.8640.

C. 105.2917.

5. A benefit of performing Task 1 is that it:

A. enables the model to price bonds with embedded options.

B. identifies benchmark bonds that have been mispriced by the market.

C. allows investors to realize arbitrage profits through stripping and reconstitution.

6. If the assumed volatility is changed as Black requested in Task 2, the forward rates shown in Exhibit 3 will most likely:

A. spread out.

B. remain unchanged.

C. converge to the spot rates.

The following information relates to Questions 7–10

Betty Tatton is a fixed income analyst with the hedge fund Sailboat Asset Management (SAM). SAM invests in a variety of global fixed-income strategies, including fixedincome arbitrage. Tatton is responsible for pricing individual investments and analyzing market data to assess the opportunity for arbitrage. She uses two methods to value bonds:

Method 1: Discount each year’s cash flow separately using the appropriate interest rate curve.

Method 2: Build and use a binomial interest rate tree.

Tatton compiles pricing data for a list of annual pay bonds (Exhibit 1). Each of the bonds will mature in two years, and Tatton considers the bonds as being risk-free; both the one-year and two-year benchmark spot rates are 2%. Tatton calculates the arbitragefree prices and identifies an arbitrage opportunity to recommend to her team.

EXHIBIT 1 Market Data for Selected Bonds

Asset	Coupon	Market Price
Bond A	1%	98.0584
Bond B	3%	100.9641
Bond C	5%	105.8247

 

Next, Tatton uses the benchmark yield curve provided in Exhibit 2 to consider arbitrage opportunities of both option-free corporate bonds and corporate bonds with embedded options. The benchmark bonds in Exhibit 2 pay coupons annually, and the bonds are priced at par.

EXHIBIT 2 Benchmark Par Curve

Maturity (years)	Yield to Maturity (YTM)
1	3.0%
2	4.0%
3	5.0%

 

Tatton then identifies three mispriced three-year annual-pay bonds and compiles data on the bonds (see Exhibit 3).

EXHIBIT 3 Market Data of Annual-Pay Corporate Bonds

Company	Coupon	Market Price	Yield	Embedded Option?
Hutto-Barkley Inc.	3%	94.9984	5.6%	No
Luna y Estrellas Intl.	0%	88.8996	4.0%	Yes
Peaton Scorpio Motors	0%	83.9619	6.0%	No

 

Last, Tatton identifies a mispriced Swiss bonds, Bond X, a three-year bond and annual-pay bonds with a coupon rate of 6%. To calculate the bonds’ values, Tatton devises the first three years of the interest rate lognormal tree presented in Exhibit 4 using historical interest rate volatility data.

EXHIBIT 4 Interest Rate Tree; Forward Rates Based on Swiss Market

Time 0	Time 1	Time 2
		6%
	4%
1%		5%
	2%
		3%

 

 

7. Based on Exhibit 1, which of the following bonds most likely includes an arbitrage opportunity?

A. Bond A

B. Bond B

C. Bond C

8. Based on Exhibits 2 and 3 and using Method 1, the amount (in absolute terms) by which the Hutto-Barkley corporate bond is mispriced is closest to:

A. 0.3368 per 100 of par value.

B. 0.4682 per 100 of par value.

C. 0.5156 per 100 of par value.

9. Method 1 would most likely not be an appropriate valuation technique for the bond issued by:

A. Hutto-Barkley Inc.

B. Luna y Estrellas Intl.

C. Peaton Scorpio Motors.

10. Based on Exhibit 4 and using Method 2, the correct price for Bond X is closest to:

A. 97.2998.

B. 109.0085.

C. 115.0085.