Coupon Bonds and Zeroes Lecture

Coupon Bonds and Zeroes Lecture - Debt Instruments and...

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Debt Instruments and Markets Professor Carpenter Coupon Bonds and Zeroes 1 Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zero-coupon bonds Bond replication No-arbitrage price relationships Zero rates Veronesi, Chapters 1 and 2 Tuckman, Chapters 1 and 2 Zeroes STRIPS Dedication Implied zeroes Semi-annual compounding Reading

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Debt Instruments and Markets Professor Carpenter Coupon Bonds and Zeroes 2 Coupon Bonds In practice, the most common form of debt instrument is a coupon bond. In the U.S and in many other countries, coupon bonds pay coupons every six months and par value at maturity. The quoted coupon rate is annualized. That is, if the quoted coupon rate is c , and bond maturity is time T , then for each \$1 of par value, the bond cash flows are: If the par value is N , then the bond cash flows are: c /2 c /2 1 + c /2 0.5 years 1 year T years c /2 1.5 years Nc /2 Nc /2 N (1 + c /2) 0.5 years 1 year T years Nc /2 1.5 years U.S. Treasury Notes and Bonds Institutionally speaking, U.S. Treasury “notes” and “bonds” form a basis for the bond markets. The Treasury auctions new 2-, 3-, 5-, 7-year notes monthly, and 10-year notes and 30-year bonds quarterly, as needed. See - management/auctions/auctions.pdf for a schedule. Non-competitive bidders just submit par amounts, maximum \$5 million, and are filled first. Competitive bidders submit yields and par amounts, and are filled from lowest yield to the “stop” yield. The coupon on the bond, an even eighth of a percent, is set to make the bond price close to par value at the stop yield. All bidders pay this price. See, for example, ? page=FISearchTreasury for a listing of outstanding Treasuries.
Debt Instruments and Markets Professor Carpenter Coupon Bonds and Zeroes 3 Class Problem The current “long bond,” the newly issued 30-year Treasury bond, is the 3 7/8’s (3.875%) of August 15, 2040. What are the cash flows of \$1,000,000 par this bond? (Dates and amounts.) Bond Replication and No Arbitrage Pricing It turns out that it is possible to construct, and thus price, all securities with fixed cash flows from coupon bonds. But the easiest way to see the replication and no-arbitrage price relationships is to view all securities as portfolios of “zero-coupon bonds,” securities with just a single cash flow at maturity. We can observe the prices of zeroes in the form of Treasury STRIPS, but more typically people infer them from a set of coupon bond prices, because those markets are more active and complete. Then we use the prices of these zero-coupon building blocks to price everything else.

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Debt Instruments and Markets Professor Carpenter Coupon Bonds and Zeroes 4 Zeroes Conceptually, the most basic debt instrument is a zero- coupon bond--a security with a single cash flow equal to face value at maturity.
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• Spring '15
• Jennifer
• coupon bonds, debt instruments, Professor Carpenter

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