1. Lecture 37 Bonds Ana Nora Evans 403 Kerchof AnaNEvans@virginia.edu http://people.virginia.edu/~ans5k Math 1140 Financial Mathematics

2. Math 1140 - Financial Mathematics Last Time 2 A bond is a legal promise to pay the owner of the bond, regular payments, ending at a specified date in the future. On the bond are specified the face value (par value), F, and the coupon rate (bond rate), r. The coupon period is the time interval between two payments.

3. Math 1140 - Financial Mathematics Last Time The regular payment, called coupon, is the interest on the face value of the bond, F, for one coupon period, at the coupon rate, r. The coupon is equal to Fr. The last payment is called the maturity value (redemption value), R. 3

4. Math 1140 - Financial Mathematics The issuer of the bond, usually a corporation, a state, local or state government, sells the rights to the coupon payments and the redemption value to an entity (investor). Who borrows money? A)The investor. B)The issuer of the bond. C)Mickey Mouse. D)Nobody. 4

5. Math 1140 - Financial Mathematics The price of the bond is the amount paid by the owner of the bond to the issuer of the bond. The price is calculated using the desired yield rate per coupon period. 5

6. Math 1140 - Financial Mathematics A)When the yield increases, the price increases. B)When the yield increases, the price decreases. C)When the yield increases, the price does not change. D)None of the above. 6

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8. Today Bonds rating and junk bonds. The book value of a bond. 8

9. Math 1140 - Financial Mathematics The credit rating of a bond is a financial indicator to potential investors. The credit rating of a bond is assigned by a credit rating agency registered with the Securities and Exchange Commission (SEC). Examples: Standard & Poor's, Moody’s. 9

10. Math 1140 - Financial Mathematics Moody’sS&PCapacity of the issuer to meet its obligations AaaAAAExtremely strong Aa1AA+Very strong Aa2AA Aa3AA- A1A+Strong A2A A3A- 10 S&P Rating US treasury bondsAA+ GermanyAAA SpainAA- ChinaAA Home DepotA- Middlesex Cnty, NJAA+

11. Math 1140 - Financial Mathematics 11 Moody’sS&PCapacity of the issuer to meet its obligations Baa1BBB+Adequate Baa2BBB Baa3BBB- Ba1BB+Less vulnerable Ba2BB Ba3BB- B1B+More vulnerable B2B B3B- S&P Rating RomaniaBBB+ MozambiqueB+ UkraineB+

12. Math 1140 - Financial Mathematics Moody’sS&PCapacity of the issuer to meet its obligations CaaCCCCurrently vulnerable CaCCHighly vulnerable CHighly vulnerable (a bankruptcy petition may have been filled) CDFailed to pay one or more of its financial obligations when it became due. 12 S&P Rating GreeceC Jefferson County's sewer system bonds C

13. Math 1140 - Financial Mathematics Greek Bonds Yield 13

14. Math 1140 - Financial Mathematics Greece’s Bond Haircut “Negotiators from the Institute of International Finance, a consortium of Greek bondholders, have agreed to swap their current bonds for new ones worth 50% of their current value, though the final figure has still to be thrashed out.”Institute of International Financebonds The Guardian, 16 Nov 2011 14

15. Math 1140 - Financial Mathematics Junk Bonds A junk bond is a bond with a rating of BB or lower. A junk bond has a high risk of default and offers a high-yield. A junk bond is also called a high-yield bond or a speculative bond. 15

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17. Math 1140 - Financial Mathematics The Book Value The book value of a bond at a given time is the value of the remaining coupons plus the redeeming value at the given time. Similar to the outstanding value of a loan. 17

18. Math 1140 - Financial Mathematics The Book Value Consider a bond with face value, F, coupon rate, r, yield, i, and n coupon payments. The book value of the bond after the k th payment is 18

19. Math 1140 - Financial Mathematics Suppose that a $2000 12- year par-value bond pays interest at 9% convertible semi-annually. Find the book value immediately after the 11 th coupon has been paid, if the yield rate is 7% convertible semi-annually. F = $2,000 R = $2,000 r = 0.09/2 = 0.045 i = 0.07/2 = 0.035 n = 12×2 = 24 k=11 There are 13 payments left. The book value is: 19

20. Math 1140 - Financial Mathematics Suppose that we have a 14- year par-value bond that pays interest at 8% convertible semi-annually. If the book value immediately after payment of the 13 th coupon is $1269.10 at a yield rate of 7% convertible semi- annually, what is the face value of the bond? n = 14×2 = 28 r = 0.08/2 = 0.04 k = 13 BV 13 = $1,269.1 i = 0.07/2 = 0.035 F = ? 20

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22. Math 1140 - Financial Mathematics Upcoming Deadlines Today – HW 12 due Nov 30 – final report and evaluations Nov 30, Dec 2, Dec 5 – presentations and evaluations 22