1. Types of Bonds Simple loan (example: loan from bank) Discount bond/loan (example: savings bond or bank loan) Coupon bond (example:corporate bond) Fixed-payment loan (example:mortgage)

2. Time Lines for Credit Market Instruments

3. Present Value Comparing returns across debt types is difficult since timing of repayment differs. Solution is the concept of present value.

4. To calculate Present Value The present value of a future flow of streams of income from the asset is the amount you would need today to make you indifferent between buying the asset and getting that amount today. To find this, ask the following: asset A gives me a flow equal to X after n years. How much would I need now, so that if I invest this amount at a given interest rate (call this i), I could get the same amount X, after n years.

5. Example I can buy a discount bond which will give me $10,000 after a year. The current interest rate at the moment is 10%. What is the Present Value of this asset? Ans: Interest rate=10%=0.1, n=1 year. PV (1+.1) =$10,000  PV (1.1)=$10,000 PV=$10,000/1.1= $9090.9. In other words, I am indifferent between getting the 10,000dollars from the bond next year and getting 9090.9 today. So if the bond costs >9090 don’t buy it. If less, buy it

6. General Formula The present value of $1 received n years in the future is $1/(1 + i) n.

7. Yield to maturity Sometimes, all we know is the price of the asset now and the future payment schedule: In this case, to compare between assets, we need to compare the yield to maturity Definition: the interest rate that equates the present value to price is the yield to maturity.

8. Example of Yield to maturity Coupon Bond. Assume you can buy a coupon bond with a face value of $5,000 and a 3 year maturity for $4,000. It gives you $500 a year as coupon payment. How to calculate YTM? Price of bond=$4,000 PV of coupon bond payments: 500/(1+i)+500/(1+i) 2 +5000/(1+i) 3 Solve $4,000 = 500/(1+i)+500/(1+i) 2 +55000/(1+i) 3 then i= YTM

9. Bond Yields and Prices Bond yields (the yield to maturity) and the price of the bond are inversely related. As interest rates rise, price of bonds falls. The simplest version of yield is calculated using the following formula: yield = coupon amount/price. When you buy a bond at par, yield is equal to the interest rate. When the price changes, so does the yield. Let's demonstrate this with an example. If you buy a bond with a 10% coupon at its $1,000 par value, the yield is 10% ($100/$1,000). Pretty simple stuff. But if the price goes down to $800, then the yield goes up to 12.5%. This happens because you are getting the same guaranteed $100 on an asset that is worth $800 ($100/$800). Conversely, if the bond goes up in price to $1,200, the yield shrinks to 8.33% ($100/$1,200)

10. Different concept of yields with changing bond prices We need two more concepts: Current yield = coupon/current price. Coupon rate = coupon/face value. Example: $1000 bond with coupon payment of $100 and current price of $800. Then current yield=$100/$800=12.5% coupon rate=$100/$100=10%

11. The arithmetic of Current Price and Face Value If current price = face value, then yield to maturity = current yield = coupon rate. (previous example: if current price=$1000, then CY=100/1000=10%, same as the coupon rate) If current price current yield > coupon rate. (previous example: if current price=$800, then CY=100/800=12.5%,more than the coupon rate) If current price > face value, then yield to maturity < current yield < coupon rate. (previous example: if current price=$1500, then CY=100/1250=8%,more than the coupon rate) Why do we care? Because we care about current yields.

12. Treasuries Fall After Fed Manufacturing Reports Spark Inflation Concerns Sept. 15 (Bloomberg) -- U.S. Treasuries fell, pushing the 10-year bond’s yield to a three-week high, as reports showing a surge in prices paid by manufacturers this month raised concern inflation will accelerate. The Federal Reserve's New York and Philadelphia branches said factories paid more for materials even as business slowed. Inflation erodes the value of fixed-income payments, and may provide the Fed with incentive to keep raising interest rates. The bond ``market is vulnerable,'' said Don Alexander, a fixed-income strategist in New York at Citibank Private Bank, with about $200 billion in assets. ``Inflationary pressures certainly are building. We don't think the Fed can deviate from their rate increases”, he said, adding that bonds are likely to fall through year-end. The yield on the benchmark 10-year note rose 5 basis points, or 0.05 percentage point, to 4.21 percent at 3:20 p.m. in New York, according to bond broker Cantor Fitzgerald LP. Yields move inversely to bond prices. The yield had ranged from 3.98 percent to 4.20 percent since Hurricane Katrina made landfall on Aug. 29 and caused economists to lower their growth forecasts.

13. Sensitivity of Bond Prices to Interest Rate Changes What happens if interest rates rise to the price of a long term bond?

14. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 4-14 Three Types of Risk Any financial claim entails 3 kinds of risk: Default or Credit Risk (The risk that a borrower will default) Liquidity Risk (The risk that the asset cannot be sold easily) Interest Rate Risk (The risk that the interest rates will move so as to make the asset less valuable)

15. Interest Rate Risk Two components: However, they partially offset each other. If interest rates increase, bond’s price drops, but we get a higher rate on the reinvestment of coupon payments. Price risk. Results from interest rate changes in accordance with first bond theorem. Reinvestment risk. Results form when coupon payments cannot be reinvested at the bonds promised yield.

16. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 4-16 How do you decide what is risky? Typically done by specialists called Ratings Agencies (Moody’s, Standard and Poor)

17. Total Rate of Return The total rate of return is the sum of current yield and actual capital gain or loss. Rate of return can differ from yield to maturity. The formula for total rate of return is: R = C/P t + (P t+1 - P t )/P t. (rate of return is current yield/price+ capital gains Example: a bond with par value of $1000 redeemable in a year is bought today for $800 and pays a coupon of $100. R=100/800+(1000-800)/800=300/800=37.5%

18. Real and Nominal Interest Rates Expected real interest rate = nominal interest rate - the expected rate of inflation. Fisher hypothesis: change in expected inflation = change in nominal interest rate. The real rate of return equals the nominal rate of return adjusted for expected inflation.

19. Real and Nominal Interest Rates, 1960-2002

20. Copyright © 2005 Pearson Addison-Wesley. All rights reserved. 4-20 Reading Bond Tables Look at Bond Basics and http://markets.on.nytimes.com/research/ markets/bonds/bonds.asp http://markets.on.nytimes.com/research/ markets/bonds/bonds.asp