ECON 311 1nd Edition Lecture 4 Outline of Last Lecture I Interest and Interest Rates II Calculating Interest Rates III Four Credit Market Instruments Outline of Current Lecture I Current Events II Four Credit Market Instruments III Calculating Yield to Maturity IV Bond Prices and Bond Yields V Difference Between Yield to Maturity and Rate of Return VI Real vs Nominal Interest Rates Current Lecture I Current Events a Bank of Japan buying short term Japanese Bonds with a negative interest rate i Japanese government is continuing to do this because they ve made a commitment to continue buying bonds EX If you have to buy either a 5 or 10 interest bond you would buy the 5 because it is a better choice than the 10 However if you can just keep your cash you wouldn t buy either of those bonds Chapter 3 Understanding Interest Rates II Four Credit Market Instruments a Simple Loan no payments till maturity b Discount Bond no payments till maturity c Coupon Bond makes interest payments regularly and pays back the left over interest and the principal at maturity These notes represent a detailed interpretation of the professor s lecture GradeBuddy is best used as a supplement to your own notes not as a substitute III IV d Fixed Payment Loan pay fixed payments till maturity mixed interest and principal Calculating Yield to Maturity YTM a Simple Loan YTM is the simple interest rate Face Value Present Value b One Year Discount Bond i Present Value C C C F c Coupon Bond P 2 n i 1 i 1 i 1 i 1 n FP FP FP d Fixed Payment Loan LV 2 i 1 i 1 i 1 n i Where P present value C coupon value F face value FP fixed payment LV loan value Bond Prices and Bond Yields EX 1 year discount bond with a face value of 5000 As you lower the bond price more interest is earned on the bond i F P P is the Formula for 1 year bon yield Price Increases as Yield to Maturity decreases 4500 11 1 4650 7 53 4800 4 17 BOND PRICES AND INTEREST RATES ARE NEGATIVELY RELATED V Difference Between Yield to Maturity and Rate of Return a If you hold a bond till maturity then i Yield to Maturity Rate of Return b But a bond can be sold before maturity c If you sell a bond PRIOR to maturity then YTM could be greater than equal to or less than the rate of return depending on if there is a capital gain or loss Rate of Return Formula RET C Pt 1 Pt Pt Pt Where C Coupon payment Pt Price of bond at time t and Pt 1 price of bond at time t 1 Pt 1 P t Rate of Capital Gain Pt C current yield Pt EX Buy a bond that has the following future payments 500 in 1 year 500 in 2 years 500 in 3 years and 10 500 in 4 years with a market interest rate of 5 So F 10 000 C 500 Find the Price of the Bond November 2015 500 476 19 1 05 1 November 2016 500 453 51 1 05 2 November 2017 500 431 92 1 05 3 November 2018 10 500 8638 38 1 05 4 Total Price of Bond 10 000 1 year after the 1st Coupon payment the market interest rate increases to 6 November 2016 500 471 70 1 06 1 November 2017 500 445 00 1 06 2 November 2018 10 500 8816 00 1 06 3 Total Price of Bond 9732 70 So RET 500 9732 70 10000 10000 10000 RET 0 05 0 0267 RET 0 0233 2 33 Alternatively 1 year after the 1st Coupon payment the market interest rate increases to 4 November 2016 500 480 77 1 1 04 November 2017 500 462 28 1 04 2 November 2018 10 500 9334 46 1 04 3 Total Price of Bond 10 227 51 RET So 500 10227 51 10000 10000 10000 RET 0 05 0 0228 RET 0 0728 7 28 EX Market Interest Rates are 5 and you buy two discount bonds one that matures in 5 years and one that matures in 10 years The 5 year bond is worth 7835 26 and the 10 year bond is worth 6139 13 If Interest Rates increase to 6 what would happen to the bond prices They would both fall but the 10 year bond would fall by more than the 5 year bond 10000 7473 80 fellby 362 46 1 06 5 5 year 10 year 10000 5586 60 fell by 550 53 1 06 5 THE LONGER A BONDS MATURITY THE MORE SENSITIVE THE PRICE TO A CHANGE IN INTEREST RATES VI Real vs Nominal Interest Rates a Real interest rate is the nominal interest rate minus the rate of inflation real interest rate nominal interest rate inflation rate b Ex Post vs Ex Ante Real Interest Rates i Ex Post real interest rate nominal interest rate actual inflation rate ii Ex Ante real interest rate nominal interest rate expected inflation e