ECON 311 1nd Edition Lecture 4 Outline of Last Lecture I. Interest and Interest RatesII. Calculating Interest RatesIII. Four Credit Market InstrumentsOutline of Current Lecture I. Current EventsII. Four Credit Market InstrumentsIII. Calculating Yield to MaturityIV. Bond Prices and Bond YieldsV. Difference Between Yield to Maturity and Rate of ReturnVI. Real vs. Nominal Interest RatesCurrent LectureI. Current Eventsa. Bank of Japan buying short term Japanese Bonds with a negative interest ratei. Japanese government is continuing to do this because they’ve made a commitment to continue buying bondsEX: 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 bondsChapter 3: Understanding Interest RatesII. Four Credit Market Instrumentsa. Simple Loan – no payments till maturityb. Discount Bond – no payments till maturityc. Coupon Bond – makes interest payments regularly and pays back the left over interest and the principal at maturityThese 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.d. Fixed-Payment Loan – pay fixed payments till maturity (mixed interest and principal)III. Calculating Yield to Maturity (YTM)a. Simple Loan YTM is the simple interest rateb. One – Year Discount Bond i=Face Value−Present ValuePresent Valuec. Coupon Bond P=C(i+1)+C(i+1)2+. ..+C(i+1)n+F(i+1)nd. Fixed – Payment Loan LV =FP(i+1)+FP(i+1)2+. . .+FP(i+1)ni. Where P=present value, C=coupon value, F=face value, FP=fixed payment,LV=loan valueIV. Bond Prices and Bond YieldsEX: 1 year discount bond with a face value of $5000As you lower the bond price more interest is earned on the bondi=F−PP is the Formula for 1 year bon yieldPrice 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 Returna. If you hold a bond till maturity then:i. Yield to Maturity = Rate of Returnb. But a bond can be sold before maturityc. 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 lossRate of Return Formula:RET=CPt+Pt +1−PtPtWhere C=Coupon payment, Pt=Price of bond at time, t and Pt+1=price of bond at time, t+1CPt=current yield Pt +1−PtPt=Rate of Capital GainEX: 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=$500Find the Price of the Bond:November 2015,500(1.05)1=$ 476.19November 2016,500(1.05)2=$ 453.51November 2017,500(1.05)3=$ 431.92November 2018,10,500(1.05)4=$ 8638.38Total Price of Bond=$ 10,0001 year after the 1st Coupon payment the market interest rate increases to 6%November 2016,500(1.06)1=$ 471.70November 2017,500(1.06)2=$ 445.00November 2018,10,500(1.06)3=$ 8816.00Total Price of Bond=$ 9732.70So: RET=50010000+9732.70−1000010000 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(1.04)1=$ 480.77November 2017,500(1.04)2=$ 462.28November 2018,10,500(1.04)3=$ 9334.46Total Pri ce of Bond=$ 10,227.51So: RET=50010000+10227.51−1000010000 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 yearsThe 5 year bond is worth $7835.26 and the 10 year bond is worth $6139.13If Interest Rates increase to 6% what would happen to the bond prices?They would both fall but the 10-year bond would fall by more than the 5-year bond5 year: 10000(1.06)5=$ 7473.80 fellby $ 362.4610 year: 10000(1.06)5=$ 5586.60 fellby $ 550.53THE LONGER A BONDS MATURITY THE MORE SENSITIVE THE PRICE TO A CHANGE IN INTERESTRATESVI. Real vs. Nominal Interest Ratesa. Real interest rate is the nominal interest rate minus the rate of inflationreal interest rate=nominalinterest rate−inflation rateb. Ex Post vs. Ex Ante Real Interest Ratesi. Ex Post: real interest rate = nominal interest rate – actual inflation rateii. Ex Ante: real interest rate = nominal interest rate – expected inflation