Copyright © 2014 Pearson Canada Inc. Chapter 4 UNDERSTANDING INTEREST RATES Mishkin/Serletis The Economics of Money, Banking, and Financial Markets Fifth Canadian Edition

Copyright © 2014 Pearson Canada Inc. 4-2 Learning Objectives 1.Detail the present value concept and the meaning of the term interest rate 2.Discern among the ways of measuring the interest rate 3.Illustrate how bond prices and interest rates are negatively related 4.Explain the difference between nominal and real interest rates 5.Assess the difference between interest rates and rates of return

Copyright © 2014 Pearson Canada Inc. 4-3 Measuring Interest Rates Present Value: –a dollar paid to you one year from now is less valuable than a dollar paid to you today –why? a dollar deposited today can earn interest and become $1 x (1+i) n

Copyright © 2014 Pearson Canada Inc. 4-4 Discounting the Future Let i = 0.10 In one year $100 x (1+0.10)= $110 In two years $110 x (1+0.10)=$121 In three years $121 x (1+0.10)= $133 In general $100 dollars in n years: $100 x (1+i) n

Copyright © 2014 Pearson Canada Inc. 4-5 Simple Present Value PV = today’s present value CF = future cash flow or payments i = interest rate

Copyright © 2014 Pearson Canada Inc. 4-6 Time Line $100 Year01 PV100 2 $100 n 100/(1+i)100/(1+i) 2 100/(1+i) n

Copyright © 2014 Pearson Canada Inc. 4-7 Four Types of Credit Market Instruments 1.Simple Loan –principal is repaid at the maturity date with interest 2.Fixed Payment Loan –principal is repaid by making the same payment (principal + interest) every period for a set period of time

Copyright © 2014 Pearson Canada Inc. 4-8 Four Types of Credit Market Instruments 3.Coupon Bond –a coupon bond pays the owner of the bond a fixed interest payment (coupon payment) every year until the maturity date, when a specified final amount (face value or par value) is repaid 4.Discount Bond –a discount bond (also called a zero-coupon bond) is bought at a price below its face value (at a discount), and the face value is repaid at the maturity date

Copyright © 2014 Pearson Canada Inc. 4-9 Yield to Maturity YTM –the interest rate that equates the present value of cash flow payments received from a debt instrument with its value today

Copyright © 2014 Pearson Canada Inc Simple Loan PV = amount borrowed = $100 CF = cash flow in one year = $110 n = number

Copyright © 2014 Pearson Canada Inc Fixed Payment Loan LV = loan value FP = fixed yearly payment N = number of years until maturity

Copyright © 2014 Pearson Canada Inc Coupon Bond P = price of coupon bond C = yearly coupon payment F = face value of the bond n = years to maturity

Copyright © 2014 Pearson Canada Inc Yields to Maturity on a 10%-Coupon-Rate Bond Maturing in Ten Years (Face Value = $1,000)

Copyright © 2014 Pearson Canada Inc Three Facts About Coupon Bonds 1.When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate 2.The price of a coupon bond and the yield to maturity are negatively related 3.The yield to maturity is greater than the coupon rate when the bond price is below its face value

Copyright © 2014 Pearson Canada Inc Consol or Perpetuity P c = price of the consol C = yearly interest payment i c = yield to maturity of the consol A bond with no maturity date that does not repay principal but pays fixed coupon payments forever

Copyright © 2014 Pearson Canada Inc Discount Bond F = face value of the discount bond P = current price of the discount bond

Copyright © 2014 Pearson Canada Inc Yield on a Discount Basis Yield on a discount basis: i db = yield on a discount basis F= face value P= purchase price

Copyright © 2014 Pearson Canada Inc The Distinction Between Interest Rates and Returns

Copyright © 2014 Pearson Canada Inc The Distinction Between Interest Rates and Returns (cont’d) The return equals the yield to maturity only if the holding period equals the time to maturity A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period The more distant a bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change

Copyright © 2014 Pearson Canada Inc The Distinction Between Interest Rates and Returns (cont’d) The more distant a bond’s maturity, the lower the rate of return the occurs as a result of an increase in the interest rate Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise

Copyright © 2014 Pearson Canada Inc One-Year Returns on Different-Maturity 10%-Coupon- Rate Bonds When Interest Rates Rise from 10% to 20%

Copyright © 2014 Pearson Canada Inc Interest-Rate Risk Prices and returns for long-term bonds are more volatile than those for shorter-term bonds There is no interest-rate risk for any bond whose time to maturity matches the holding period

Copyright © 2014 Pearson Canada Inc Real and Nominal Interest Rates Nominal interest rate makes no allowance for inflation Real interest rate is adjusted for changes in price level so it more accurately reflects the cost of borrowing Ex ante real interest rate is adjusted for expected changes in the price level Ex post real interest rate is adjusted for actual changes in the price level

Copyright © 2014 Pearson Canada Inc Fisher Equation i = nominal interest rate r = real interest rate π e = expected inflation rate

Copyright © 2014 Pearson Canada Inc Fisher Equation (cont’d) When the real interest rate is low, there are greater incentives to borrow Low interest rates reduces the incentives to lend The real interest rate is a better indicator of the incentives to borrow or lend

Copyright © 2014 Pearson Canada Inc Real and Nominal Interest Rates