1. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-1 Distinction Between Real and Nominal Interest Rates Real interest rate 1.Interest rate that is adjusted for expected changes in the price level: it is adjusted by subtracting expected rate of inflation 2.Real interest rate more accurately reflects true cost of borrowing 3.When the real rate is low, there are greater incentives to borrow and less to lend

2. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-2 Distinction Between Real and Nominal Interest Rates Real interest rate We usually refer to this rate as the ex ante real rate of interest because it is adjusted for the expected level of inflation. After the fact, we can calculate the ex post real rate based on the observed level of inflation.

3. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-3 Distinction Between Real and Nominal Interest Rates (cont.) If i = 5% and π e = 0% then If i = 10% and π e = 20% then Nominal and real rates often do not move together…

4. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-4 U.S. Real and Nominal Interest Rates Sample of current rates and indexes http://www.martincapital.com/charts.htm

5. Distinction Between Interest Rates and Returns For any security, the rate of return is defined as the payments to the owner plus the change in its value, expressed as a fraction of its purchase price How well a person does by holding a bond over a particular time period is accurately measured by the rate of return Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-5

6. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-6 Distinction Between Interest Rates and Returns Rate of Return: we can decompose returns into two pieces: where = current yield, and = capital gains.

7. Distinction Between Interest Rates and Returns $ 1,000-face-value coupon bond maturing in 10 Years Coupon rate: 10% Bought for $ 1,000 Held for one year Sold for $ 1,200 YTM? R? Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-7

8. Distinction Between Interest Rates and Returns The yield to maturity is known at the time the bond is purchased The price at the maturity date is already fixed at the face value Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-8

9. Distinction Between Interest Rates and Returns The return on a bond, which tells you how good an investment it has been over the holding period, is equal to the yield to maturity in only one case: when the holding period and the maturity of the bond are identical. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-9

10. Distinction Between Interest Rates and Returns The return on a bond will not necessarily equal the interest rate on that bond… Let’s look at what happens to the returns on bonds of different maturities when interest rates rise. We calculate the one-year return on several 10% coupon rate bonds all purchased at par, when interest rates on all these bonds rise from 10% to 20%. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-10

11. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-11 Key Facts about the Relationship Between Rates and Returns Sample of current coupon rates and yields on government bonds http://www.bloomberg.com/markets/iyc.html

12. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-12 Maturity and the Volatility of Bond Returns Key findings from Table 3-2 1.The only bond whose return equals the initial YTM is one with maturity = holding period 2.For bonds with maturity > holding period, i  P  implying capital loss 3.Longer is maturity, greater is price change associated with interest rate change 4.Bond with high initial interest rate can still have negative return if i 

13. Interest rate risk Price changes of +20% and -20% within a year are common for bonds more than 20 years away from maturity! Changes in interest rates make investments in long-term bonds quite risky: interest rate risk Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-13

14. Interest rate risk Bonds whose term to maturity is longer than the holding period are subject to interest-rate risk Interest-rate risk is especially important for long-term bonds Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-14

15. Interest rate risk But… the fact that two bonds have the same term to maturity does not mean that they have the same interest-rate risk. A long-term discount bond with 10 years to maturity makes all of its payments at the end of the 10 years, whereas a 10% coupon bond with 10 years to maturity makes substantial cash payments before the maturity date. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-15

16. Interest rate risk Since the coupon bond makes payments earlier than the zero-coupon bond, we might intuitively guess that the coupon bond’s EFFECTIVE MATURITY, the term to maturity that accurately measures interest-rate risk, is shorter than it is for the zero-coupon bond (all else being equal) Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-16

17. Interest rate risk The effective maturity is called DURATION Duration is a weighted average of the maturities of the cash payments Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-17

18. Reinvestment Risk If an investor’s holding period is longer than the term to maturity of the bond, the investor is exposed to “reinvestment risk”. Reinvestment risk occours because the proceeds from the bond need to be reinvested at a future interest rate that is uncertain Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-18

19. Reinvestment Risk Reinvestment risk is especially important for short-term bonds If the holding period is longer than the term to maturity of the bond, the investor benefits from a rise in interest rate and is hurt by a fall in interest rates. Copyright © 2009 Pearson Prentice Hall. All rights reserved. 3-19