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# Econ315 Money and Banking: Learning Unit #13: Term Structure of Interest Rates

Money and Banking

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### Econ315 Money and Banking: Learning Unit #13: Term Structure of Interest Rates

1. 1. 4210011 0010 1010 1101 0001 0100 1011 Learning Unit #13 Term Structure of Interest Rates
2. 2. 421 0011 0010 1010 1101 0001 0100 1011 Objectives of Learning Unit • You have learned in the previous Learning Unit how differences in characteristics of financial instruments lead to different market interest rates. − Risk, liquidity, and tax attributes • In this Learning Unit, you will learn one more important characteristic of financial instruments. – Maturity
3. 3. 421 0011 0010 1010 1101 0001 0100 1011 Maturity and Interest Rates • Although some financial instruments are issued by the same borrowers and have the same characteristics except for maturities, they often have different interest rates. • Example: How much are interest rates on 3 month maturity CD, 6 month maturity CD, 1 year maturity CD, and 3 year maturity CD at your bonk? Are they same? These CDs are identical (risk, tax treatment, etc.) except for maturity.
4. 4. 421 0011 0010 1010 1101 0001 0100 1011 Maturity and Interest Rates of U.S. Treasury Securities • U.S. Treasury securities with different maturity have different interest rates. − In general, interest rates on three-month U.S. Treasury bills are lower than those of 20-year U.S. Treasury bonds. − A spread between Treasury bills and Treasury bonds changes over time.
5. 5. 421 0011 0010 1010 1101 0001 0100 1011 Yield Curve • Yield curve: A plot of the interest rates (yield to maturity) for particular types of bonds with different terms to maturity, but the same risk, liquidity, and tax treatments. • Yield curves are classified in terms of their shapes and are used to explain the condition in financial markets and the economy.
6. 6. 421 0011 0010 1010 1101 0001 0100 1011 Example of Yield Curve • Interest rates on CDs are 3% on 1-year maturity, 4% on 2-year maturity, and 5% on 3-year maturity. – Click your mouse to see how a yield curve is drawn on this example. Maturity Interest Rate 4% 2 year 3% 1 year 5% 3 year Yield curve
7. 7. 421 0011 0010 1010 1101 0001 0100 1011 Variations of Yield Curves • Yield curve may be upward-sloping, flat, downward- sloping (inverted), or any shapes between. – Different shapes appear under different economic conditions. – They are used to explain or predict an economic condition.
8. 8. 421 0011 0010 1010 1101 0001 0100 1011 Example of Yield Curve on Barron’s • Dow Jones’ publishes a yield curve of U.S. Treasury securities every day on the Wall Street Journal and weekly on Barron’s. • They compare the most recent yield curve with a yield curve one month ago and another one year ago, and examine − Shape of yield curve − Changes in yield curve • Yield curve section from Barron’s, January 7, 2008 – See “How to Interpret Yield Curve of Barron’s” on Blackboard
9. 9. 421 0011 0010 1010 1101 0001 0100 1011 Three Theories to Explain Yield Curve • Why does a yield curve have different shapes? Why does it change from time to time? • Three different reasons for yield curves (different interest rates among financial instruments with different maturities) – Liquidity premium theory – Segmented market theory – Expectations theory
10. 10. 421 0011 0010 1010 1101 0001 0100 1011 Liquidity Premium Theory • Normally, the yield curve is upward sloping. – Interest rates on short-term securities are normally lower than interest rates on long-term securities. − Figure 4 on slide #4 shows that in most years interest rates on three-month U.S. Treasury bills are lower than those of 20-year U.S. Treasury bonds. • One important difference between short-term securities and long-term securities is their liquidities. − Liquidity of short-term securities is higher than liquidity of long-term securities. − Even if you cannot sell them, short-term securities will mature sooner than long-term securities and owners of short-securities will receive full payments sooner.
11. 11. 421 0011 0010 1010 1101 0001 0100 1011 Liquidity and Yield Curve • Liquidity of short-term securities > liquidity of long- term securities. • Saver/lenders prefer liquidity. • Demand for short-term securities > Demand for long- term securities. • Interest rates on short-term securities < Interest rates on long-term securities. Long-term High interest rate Short-term Low interest rate Upward-sloping yield curve
12. 12. 421 0011 0010 1010 1101 0001 0100 1011 Liquidity Premium Theory and Actual Yield Curve • Although the liquidity premium theory can explain the yield curve most time, it cannot explain why a yield curve becomes sometimes flat, downward-sloping, and any shapes between. • Segmented market and expectations theories complement the liquidity premium theory.
13. 13. 421 0011 0010 1010 1101 0001 0100 1011 Segmented Market Theory • The segmented market theory assumes that the interest rate on each instrument is determined in a separate market with a separate market demand and supply. − A short-term interest rate is determined by demand for and supply of sort-term securities in the short-term security market. − A long-term interest rate is determined by demand for and supply of long-term securities in the long-term security market.
14. 14. 421 0011 0010 1010 1101 0001 0100 1011 Example of Segmented Market Theory #1 • Demand for short-term securities is relatively greater than demand for long-term securities. • Assume same supply in both short-term and long-term securities markets. P Short-term Q S P Q Long-term S i maturity ii Upward sloping Low interest rate High interest rate is iL is iL Short-term Long-term
15. 15. 421 0011 0010 1010 1101 0001 0100 1011 Example of Segmented Market Theory #2 • Demand for short-term securities is relatively less than demand for long-term securities. • Assume same supply in both short-term and long-term securities markets. P Short-term Q S P Q Long-term S i maturity ii iS Short-term iS iL Long-term iL Downward sloping High interest rate Low interest rate
16. 16. 421 0011 0010 1010 1101 0001 0100 1011 Example of Segmented Market Theory #3 • Demand for short-term securities is equal to demand for long- term securities. • Assume same supply in both short-term and long-term securities markets. P Short-term Q S P Q Long-term S i maturity ii iS iS Short-term iL Long-term iL Flat yield curve
17. 17. 421 0011 0010 1010 1101 0001 0100 1011 Segmented Market Theory and Shapes of Yield Curve • Markets of securities can be divided into three different maturities: short-term, mid- term, and long-term. Then, depending on relative demand and supply in each market, a yield curve may have V-shape or Λ-shape. • By segmenting into more markets, any shapes of yield curve can be explained by relative demand and supply in each maturity market.
18. 18. 421 0011 0010 1010 1101 0001 0100 1011 Limitation of Segmented Market Theory • Although the segmented market theory can explain any shapes of yield curve, based on relative demand and supply of each maturity security, it cannot explain why demands and supplies differ among markets. • In reality, demand for each maturity securities is not completely independent to each other, so as supply. • The expectations theory considers this interdependency among securities and provides a reason for different demands.
19. 19. 421 0011 0010 1010 1101 0001 0100 1011 Expectations Theory • The expectations theory considers an interdependency among securities and provides a reason for different demands. − If you want to save \$1,000 for two years, you may purchase either one-year CD today (and roll over to another one year CD next year) or two-year CD today. − Two strategies (1-year CDs or 2-year CD) are perfect substitute. − If one strategy provides a higher return the other strategy, saver/lenders will prefer the former over the later and change their demands, leading changes in an equilibrium in to markets (1-year CD market and 2-year CD market). − Both markets will be at an equilibrium only if both strategies provide the same return.
20. 20. 421 0011 0010 1010 1101 0001 0100 1011 Example of Two Strategies • You save \$1,000 for two years. • Strategy #1: You purchase 1-year CD today which provides 3% annual interest rate. • Strategy #2: You purchase 2-year CD today which provides 4% annual interest rate. • If you take Strategy #1, you will reinvest your saving next year (purchase 1-year CD) at X% annual interest rate which is unknown today. • A rate of return from Strategy #1 is FV = \$1,000 x (1+3%) x (1+X%) = ??? – A return from this strategy depends on an interest rate on one-year CD next year. • A rate of return from Strategy 32 is FV = \$1,000 x (1+4%)2 = \$1,081.60
21. 21. 421 0011 0010 1010 1101 0001 0100 1011 Expectation and Choice of Strategy • If you expect that an interest rate on one-year CD is still 3% next year, how much will be a return from Strategy #1? Which strategy will you choose? How will your choice affect the market of 2-year CD today and its interest rate? – Strategy #1 will provide \$1,060.90, so you should choose Strategy #2. An increase in demand for 2-year CD will lower its interest rate. • If you expect that an interest rate on one-year CD increases to 7% next year, how much will be a return from Strategy #1? Which strategy will you choose? How will your choice affect the market of 2-year CD today and its interest rate? – Strategy #1 will provide \$1,102.10, so you should choose Strategy #1. A decrease in demand for 2-year CD will raise its interest rate. • If you expect that an interest rate on one-year CD increases to 5% next year, how much will be a return from Strategy #1? Which strategy will you choose? How will your choice affect the market of 2-year CD today and its interest rate? – Strategy #1 will provide \$1,081.50, so it is indifferent to choose either strategy. Since there is no needs to change your demand, its interest rate will not change (equilibrium).
22. 22. 421 0011 0010 1010 1101 0001 0100 1011 Expectations and Equilibrium • Both markets reach an equilibrium only if no more changes in demand in both markets. • Only if saver/lenders expect that the one-year CD will have 5% interest rate next year, the markets are at an equilibrium today.
23. 23. 421 0011 0010 1010 1101 0001 0100 1011 Expectations Theory • The interest rate on a long-term bond is equal to an average of short-term interest rates that savers expect to occur over the life of the long-term bond. • Formula: in = (i1+i2+..+in)/n in : Interest rate on n-year maturity bond today i1: Interest rate on 1-year maturity bond today i2: Interest rate on 1-year maturity bond next year in: Interest rate on 1-year maturity bond n-1 year later 0 1 2 3 n-1 n i1 i2 i3 in PV FV
24. 24. 421 0011 0010 1010 1101 0001 0100 1011 Numerical Example of Expectations Theory • Saver/lenders expect 1-year interest rate in next three years as 1-year Interest ratethis year 3% next year 5% two year later 7% Then, long-term interest rates today are One year rate: i1 =3% Two year rate: i2 =(3%+5%)/2=4% Three year rate: i3 =(3%+5%+7%)/3=5%
25. 25. 421 0011 0010 1010 1101 0001 0100 1011 Yield Curve and Expectations • When the short-term interest rate is expected to increase in future, ⇒ The long-term interest rate is higher than the short-term interest rate today. ⇒ yield curve is upward-sloping today. • For example, when one-year interest rate is 3% today, and is expected to rise to 5% next year and 7% two years later, then interest rates today are 3% on 1-year maturity, 4% on 2-year maturity, and 5% on 3-year maturity. Maturity Interest Rate 4% 2 year 3% 1 year 5% 3 year Yield curve
26. 26. 421 0011 0010 1010 1101 0001 0100 1011 Reasons for Changes in Interest Rate Over Time • There are many reasons for changes in interest rates in future. – A change in real interest rate in future (r) – A change in inflation rate in future (π) i = r + π • If an economic condition changes in future (e.g. changes in wealth and income, changes in risk, changes in profitability of business investment opportunities), demand or supply of bonds will change in future and a equilibrium real interest rate will also change in future.
27. 27. 421 0011 0010 1010 1101 0001 0100 1011 Changes in Expected Inflation and Yield Curve • If Saver/lenders anticipate the inflation rate to increase in future. ⇒ The short-term interest rate is expected to increase in future for a given real interest rate (π↑ ⇒ i↑). ⇒ The long-term interest rate is higher than the short-term interest rate today. ⇒ yield curve is upward-sloping today.
28. 28. 421 0011 0010 1010 1101 0001 0100 1011 Yield Curve and Market Expectations • A yield curve today tells you how professional traders in markets anticipate future inflation (π) and economic conditions (r). − If they expect the U.S. economy to be in an expansion phase of business cycle, they should expect interest rates to rise in future, so the yield curve today should be upward- sloping. − If they expect the inflation rate to rise in U.S. economy, they should expect nominal interest rates to rise in future, so the yield curve today should be upward-sloping. − Thus, an upward-sloping yield curve today may indicate traders’ expectation of either an expansion or inflation in the U.S. economy near future.
29. 29. 421 0011 0010 1010 1101 0001 0100 1011 Interpreting Actual Yield Curve • Three theories of yield curve are complement. When we interpret an actual yield curve, we must apply all three theories. • Due to the liquidity premium theory, even though we expect no change in short-term interest rates near future, the yield curve should be slightly upward- sloping. – Expectations theory indicates a flat yield curve. – Liquidity premium theory indicates an upward-sloping curve. – Two factors together produces a slightly upward-sloping yield curve.
30. 30. 421 0011 0010 1010 1101 0001 0100 1011 Expectations Theory with Liquidity Premium
31. 31. 421 0011 0010 1010 1101 0001 0100 1011 Expectations of Future Short-Term Interest Rates Fall moderately Fall sharply Rise Stay the same Yield to Maturity Terms to Maturity When short-term interest rates in future are expected to
32. 32. 421 0011 0010 1010 1101 0001 0100 1011 Interpreting Yield Curve • Steep upward-sloping yield curves in 1985 and 2011 indicate traders’ expectations of rising future interest rates. • Moderately upward-sloping yield curves in 1980 and 1997 indicate traders’ expectations on no change in future interest rates. • A flat yield curve in 2006 indicates traders’ expectations of falling future interest rates. • A downward-sloping (inverted) yield curve in 1981 indicates traders’ expectations of sharply falling future interest rates.
33. 33. 421 0011 0010 1010 1101 0001 0100 1011 Disclaimer Please do not copy, modify, or distribute this presentation without author’s consent. This presentation was created and owned by Dr. Ryoichi Sakano North Carolina A&T State University
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Money and Banking

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