ECON 354 Money and Banking. Risk Structure of Long-Term Bonds in the United States 20. Professor Yamin Ahmad

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1 Lecture 5 Risk Term Structure Theories to explain facts ECO 354 Money and Banking Professor Yamin Ahmad Big Concepts The Risk Structure of Interest Rates The Term Structure of Interest Rates Premiums: Risk Liquidity nual Yield (% %) An Risk Structure of Long-Term Bonds in the United States Corporate Aaa Bonds Corporate Baa Bonds State and Local Bonds US Government Long Term Bonds Apr-53 Aug-54 ov-55 Mar-57 Jul-58 ov-59 Mar-61 Jul-6 ov-63 Mar-65 Jul-66 ov-67 Mar-69 Jul-70 ov-71 Mar-73 Jul-74 ov-75 Mar-77 Jul-78 ov-79 Mar-81 Jul-8 ov-83 Mar-85 Jul-86 ov-87 Mar-89 Jul-90 ov-91 Mar-93 Jul-94 ov-95 Mar-97 Jul-98 ov-99 Mar-01 Jul-0 ov-03 Mar-05 Jul-06 ov-07 Mar-09 A Effects of Increase in Default Risk on Corporate Bonds Corporate Bond Market R e on corporate bonds, D c, D c shifts left Risk of corporate bonds, D c, D c shifts left P c, i c Treasury Bond Market Relative R e on Treasury bonds, D T, D T shifts right Relative risk of Treasury bonds, D T, D T shifts right P T, i T Outcome: Risk premium, i c i T, rises

2 Increase in Default Risk on Corporate Bonds Price of Bonds, P($) Interest Rate i (%) Price of Bonds, P($) Interest Rate i (%) P Increasing i increases P Increasing i increases Bond Ratings Moodys S&P Fitch Definitions Aaa AAA AAA Prime Maximum Safety Aa1 AA+ AA+ High Grade Quality S c S T Aa AA AA i T P T i T Aa3 AA- AA- P C 1 i C 1 P T 1 P C i C D T i 1 T A1 A+ A+ Upper Medium Grade A A A A3 A- A- D c D 1 c Risk Premium D 1 T Baa1 BBB+ BBB+ Lower Medium Grade Baa BBB BBB Quantity of Corporate Bonds Quantity of Treasury Bonds Baa3 BBB- BBB- (a) Corporate Bond Market (b) Default free (US Treasury) Bond Market Bond Ratings Moodys S&P Fitch Definitions Ba1 BB+ BB+ on Investment Grade Ba BB BB Speculative Ba3 BB- BB- B1 B+ B+ Highly Speculative B B B B3 B- B- Caa1 CCC+ CCC Substantial Risk Caa CCC - In poor standing Caa3 CCC- - Ca - - Extremely speculative C - - May be in default - - DDD Default - - DD - - D D Liquidity Corporate Bond Market 1. Less liquid corporate bonds D c, D c shifts left. P c, i c Treasury Bond Market 1. Relatively more liquid Treasury bonds, D T, D T shifts right. P T, i T Outcome: Risk premium, i c i T, rises Risk premium reflects not only corporate bonds default risk, but also lower liquidity

3 Municipal Bonds Puzzle: Why are interest rates on municipal bonds lower than Treasuries? Municipal bonds are not default free! Great depression; Orange County, CA in 1994 Answer: Interest payments on municipal bonds are exempt tfrom federal lincome taxes, and often from state taxes in the state where they are issued. Practice Question Consider the two markets: Market for municipal bonds Market for US Treasury bonds Graphically, show what happened in these markets as a result of interest on municipal bonds having tax free status. Interest es Rates on Different e Maturity Bonds Move Together e Yield Curves What do Yield Curves Look Like? Charting The Curves

4 Term Structure Facts We would wish to explain the following facts: 1. Interest rates for different maturities move together over time. Yield curves tend to have steep upward slope when short rates are low and downward slope when short rates are high 3. Yield curve is typically upward sloping Three Theories of Term Structure 1. Expectations Theory. Segmented Markets Theory 3. Liquidity Premium (Preferred Habitat) Theory What We Can Explain Expectations Theory explains 1 and, but not 3 Segmented Markets explains 3, but not 1 and Solution: Combine features of both Expectations Theory and Segmented Markets Theory to get Liquidity Premium (Preferred e ed Habitat) Theory and explain all facts Expectations Theory Key Assumption: Bonds of different maturities are perfect substitutes Implication: R e on bonds of different maturities are equal Investment strategies for two-period horizon 1. Buy $1 of one-year bond and when it matures buy another one-year bond. Buy $1 of two-year bond (which pays out every year) and hold it

5 Expected return from Strategy i i i i 1 t 1 t 1 1 t t Since (i t ) is extremely small, expected return is approximately (i t ), i.e. i i 1 t t What about the expected return from Strategy 1? i t Expected Return from Strategy 1 i e t it 1 i e e t i t 1 ii t t Since i t (i e t+1) is also extremely small, expected return is approximately i t + i e t+1 Question: Under what conditions would you be indifferent in choosing between Strategy 1 and Strategy? Answer: Only if the expected returns from strategy 1 and strategy t were equal! Expectations Theory From implication above you would be indifferent between the two strategies if and only if the expected returns of the two strategies were equal. Therefore: (i t ) = i t + i e t+1 Solving for i t: e it it it i.e. if and only if the return on a two period bond were equal to the average expected return on two one period bonds over the two periods. 1 Expected Return from Strategy 1 More generally for n-period bond: i nt i i i i n e e e t t1 t... t n1 In words: Interest rate on long bond = average short rates expected to occur over life of long bond

6 umerical Example umerical example: Consider the following one-year interest rates expected to occur over the next five years: 5%, 6%, 7%, 8% and 9% Interest t rate on two-year bond: (5% + 6%)/ = 5.5% Interest rate for five-year bond: (5% + 6% + 7% + 8% + 9%)/5 = 7% Calculate the interest rate for the three and four year bonds: Answer: Expectations Theory and Term Structure Facts Explains why yield curve has different slopes: 1. When short rates expected to rise in future, average of future short rates = i nt is above today s short rate: therefore yield curve is upward sloping. When short rates expected to stay same in future, average of future short rates are same as today s, and yield curve is flat 3. Only when short rates expected to fall will yield curve be downward sloping Implications of Expectations Theory Expectations Theory explains Fact 1 that short and long rates move together 1. Short rate rises are persistent. If i t today, i e t+1, i e t+ etc. average of future rates i nt 3. Therefore: i t i nt, i.e., short and long rates move together Implications of Expectations Theory Explains Fact that yield curves tend to have steep slope when short rates are low and downward slope when short rates are high 1. When short rates are low, they are expected to rise to normal level, e, and long rate = average age of future short rates will be well above today s short rate: yield curve will have steep upward slope. When short rates are high, they will be expected to fall in future, and long rate will be below current short rate: yield curve will have downward slope

7 Implications of Expectations Theory Doesn t explain Fact 3 that yield curve usually has upward slope Short rates as likely to fall in future as rise, so average of future short rates will not usually be higher than current short rate: therefore, yield curve will not usually slope upward Segmented Markets Theory Key Assumption: Bonds of different maturities are not substitutes at all Implication: Markets are completely segmented: interest rate at each maturity determined separately Implications of Segmented Markets Theory Explains Fact 3 that yield curve is usually upward sloping People typically prefer short holding periods and thus have higher demand for short-term bonds, which have higher price and lower interest rates than long bonds Does not explain Fact 1 or Fact because assumes long and short rates determined independently Liquidity Premium (Preferred Habitat) Theories Key Assumption: Bonds of different maturities are substitutes, btitt but btare not perfect substitutes btitt Implication: Modifies Expectations Theory with features of Segmented Markets Theory Investors prefer short rather than long bonds must be paid positive liquidity (term) premium, l nt, to hold long-term bonds Results in following modification of Expectations Theory: e e e it it 1it... itn 1 i nt n l nt

8 Liquidity Premium (Preferred Habitat) Theory i nt i i e e e i t t1 t... i t(n1) l n nt where l nt is the liquidity premium for the n-period bond at time t l nt is always positive Rises with the term to maturity Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theories Liquidity Premium (Preferred Habitat) Interest Rate Theory Yield Curve i nt Expectations Theory Yield Curve Liquidity Premium l nt Years to Maturity, n Liquidity Premium (Preferred Habitat) Theory Interest rates on different maturity bonds move together over time; explained by the first term in the equation Yield curves tend to slope upward when short-term rates are low and to be inverted when short-term rates are high; explained by the liquidity premium term in the first case and by a low expected average in the second case Yield curves typically y slope upward; explained by a larger liquidity premium as the term to maturity lengthens umerical Example Consider the following one-year interest rates expected to arise over the next five years: 5%, 6%, 7%, 8% and 9% Investors have a preference for holding short-term bonds, and as such charge the following liquidity premia for one to five year bonds: 0%, 0.5%, 0.5%, 0.75% and 1.0% Question: Calculate the interest rate being offered by these one to five year bonds.

9 Liquidity Premium (Preferred Habitat) Theories: Term Structure Facts Explains all 3 Facts Explains Fact 3 of usual upward sloped yield curve by investors preferences for short-term bonds Explains Fact 1 and Fact using same explanations as expectations hypothesis because it has average of future short rates as determinant of long rate Market Predictions of Future Short Rates Interpreting Yield Curves Application: The Subprime Collapse and the Baa Treasury Spread Corporate Bond Risk Premium and Flight to Quality Jan-07 Mar-07 May-07 Jul-07 Sep-07 ov-07 Jan-08 Mar-08 May-08 Jul-08 Sep-08 ov-08 Jan-09 Corporate bonds, monthly data Aaa-Rate Corporate bonds, monthly data Baa-Rate 10-year maturity Treasury bonds, monthly data