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## Chapter 6. Risk and Term Structure of Interest Rates

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**Chapter 6. Risk and Term Structure of Interest Rates**• Risk Structure • Term Structure**Not all interest rates are created equal!**• many interest rates at one time • interest rates move together over time**January 2004**• 3 mo Tbill 2.33% • 3 mo Commerical Paper 2.52% • prime rate 5.25% • 10 yr. Tnote 4.23% • 10 yr. AAA corporate 5.46% • 10 yr. BAA corporate 6.15% • 30 yr. mortgage 5.71%**measurement**• difference between two interest rates • spread • measured in • percentage points • basis points • 1 percentage pt. = 100 basis pts.**example 1**• 3 mo. Tbill 2.33% • 3 mo. Commercial paper 2.52% • spread • .19 percentage pts. • 19 basis pts.**example 2**• 10 yr Tnote 4.23% • 10 BAA corporate 6.15% • spread • 1.92 percentage pts. • 192 basis pts.**I. Risk Structure of Interest Rates**• debt with same maturity, but different characteristics • default risk • liquidity • tax treatment**Patterns**• Baa always the highest yield • Municipal’s always the lowest (1940) • Baa > AAA > U.S. > municipal • size of the spread varies**A. Default Risk**• risk of not receiving timely payment of principal and interest • depends on • creditworthiness of issuer • structure of bond**U.S. government debt**• zero default risk • backed by “full faith and credit” of U.S. government • why? • power to tax largest economy • power to issue stable currency**Other issuers**• private • foreign • municipal • all have some default risk • rated for default risk**Bond ratings**• bond issuer pays rating agency • Moody’s, S&P, Fitch • p. 123 • high credit rating • low default risk • bond ratings may change over time**default risk & yield**• investors are risk averse higher default risk lower credit rating higher yield**so default risk explains**BAA Corp yields AAA Corp yields Treasury yields < <**default risk is not constant!**• varies over the business cycle • higher in recessions • lower in expansions • Baa vs. Treasury bond yield • 12/99 191 basis pts. • 12/01 296 basis pts.**B. Liquidity**• how quickly/cheaply can bond be sold for cash? lower yield higher liquidity**liquidity is not rated**• Treasuries most liquid • depends on size of issuer • related to default risk • bonds in default very illiquid • higher-rated bonds tend to be more liquid**C. Tax treatment**Q. why do municipal bonds have lower yields than Tbonds? • muni’s less liquid • muni’s not default-free A. tax treatment**municipal bond interest**• exempt from federal income tax • possibly exempt from state income tax • if issuer & bondholder are in same state**Treasury bond interest**• exempt from state income tax Corporate bond interest • fully taxable**example: federal taxes**• bond where F=$10,000 • coupon rate = 10% • annual coupon pmts = $1000**municipal bond**• before taxes: • $1000 in interest pmts. • after taxes: • $1000 in interest pmts**Corporate bond**• before taxes: • $1000 interest pmts. • after taxes • (33% marginal rate) • $1000(1-.33) = $670 interest pmts.**So, after taxes**• muni has 10% coupon rate • corp has 6.7% coupon rate • muni can offer a lower yield and still be competitive**tax treatment explains**muni yields Treasury yields Corp yields < <**impact of tax rates**• higher tax brackets derive more benefit from muni’s • changing tax rates will affect the corporate-municipal yield spread**II. Term structure of interest rates**• bonds with the same characteristics, but different maturities**focus on Treasury yields**• same default risk, tax treatment • similar liquidity • many choices of maturity -- 4 weeks to 30 years**relationship between yield & maturity is NOT constant**• sometimes short-term yields are highest, • sometimes long-term yields are highest**A. Yield curve**• plot of maturity vs. yield • slope of curve indicates relationship between maturity and yield**yield**maturity upward sloping • yields rise w/ maturity (common) • July 1992, currently**yield**maturity downward sloping (inverted) • yield falls w/ maturity (rare) • April 1980**3 facts about the yield curve**• based on historical data on U.S. Treasury yields 1. interest rates on bonds of different maturities generally move together**2. If short-term rates are low, the yield curve slopes up.**If short-term rates are high, the yield curve slopes down. 3. The yield curve usually slopes up.**Understanding the yield curve**• what causes the 3 facts? • what does the shape of the yield curve tell us? • must understand why/how maturity affects yield**3 theories of term structure**• assumptions about investor preference • implications for maturity and yield • check implications against 3 facts about yield curve**B. The Expectations Theory**• Assume: bond buyers do not have any preference about maturity i.e. bonds of different maturities are perfect substitutes**if assumption is true,**then investors care only about expected return • for example, • if expect better return from short-term bonds, only hold short-term bonds**but investors hold both short-term an long-term bonds**• so, • must EXPECT similar return: long-term yields = average of the expected short-term yields**example**• 5 year time horizon • investors indifferent between (1) holding 5-year bond (2) holding 1year bonds, 5 yrs. in a row as long as expected return is same**expected one-year interest rates:**5%, 6%, 7%, 8%, 9% over next 5 years so 5-year bond must yield (approx)**yield**7% 5% maturity 1 yr. 5 yrs. yield curve • if ST rates are expected to rise, • yield curve slopes up**under exp. theory,**• slope of yield curve tells us direction of expected future short-term rates**yield**maturity ST rates expected to fall**yield**maturity ST rates expected to stay the same**yield**maturity ST rates expected to rise, then fall**theory vs. reality**• does the theory explain the 3 facts? 1. interest rates move together? YES. If ST rates rise, then average will rise (LT rate)**2. interest rates low, slopes up**interest rates high, slopes down YES. ST rates low, must be expected to rise, so yield curve slopes up ST rates high, must be expected to fall, so yield curve slopes down