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Chapter 6 - FIGURE 1 Long—Term Bond Yields 1919-2008...

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Unformatted text preview: FIGURE 1 Long—Term Bond Yields, 1919-2008 Annual Weld {%) 18 16 1¢ corporate Aaa Bonds 1 2 10 Longiferm Bonds/ ' '7 glaze anal Local fiwemmeni {é‘éunici aé} 1920 193D 1940 1950 1960 1970 1980 1990 2000 2010 Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941—1970; Federal Reserve: www.federalreserve.gav/releasesfh15!data.htm. 8/26/2010 8/26/2010 Risk Structure of Interest Rates . Bonds with the same maturity have different interest rates due to: — Default risk — Liquidity — Tax considerations 226%; premium 3 is: .. '1"? - - - . 7—: uwrdmi s. _ ,» “mi‘ix 7393. :2 ‘gYT’rea‘fafiES’i‘ -:_}l-'i Ks??? x» xi ri-ixit m: 'x E V‘Hwfl "313% a» E . \ 5LT -: \mereet on its: H grim“ Risk Structure of Interest Rates . Default risk: probability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value — US. Treasury bonds are considered default free (government can raise taxes).é— i0 w; 59%;; figs; — Risk premium: the spread between the interest rates on bonds with default risk and the interest rates on (same maturity) Treasury bonds 8/26/2010 FIGURE 2 Response to an Increase in Default Risk on Corporate Bonds Price of Bonds P Price of Bonds, P Quantity of Corporate Bonds Quantity of fieasury Bonds (a) Comarate bond market to) Deficit—free (MS. Treasury) bond market -" .: ”Mi iv “up; 7“"? ‘K 7/? ' Table 1 Bond Ratings by Moody’ s, ; Standard and Poor’,s and Fitch msirf. k Ntyéégws 5"" ' \ WM N 8/26/2010 - Risk Structure of Interest Rates . Liquidity: the relative ease with which an asset can be converted into cash — Cost of selling a bond .1 fl — Number of buyers/sellers in a bond market 0 Income tax considerations LINN?“ ‘ — Interest payments on municipal bonds are exempt from federal income taxes. '-\ is: mmw 333‘ skew _ f>1flxwmumgr D lfl Jifcé'ffl :, {fig . 5‘5" FIGURE 3 nterest Rates ‘on swab w M W Municipal and Treasury Bonds egg} it; in w 3., Price of Bonds. P '8': P: Quantity 01 Municipal Bonds Quantizy of Treasury fiends (a) Market for municipal bends (b) Marine: for Treasury bonds Term Structure of Interest Rates «- Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to maturity is different Vic/id, CA)?” mg; 2:“ ll :1 a j?" 2 W a: "‘3 J , ‘3 w, :W her“: r” ii-wr‘ ! a s t a , 3 \ziJJJlfir’ p «Pig :1‘ Jifauffi! K s )5 f 3 Term Structure of Interest Rates . Yield curve: a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations — Upward-sloping: long-term rates are above short-term rates — Flat: short- and long—term rates are the same — Inverted: long-term rates are below short—term rates 8/26/2010 8/26/2010 Facts Theory of the Term Structure of Interest Rates Must Explain 1. Interest rates on bonds of different maturities move together over time 2. When short-term interest rates are low, yield curves are more likely to have an upward slope; when short—term rates are . t . high, yield curves are more likely to slope r r downward and be inverted 3. Yield curves almost always slope upward Three Theories to Explain the Three Facts 1. Expectations theory explains the first two facts but not the third 2. Segmented markets theory explains fact three but not the first two 3. Liquidity premium theory combines the two theories to explain all three facts 8/26/2010 FIGURE 4 Movements over Time of Interest Rates on US. Government Bonds with Different Maturities interest Hate We} 15 14 12 1D smegma: Bill’s {Shmofezm} 1950 1955 1966 1965 1970 1975 1980 1985 $990 1995 2000 2005 2019 Sources: Federal Reserve: www.federa¥reserve.gov/releases/h15/data.htm. Expectations Theory 0 The interest rate on a long- -term bond will equal an averagv eof the short— term interest rates that—We expect to occur over the life of the long- -term bond . Buyers of bonds do not prefer bonds of one Scwéeflag :55 e; ’55 maturity over another; they will not hold com“ a 5 or aao-E- 3’5 any quantity of a bond if its expected return,avc3 oé ’ ' ~ is less than that of another bond with a algae; = « different maturity @5313" a 4; . 3 W 4» fiE-v'al ”we. J55 3 . Bond holders consider bonds with different +€rm aggp Z “5' w r ‘ maturities to be perfect substitutes . / 5 “*1?in {3" )1 t. ’1 l I :3, I Expectations Theory: Example . Let the current rate on one—year bond be 60/0. - You expect the interest rate on a one—year bond to be 8% next year. . Then the expected return for buying two one—year bonds averages (6% + 8%)/2 = 7%. . The interest rate on a two—year bond must be 7% for you to be willing'to purchase it. Expectations Theory For an investment of $1 1', = today's interest rate on a one-period bond if“: interest rate on a one-period bond expected for next period i2t = today's interest rate on the two-period bend 8/26/2010 Expectations Theory (cont’d) Expected return over the two periods from investing $1 in the two—period bond and holding it for the two periods (1+i21)(1+i2r)“1 =1+2i2r +(1‘2t)2 —1 m 21.2: + (1.2:)2 Since (i2!)2 is very small the expected return for holding the two-period bond for two periods is 21'” Expectations Theory (cont'd) If two one-period bonds are bought with the $1 investment (1+it)(1+i,:1)—1 1+1} +i§1+it(if+})—1 2', +1}; +405“) it (1:1) is extremely small Simplifying we get '6 1t + lH-l 8/26/2010 Expectations Theory (cont’d) Both bonds Will be held only if the expected returns are equal 21",, mi +if+1 - it +it+1 12r: 2 The two~pe1iod rate must equal the average of the two one-period rates For bonds with longer maturities i +i +412 +.. ._+if+(n 1) . [+1 Im_ _ n The n—period interest rate equals the average ofthe one-period interest rates expected to occur over the n-period life of the bond Expectations Theory \mg\ @ iii: 193m “ S,- ”w;- ' J'— J Lrl‘“ i/ “ii-m l‘r? " . Explains why the term structure of interest rates changes at different times 0 Explains why interest rates on bonds with different maturities move together over time (fact 1) . Explains why yield curves tend to slope up when short-term rates are low and slope down when short-term rates are high (fact 2) . Cannot explain why yield curves usually slope upward (fact 3) 8/26/2010 10 8/26/2010 ‘ ”a . . “ 1'3 . “ if? a w ,7 = ~ tmt were ? Wt +- Kitty; . {5;}. 5 j: t, 5}“. 5wa ”:3 M c J W it. file-lattes” ”ii-«i f" ti ‘ a 2 5’" V .1 g“? 15* “Ii-5, rm; r3515: i am We 7' l 7 — 5 w 5? we?) C‘L‘t 9. V556 0‘ 713‘) “3*" ” "‘33 V 5"“? Segmented Markets Theory - Bonds of different maturities are not substitutes at all _ “555M . The interest rate for each bond with a different 4Q may w" (”123? /"'=’ ’ i’ maturity is determined by the demand for and nifty”: if?” L; 3" supply of that bond £337“ 555 at}; ”i ‘a ‘ t. c 5 z" . Investors have preferences for bonds of one * ' maturity over another . If investors generally prefer bonds with shorter ‘ maturities that have less interest-rate risk, then this explains why yield curves usually slope upward (fact 3) Liquidity Premium & Preferred Habitat Theories . The interest rate on a long-term bond will equal an average of short-term interest rates expected to occur over the life of the long—term bond plus a liquidity premium that responds to supply and demand conditions for that bond . Bonds of different maturities are partial (not perfect) substitutes 11 8/26/2010 Liquidity Premium Theory . .g .g -e . It +1”: +1H2 +...+1t+(n_1) z = —+Z nt n nt where [m is the liquidity premium for the n-period bond at time t or [nr is always positive Rises with the tenn to maturity ”s jg W, ‘1} 9 r w "= Preferred Habitat Theory . Investors have a preference for bonds of one maturity over another 0 They will be wifling to buy bonds of different maturities oniy if they earn a somewhat higher expected return 0 Investors are iikely to prefer short-term bends over longer-term bonds 12 FIGURE 5 The Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theory interest Liquidity Premium (Preferred Hahitalfiheory Rate, in, View Curve \ Liquidity Premium, {m Expectations Theory Yield Curve 0 5 $0 $5 20 25 30 Years to Maturity, n Liquidity Premium and Preferred Habitat Theories . 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 slope upward; explained by a larger liquidity premium as the term to maturity lengthens 8/26/2010 '13 FIGURE 6 Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates According to the Liquidity Premium (Preferred Habitat) Theory field In Yield Io Maturity Malurify \ Term in Maturity Term En Maturity (a) Future short-term (mares! rates an) FM snort-term inferestrafes Waite rise smearedtosieymesama field in E Yieid to Maturity Mammy Ten'rito Maturity Term lo Maturily {c} Fu'l‘urs shad-term inlemsl rate: (d) Future Mort—fem: imam! rates -umkwmmwy “nudeWl-h-mb FIGURE 7 Yield Curves for US. Government Bonds interest flake (9.6) 16 14 March 23 1335 5.1.3116; 15w )2 March 3, 1997 ‘ W t February 6, 2006 M January 15‘ 2003 2 i r . 5 10 15 20 Terms 10 Mammy films) Sources: Federal Reserve Bank of St. Louis; US. financial Data, various issues; Wal! Street Journal, various dates. 8/26/2010 14 8/26/2010 Application: The Subprime Collapse and the Baa-Treasury Spread Corporate Bond Risk Premium and Flight to Quality — Corporate bonds. monthly data Aaa-Rate —— Corporate bonds, monthly data Baa-Rate 15 ...
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