Ch. 6 (BUS G-345; Money, Banking; and Capital Markets; Self)

Ch. 6 (BUS G-345; Money, Banking; and Capital Markets;...

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Unformatted text preview: Chapter 6: The Risk and Term Structure of Interest Rates After this chapter you should be able to... l.Understand the meaning of the risk structure of interest rates. 2.Be able to interpret through the supply and demand model the risk premium for bonds of different default risk and the same maturity. 3.Understand the meaning of interest rate immen- 4.Understand the meaning of the term structure . HEW—mm“. of interest rates. m- 5.Understand and be able to interpret yield curves. 6.Understand expectations theory, segmented markets theory, liquidity premium theory, and preferred habitat theory of the term structure of interest rates. 7. Be able to explain if the theories in (6) have explained particular empirical facts. Risk Structure of Interest Rates Bonds with the same maturity have different interest rates due to three considerations. , JchWH mi ; worm/2, , %ol#6€fl$a’ewa%akj 1. Default risk: probability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value. 0 US. Treasury bonds are considered default free (government can raise taxes). _.._.--—--""-"_" - 'sk premium: the spread between the interest rates on bonds with default risk and the interest rates on (same maturity) Treasury bonds To illustrate we will use the supply and demand model for two bonds of the same maturity. One bond is the default-flee Treasury bond and the other a corporate bond. Both are zero coupons. Igbir-J‘ifi #8:; .3? {2" fqufgfigfi 33’} 5‘16: ?".‘9 Juana ’_ if. I. ,J [@1ij J, (afiwg. 140 first? If: g I 1'3 0 351,-: m (: IL,{?;N / 2 mike it, If»: {A (Tl Generally considered investment grade Short ieng _ {911$ ' 03m 0558 .= 38 ESE #23 Eu 3 fact so 3530 680 o> \(E, __w»_..‘m\\,.\.\xu. m§wfig Exam, M‘§& 3183-999 map Alqluow ‘spuoq e1eJodJ03 — a $91139 AlqllJOLU ‘SbUOQ Mnseeu Ammew JéeA-OL _ i— BIBS-999’ BIRD AIHIUOLU ‘Spuoq eleJOdJOQ ._l J fillIBnD o; 1q61H pue LungweJd xsm puog emJodJoo 2. Liquidity: the relative ease with which an asset can be converted into cash 0 Cost of selling a bond 0 Number of buyers/ sellers in a bond market 3. Tax considerations ‘_—____—"_'—'“——'—-————-_.4 0 One important example for the US. market is the interest payments on municipal bonds are exempt fromws a w t I. 1': i «L ': 'J-r"3'[{';u."_r \ FIGURE 1: Long-Term Bond Yields, 1919—2008 Annual Yield (%) 1 8 16 14 12 _ U.S. Government / Long-Term Bands I I State and Local Government (Municipal) r 1920 1930 1940 1950 1 960 1970 1 980 1 990 2000 2010 Sources: Board of Governors of the Federal Reserve System, Banking and Monetary Statistics, 1941—1970; Federal Reserve: wwwfederalreservegovfreleasesfhl Sfdatahim. 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. W: a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations. ° Upwfildfimflg_g_ long—term rates are above short-term rates 0 Egg: short— and long-term rates are the same 0 Inverted: long-term rates are below short— term rates Facts Theory of the Term Structure of Interest Rates Must Explain 1. Interest rates on bonds of different maturities move together over time / ,4. l... . . Interest Rate (%) 16 14 Three-to _ 12 Five-Near . Averages 1 1o a 20-Year Bond f4. 6 Averages -"' ' 4 H I! 1. ,. ff?! . 2 V - Three-Month Bills _ _ (Short-Term) o 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2. When short-term interest rates are low, yield curves are more likely to have an upward slope; when short-term rates are high, yield curves are more likely to slope downward and be inverted. 3. Yield curves almost always slope upward Let’s look at some theories. 10 _ E¥B?9£a_t19n_s_The9_ry_ o The interest rate on a long—term bond will equal an averagehof the short—term interest rates that people eggpth tooccur over the life of the long- term bond 0 Buyers of bonds do not prefer bonds of one maturity over another; they will not hold any quantity of a bond if its expected return is less than that of another bond with a different maturity - Bond holders consider bonds with different maturities tobe ' " - r 6'" For example, suppose you had the choice between a one year bond paying 5% return and a two year bond. If you thought the return on a one year bond the following year would be 7% then you would be indifferent between a two year bond paying 6% annual rate and a one year bond purchase in each year. 11 More generally we can write these results as the following for an investment of $1. Let, it = today's interest rate on a one-period bond aim = interest rate on a one-period bond expected for next period igt = today's interest rate on the two-period bond Then the expected return over the two periods from investing $1 in the two-period bond and holding it for the two periods is (1+i2t)(1+12t)—1=1+212tMar—1 = 2 a + (a )2 Since (lgt )2 is very small we can approximate the expected return forholding the two-period bond for two periods 2152 i215) l2 If two one—period bonds are bought with the $1 investment then the two year return would be (1 +100 + Sim) — 1 I it + eit+l +it(eit+l) Since it( 6it“) is extremely we can approximate the expected return to be it + eit+1 Therefore if they are perfect substitutes both bonds will be held only if the expected returns equal I ___ I e. o _ o e- 2 12t “— 1t + lt+1 01' 12t —' (1t + lt+1)/2 We can extend this to n periods by the following expected return on the 11 period bond to equal, int = (it + eit+1 + ---+ eit+n-1) / n 13 Expectation y does the following: o Explains why the term structure of interest rates changes at different times «- Explains why interest rates on bonds with differentmaturities movewtogether over time (fact 1) o 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) 0 Cannot explain why yield curves usually slope upward (fact 3) '14 Segmented Markets Theory 0 Bonds of different maturities are m? o The interest rate for each bond with a different maturity is determined by the demand for and supply of that bond 0 Investors have preferences for bonds of one maturity over another 0 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) I v: A? -_,,J _ ,l I _ -. .rlzl— [lb/(JHF ‘,.- --' y. ia LII/1,31” :‘ ? d. \1; I "'-'1f 15 Liquidity Premium Theory \_________~\ 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 Maori Maia (fie-if WT fife-9f This changes our expected return on the 11 period bond to the following, int = lnt+ (it + eit+1 + m+ eit+n-1) / 11 Where 1m is always positive and increases with term maturity. It is the liquidity premium term. For Preferred Habitat theory, 1m, would be called a preference term. 16 Preferred Habitat Theory says2 - Investors have a preference for bonds of one maturity over another 0 They will be Willing to buy bonds of different maturities only if they earn a somewhat higher expected return 0 Investors are likely to prefer short-term bonds over longer—term bonds 1? FIGURE 5: The Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theory interest Liquidity Premium (Preferred Habitat) Theory ' Yield Curve \ Liquidity Premium, inf Expectations Theory Yield Curve 0 5 10 15 20 25 30 Years to Maturity, n 18 fluidity Premium and Preferred Habitat Theories say the following, 0 Interest rates on different maturity bonds move togethQI over time; explained by the alvc/ W term in the equation 0 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 0 Yield curves typically slope upward; explained by a larger liquidity premium as the term to maturity lengthens *l'cJ-z.r.-:~r- -. . .- -- a: .. -- :.' ' " V t' 19 FIGURE 6: Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates According to the Liquidity Premium (Preferred Hflmfi‘l‘gurq :6 in Yield to Yield to Maturity Maturity Term to Maturity Term to Maturity (a) Future short-term interest rates {b} Future short-term interest rates expected to rise W h_"-—-—.____——I- Yield to Yield to Maturity Maturity Term to Maturity Term to Maturity (0) Future short-term interest rates (at) Future short-term interest rates expected to fat! moderater mex ected to fat! sharpty 6i 4" ( we; 2 9h cm Mort-’0 at _ e- mi 1', a Mr" 20 FIGURE 7 Yield Curves for US. Government Bonds Interest Rate (%) 16 14 12 March 28, 1985 ‘ May 16. 1930 10 8 March 3r 1997 6 February 6. 2006 4 .. January 15, 2009a 2 / 5 10 15 20 Terms to Maturity (Years) 21 ...
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This note was uploaded on 12/21/2011 for the course BUS 100 taught by Professor Intro during the Fall '11 term at UCSB.

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Ch. 6 (BUS G-345; Money, Banking; and Capital Markets;...

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