The Economics of Money, Banking, and Financial Markets 8th Canadian Edition, Chapter 6, Risk and Term Structure of Interest Rates PDF

The Economics of Money, Banking, and Financial Markets Eighth Canadian Edition Chapter 6 The Risk and Term Structure of Interest Rates Copyright © 2023 Pearson Ca...

The Economics of Money, Banking, and Financial Markets Eighth Canadian Edition Chapter 6 The Risk and Term Structure of Interest Rates Copyright © 2023 Pearson Canada Inc. 6-1 Learning Objectives 1. Identify and explain the three factors affecting the risk structure of interest rates. 2. List and explain the three theories of why interest rates vary across different maturities. Copyright © 2023 Pearson Canada Inc. 6-2 Risk Structure of Interest Rates (1 of 3) Yields of different bonds of the same maturity can differ substantially Key factors explaining the difference in yields of bonds of similar maturity: – Risk of default – Liquidity – Tax considerations Copyright © 2023 Pearson Canada Inc. 6-3 Figure 6-1: Long-Term Bond Yields, 1978–2020 Interest rates on different categories of bonds differ from one another in any given year, and the spread (or difference) between the interest rates varies over time. Sources: Statistics Canada CANSIM series V122544, V122517 (extended with the average of provincial bond interest rates from Bloomberg), and V122518 (extended with the 30-year A-rated corporate bond interest rate from Bloomberg). Copyright © 2020 Pearson Canada Inc. 6-4 Risk Structure of Interest Rates (2 of 3) Default Risk: probability that the issuer of the bond is unable or unwilling to make interest payments or pay off the face value – Government of Canada bonds are considered default- free bonds (while default is not impossible, the government can raise taxes or print money to repay) Risk Premium: the spread between the interest rates on corporate bonds and Canada bonds (that have the same maturity) Credit-rating agencies assess and rate riskiness Copyright © 2023 Pearson Canada Inc. 6-5 Risk Structure of Interest Rates (3 of 3) Liquidity: – the ease with which an asset can be converted into money (“cash”)  cost of selling a bond  number of buyers/sellers in a bond market Income Tax Considerations: – Example: in the U.S. interest payments on municipal bonds are exempt from federal income taxes Copyright © 2023 Pearson Canada Inc. 6-6 Countercyclical Default Risk and Flight to Safety It stands to reason that default risk ought to be high when economy is in recession When default risk is high, we might expect a “flight to safety”: reduces demand for risky bonds and increases demand for riskless bonds, which moves credit spreads up This is consistent with what we see in the previous slide: credit spreads tend to rise during recessions; in fact, they are countercyclical and coincident. Later, in our discussion of the term structure of interest rates, we will argue that term spreads are countercyclical and lagging. Copyright © 2023 Pearson Canada Inc. 6-7 Figure 6-2: Response to an Increase in Default Risk on Corporate Bonds Initially, Pc1 = PT1, ic1 = iT1, and the risk premium is zero. An increase in default risk on corporate bonds shifts the demand curve from Dc1 to Dc2; simultaneously, it shifts the demand curve for Canada bonds from DT1 to DT2. The equilibrium price for corporate bonds falls from Pc1 to Pc2, and the equilibrium interest rate on corporate bonds rises to ic2. In the Canadas market, the equilibrium bond price rises from PT1 to PT2, and the equilibrium interest rate falls to iT2. The brace indicates the difference between ic2 and iT2, the risk premium on corporate bonds. (Note that because Pc2 is lower than PT2, ic2 is greater than iT2.) Copyright © 2020 Pearson Canada Inc. 6-8 Corporate-Canada Bond Spread 1978 - 2008 Copyright © 2023 Pearson Canada Inc. 6-9 U.S. Credit Spreads and the 2007-2009 Financial Crisis Copyright © 2020 Pearson Canada Inc. 6 - 10 U.S. Credit Spreads During the Great Depression Copyright © 2020 Pearson Canada Inc. 6 - 11 Figure 6-3 Interest Rates on Municipal and Treasury Bonds in the United States When a municipal bond is given tax-free status, demand for the municipal bond shifts rightward from Dm1 to Dm2 ,and demand for the Treasury bond shifts leftward from DT1 to DT2. The equilibrium price of the municipal bond rises from Pm1 to Pm2 so its interest rate falls, while the equilibrium price of the Treasury bond falls from PT1 to PT2 and its interest rate rises. The result is that municipal bonds end up with lower interest rates than Treasury bonds. Copyright © 2020 Pearson Canada Inc. 6 - 12 Term Structure of Interest Rates Risk structure looks at multiple bonds with same maturity. Now look at single type of bond with different maturity dates – Example: Canada bonds with different maturity dates – Bonds usually have different interest rates because the time remaining to maturity is different Yield Curve: a plot of the yield on bonds with differing terms to maturity but the same risk, liquidity and tax considerations – Graphical representation of the term structure Copyright © 2023 Pearson Canada Inc. 6 - 13 The Yield Curve for Canada Bonds as of August 2022 4 3.5 3 Interest Rate (%) 2.5 2 1.5 1 0.5 0 1m 3m 6m 1y 2y 3y 5y 10y Long term Maturity Sources: Statistics Canada CANSIM series V122531, V122532, V122533, V122538, V122539, V122540, V122543, and V122544, and the authors’ calculations. Copyright © 2020 Pearson Canada Inc. 6 - 14 Yield curve terminology Bond prices change all the time – Therefore, the term structure / yield curve changes all the time Describing the yield curve – 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 Copyright © 2023 Pearson Canada Inc. 6 - 15 Facts That the 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 high, yield curves are more likely to slope downward and be inverted 3. Yield curves almost always slope upward Copyright © 2023 Pearson Canada Inc. 6 - 16 Three Theories to Explain the Three Facts We will explore three theories: 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 Copyright © 2023 Pearson Canada Inc. 6 - 17 Expectations Theory (1 of 6) The interest rate on a long-term bond equals the average of the expected present and future short-term interest rates over the lifetime of the bond – Bond holders consider bonds with different maturities to be perfect substitutes – Thus, they do not prefer bonds of one maturity over another and will not invest in a bond if its expected return is less than that of another bond with a different maturity Copyright © 2023 Pearson Canada Inc. 6 - 18 Expectations Theory (2 of 6) For an investment of $1 it = today’s interest rate on a one-period bond iet+1 = interest rate on a one-period bond expected for next period i2t = today’s interest rate on the two-period bond Copyright © 2023 Pearson Canada Inc. 6 - 19 Expectations Theory (3 of 6) Expected return over the two periods from investing $1 in the two-period bond and holding it for two periods (1  i2t )(1  i2t )  1 2 1  2i2t  (i2t )  1 2 2i2t  (i2t ) Since (i 2t)2 is very small the expected return for holding the two-period for two perids is Copyright © 2023 Pearson Canada Inc. 6 - 20 Expectations Theory (4 of 6) If two one-period bonds are bought with the $1 investment (1  it )(1  i )  1 e t 1 1  it  i  it (i )  1 e t 1 e t 1 it  i  it (i ) e t 1 e t 1 it (i ) is extremely small e t 1 Simplifying we get it  ite1 Copyright © 2023 Pearson Canada Inc. 6 - 21 Expectations Theory (5 of 6) Both bonds will be held only if the expected returns are equal 2i2t it  ite1 it  ite1 i2t  2 The two-period rate must equal the average of the two one-period rates. For bonds with longer maturities: it  ite1  ite2 ...  ite( n 1) int  n The n-period interest rate equals the average of the one- period interest rates expected to occur over the n-period life of the bond Copyright © 2023 Pearson Canada Inc. 6 - 22 Expectations Theory: Example (6 of 6) Let the current rate on one-year bond be 9% You expect the interest rate on a one-year bond to be 11% next year Then the expected return for buying two one-year bonds averages (9% + 11%)/2 = 10% The interest rate on a two-year bond must be 10% for you to be willing to purchase it Copyright © 2023 Pearson Canada Inc. 6 - 23 Expectations Theory -- Application The 1 year interest rate over the next 5 years is expected to be 5, 6, 7, 8 and 9 percent. What is i2t and i5t? What is happening to the yield curve? it  ite1  ite2 ...  ite( n  1) int  n it  ite1.05 .06 i2t   .055 (or 5.5%) Hence, 2 2.05 .06 .07 .08 .09 i5t  .07 (or 7%) 5 Using the same equation we can show that i3t = 6%, i4t = 6.5%. Thus, the yield curve is upward slopping. Copyright © 2023 Pearson Canada Inc. 6 - 24 Expectations Theory and the Term Structure of Interest Rate Facts Explains why the term structure of interest rates changes at different times 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) Copyright © 2023 Pearson Canada Inc. 6 - 25 Segmented Markets Theory No substitution between demand for bonds of different maturities – The interest rate for each bond is determined by the demand for and supply of that bond (no spillover from other segments of the bond market) 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) Copyright © 2023 Pearson Canada Inc. 6 - 26 Liquidity Premium Theory (1 of 2) 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 – Liquidity premium also referred to as a term premium Bonds of different maturities are partial (imperfect) substitutes Copyright © 2023 Pearson Canada Inc. 6 - 27 Liquidity Premium Theory (2 of 2) it  ite1  ite2 ...  ite( n 1) int   lnt n where ℓnt is the liquidity premium for the n-period bond at time t ℓnt is generally positive and increasing in the term to maturity n Copyright © 2023 Pearson Canada Inc. 6 - 28 Preferred Habitat Theory (PHT) Closely related to the liquidity premium theory Investors have a preference for bonds of one maturity over another They will be willing to buy bonds of different maturities only if they earn a somewhat higher expected return The PHT has the same prediction as the liquidity preference theory if most investors prefer short-term bonds over longer-term bonds Copyright © 2023 Pearson Canada Inc. 6 - 29 Figure 6-5: The Relationship Between the Liquidity Premium (Preferred Habitat) and Expectations Theory Because the liquidity premium is always positive and grows as the term to maturity increases, the yield curve implied by the liquidity premium and preferred habitat theories is always above the yield curve implied by the expectations theory and has a steeper slope. For simplicity, the yield curve implied by the expectations theory shown here assumes unchanging future one-year interest rates. Copyright © 2020 Pearson Canada Inc. 6 - 30 The Liquidity Premium Theory and the Facts about the Term Structure Interest rates on different bonds move together – Explained by first term in the equation Yield curves upward-sloping when short-term rates are low; and sometimes inverted when short-term rates are high – Explained by the liquidity premium term in the first case; and lower expected future interest rates in the 2nd case Yield curves typically upward-sloping – Explained by liquidity premiums which increase in the term to maturity Copyright © 2023 Pearson Canada Inc. 6 - 31 Figure 6-6: Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates According to the Liquidity Premium (Preferred Habitat) Theory (1 of 2) A steeply rising yield curve, as in panel (a), indicates that short-term interest rates are expected to rise in the future. A moderately steep yield curve, as in panel (b), indicates that short-term interest rates are not expected to rise or fall much in the future. Copyright © 2020 Pearson Canada Inc. 6 - 32 Figure 6-6: Yield Curves and the Market’s Expectations of Future Short-Term Interest Rates According to the Liquidity Premium (Preferred Habitat) Theory (2 of 2) A flat yield curve, as in panel (c), indicates that short-term rates are expected to fall moderately in the future. Finally, an inverted yield curve, as in panel (d), indicates that short-term interest rates are expected to fall sharply in the future. Copyright © 2020 Pearson Canada Inc. 6 - 33 Figure 6-7: Yield Curves for Government of Canada Bonds Yield curves for government of Canada bonds for different dates from 1986 to 2021. Sources: Statistics Canada CANSIM series V122531, V122532, V122533, V122538, V122539, V122540, V122543, and V122544, and the authors’ calculations. Copyright © 2020 Pearson Canada Inc. 6 - 34 Application – Forecasting Interest Rates What is the expected 1-year interest rate for next year? Assume that the expected return over two periods from investing $1 in a two-period bond must equal the expected return from investing $1 in one-period bonds. That is, (1 + i2t) (1 + i2t) ‑ 1 = (1 + it) (1 + iet+1) ‑1 By solving the equation for iet+1 yields (1  i2t ) 2 i e t 1  1 1  it Thus, if it = 5% and i2t = 5.5%, then it+1e = 6%. This is the expected one-year interest rate one year in the future. Copyright © 2023 Pearson Canada Inc. 6 - 35 Application – Forecasting Interest Rates (Cont’d) What is the expected 1-year interest rate two years hence? For a 3-year holding period, we have (1 + i3t) (1 + i3t) (1 + i3t) ‑ 1 = (1 + it) (1 + iet+1) (1 + iet+2) ‑1 Solving this equation for iet+2 yields 3 (1  i ) ite2  3t 2 1 (1  i2t ) Copyright © 2023 Pearson Canada Inc. 6 - 36 Application – Forecasting Interest Rates (Cont’d) What is the expected 1-year interest rate n years hence? It is (1  in 1,t ) n 1 iten  1 (1  int ) n If we introduce the idea of liquidity premium ℓnt, then the formula becomes (1  in 1,t   n 1,t ) n 1 e it n  1 (1  int  nt ) n Thus, managers of financial institutions can easily produce interest-rate forecasts. First, they need to estimate ℓnt, for various n. Then they need merely apply the second formula in this slide to derive the market’s forecasts of future interest rates. Copyright © 2023 Pearson Canada Inc. 6 - 37 Forecasting Interest Rates: An Example Suppose that ℓ1t = 0, ℓ2t = 0.25%, it = 5%, and i2t = 5.75%. Then 2 2 (1  i  l ) (1 . 0575 . 0025) ite1  2t 2t  1  1 0.06 (or 6%) (1  it ) (1 .05) Copyright © 2023 Pearson Canada Inc. 6 - 38  A First Lok at Quantitative Easing and Unconventional Monetary Policy The interest rates relevant for most investment and consumption decisions are long term (e.g. mortgage) and risky (e.g. Baa corporate bond) Conventional monetary policy targets short term and riskless interest rates (e.g. the overnight interest rate in Canada and the federal funds rate in the United States) In practice, something like the interest rate on a 10-year Canada bond serves as a benchmark interest rate for all other kinds of interest rates --- mortgage rates, credit card rates, student loan rates These are the rates relevant for economic decisions on spending and saving Our theory of bond pricing helps us understand the connection between these different kinds of interest rates Copyright © 2023 Pearson Canada Inc. 6 - 39  Monetary Policy in Normal Times Think of a world where the liquidity premium theory holds A central bank lowers (raises) short term interest rates and is expected to keep these low (high) for some time This ought to also lower (raise) longer term rates to the extent to which longer term rates are the average of expected shorter term rates Holding risk factors constant, substitutability between bonds means that riskier yields also ought to fall (increase) Copyright © 2023 Pearson Canada Inc. 6 - 40 Nominal Interest Rates in the United States (2001:M1-2021:M11) 8.00 7.00 6.00 Monthly interest rate (%) 5.00 4.00 3.00 2.00 1.00 0.00 2001 2001 2002 2003 2004 2005 2006 2006 2007 2008 2009 2010 2011 2011 2012 2013 2014 2015 2016 2016 2017 2018 2019 2020 2021 Copyright © 2023 Pearson Canada Inc. 6 - 41  Term Structure Puzzle? In the 1990s other rates tracked the policy rate reasonably closely, but this falls apart in the 2000s (see the figure in the previous slide) This has been referred to as the “term structure puzzle” From the perspective of the expectations hypothesis, we would expect longer maturity, riskier rates to move along with shorter maturity rates. But this is not what we see in 2000s Copyright © 2023 Pearson Canada Inc. 6 - 42  Unconventional Monetary Policy In a world where the policy rate is at or very near zero, conventional monetary loosening isn’t on the table Unconventional monetary policy: Quantitative Easing (or Large Scale Asset Purchases): purchases of longer maturity government debt or risky private sector debt. Idea: raise demand for this debt, raise price, and lower yield. Forward Guidance: promises to keep future short term interest rates low. Idea is to work through expectations hypothesis and to lower long term yields immediately. Copyright © 2023 Pearson Canada Inc. 6 - 43