资本市场和金融机构2InterestRa.ppt

1,Interest Rates,Definition Fluctuation of interest rates Shifts on Demand Shifts on Supply Types of interest rates Analysis of Bond Valuation Risk and Term Structure of Interest Rates (TSIR) 5.1 Determinants of Risk Structure (RSIR) 5.2 TSIR (Yield Curve). Theories: A) Pure Expectations Theory B) Market Segmentation Theory C) Liquidity Theory Predictive Power of the Yield Curve 6.1 Future interest rates 6.2 Economic growth Conclusions,2,1. Interest Rate (i),i = Cost of borrowing or lending money It plays a pivotal role in: the Investment and Financing of assets (real, financial) by individuals, companies, governments and FI the performance of the economy Determined in the Debt Markets (supply and demand) and by government intervention. Central Bank Monetary policy (i, M) Is there an appropriate level of i?,3,Interest Rate,How the interest rates are determined? What explains the fluctuation of interest rates? Most accurate measure of interest rate: Yield to maturity Example applied to bond valuation,4,Determination of Interest Rate (i) Approaches 1) Analysis of Demand of loanable funds and Supply of loanable funds 2) Analysis of Demand for and supply of bonds Supply of loanable funds by households and firms. The higher the i the higher the quantity of loanable funds offered Demand of loanable funds by households and firms Reasons for Consumer? For Firms? Total Demand = Demand by households and firms Determinants of the Demand and Supply,5,Supply and Demand for Loanable Funds,Interest Rate (i),Supply,Quantity of loanable funds,Demand,Q*,i*,6,What determines the supply of loanable funds? The supply of loanable funds is determined by the interest rate offered to savers. A higher interest rate induces households to consume less today (save) in favor of greater consumption in the future. Firm also may have excess of cash that may be loaned (e.g., purchase of other firms bond issue) instead of invested (real assets) because of the non availability of projects with +NPV. What determines the demand for loanable funds? It comes from: consumers who wish to consume more today than tomorrow, individuals, financial and non-financial firms to invest in financial assets financial and non-financial firms to invest in real assets Demand depends on the interest rate at which these three groups can borrow. The lower the interest rate the higher the demand and vice-versa.,7,2. Fluctuation of interest rates What might cause the supply or demand for loanable funds to shift, and how would that affect interest rates? Factors that shift the demand curve. a) Recession: It decreases demand at all interest rates, shifting the demand curve inwards and causing the equilibrium interest rate to fall.,Quantity ($),A,B,Interest Rate,S,D,D,i,i,Q,Q,8,b) An increase of the government deficit. C) Rise in expected inflation shifts the demand curve to the right. Same as (b) Nominal Interest rate = real interest rate + rate of expected inflation D) increase on the growth rate of population. Same as (b) e) Business cycle expansion. Expected increase in economic growth Same as (b),i,Q ($),D,D,S,A,B,9,Examples that shift the Supply curve to the right Increases in the money supply by the Central Bank, causing the interest rate to fall. b) Increases in real personal income make people more willing to make loans (e.g. deposits in banks accounts) c) Increase in tax exempt financial instruments. Note: if we assume that the central bank controls the amount of money supply at fixed quantity the Supply Curve for money S would be a vertical line.,i,Q ($),S,S,A,B,10,3. Variety of Interest Rates,T-bill rate ( 1year) Discount rate: Central Bank charges to banks In Canada is called the Overnight Bank Rate Commercial paper rate: Short term discount bonds Prime rate: Short term Rate charged to largest firms (creditworthy) Corporate bond rate: Long term rate for debt issued by firms LIBOR: Rate that largest creditworthy international banks dealing in Eurodollars charge each other for large loans. Fixed rates, floating rates, etc. They differ because of the differences in maturity, risk of lenders ,11,4. Analysis of Bond Valuation It sheds light on the concept of interest rate. Bond. Contract in which a borrower agrees to pay a bondholder (the lender) a specific amount of money in a period of time. Example: How much would you pay for a bond that promises a coupon rate of $100 each year for a period of 10 years and the principal amount of $1,000 (par value=nominal value = face value) at the end of the 10th year? Assume i= 5%, i=10%, i=15%,12,Formula P = Coupon/(1+i) + Coupon/(1+i)2 + Coupon/(1+i)10 + Face Value/(1+i)10,C=$100,C=$100,C=$100,P=?,1,2,3,9 10,C=$100,$100 + $1,000,If i = 5% P = $100/(1+0.05) + $100/(1+0.05)2 + $100/(1+0.05)10 + $1,000/(1+0.05)10 = $1,386 i = 10% P = $100/(1+0.10) + $100/(1+0.10)2 + $100/(1+010)10 + $1,000/(1+0.010)10 = $1,000 i = 15% P = $100/(1+0.15) + $100/(1+0.15)2 + $100/(1+015)10 + $1,000/(1+0.015)10 = $749 Which i (discount rate or yield to maturity) from above makes the present value of a bonds payments equal to its current price P? A:?,i = 5%,13,YTM = Interest rate that equates the Present Value of payments received from a debt instrument (e.g., bond) with its value today P. Alternatively, is the rate of interest earned on a bond if it is held to maturity. The YTM is the most important and accurate way of calculating interest rates. If P = $1,386 What is the YTM = i? $1,386 = $100/(1+i) + $100/(1+i)2 + $100/(1+i)10 + $1,000/(1+i)10 = $1,000 A: YTM = i = 5% If P = $1,000 What is the YTM? YTM = 10% If P = $749 What is the YTM? YTM = 15% What is the relationship between the Bond price and the i? Why? Price of bond Fig. Yield to maturity of a bond = effective yield on a bond = i,$1,000,10%,Interest Rate = i = YTM,5%,$1,386,$749,15%,Scenarios: Assume you bought the bond in $1,000 and interest rates increased to 15%. Did you benefit? Assume you bought a corporate bond and the credit rating of the firm is downgraded to junk (default) What is the expected effect in the interest rate (YTM)?,14,Perpetuity Bond paying out a fixed amount of money each year forever. Example The Canadian government issues a bond that will pay to perpetuity $50 a year. If the interest rate is 3% annual, a) what is the bond worth today? b) Would you buy the bond for $1,500? The present value of a perpetuity is easily obtained as PDV = perpetuity/R A: Effective Yield (YTM) on a Bond (perpetuity) Percentage return that one receives by investing in a bond Assume price of the perpetuity above is $1,666.67 and you receive a perpetual coupon rate of $50 per year. What is the effective yield rate or rate or return? A: Now, suppose the current interest rate is 4%. Would you pay $1,666.67 for the bond?,15,5. Risk and Term Structure of Interest Rates,Variety of different interest rate = f(maturity, risk, liquidity, taxes). I) Assuming various debt instruments (bonds) have same maturity, their is will differ because of differences in risk. Risk Structure of Interest Rates (RSIR). RSIR expresses the relations of interest rates for various bond instruments whose determinants are (1) default risk, (2) liquidity, and (3) taxes (See Fig.1, p. 110, Miskhin et al. - Long Term Bonds) II) Assuming various bonds have same risk their is may differ because of the differences in maturities. Term Structure of Interest Rates (TSIR). TSIR expresses the the relationship among is (YTMs) on zero coupon discount bonds with different maturities.,16,5.1 Determinants of RISK STRUCTURE OF INTEREST RATES (RSIR) Interest rates on corporate bonds are higher than those on Canada bonds (See Figure 1) Reasons 1. Higher Default Risk 2. Lower Liquidity 3. Tax considerations on is payments. Canadian (Cdn) bonds are default-free bonds Difference in is = Risk Premium 1.Effect of Default risk on interest rates Assume initially a corporate bonds with no default risk, like Canada bonds (with same maturity). Possibility of a strong recession increases the possibility of default of corporate bonds. What will the effect be on interest rates of corporate bonds and Canada bonds? What will happen to the risk premium of corporate bonds?,i,i,Price of bonds, P,P,Quantity of Corporate Bonds Quantity of Canada Bonds (a) Corporate bond market (b) Default-free Cdn bond market,ic1,Pc1,Pc2,ic2,PT2,PT1,iT2,iT1,iT2,ic2,Risk Premium = ic2 - iT2,Dc2,Dc1,Sc,DT1,DT2,ST,Decrease in Interest rate,17,Investment advisory firms providers of default risk information on bonds: Standards and Poors Canada, Dominion Bond Rating Service. Investment grade-bonds (AAA) vs. Junk bonds (D) (See Fig. 3, p. 113, Mishkin et al.) Risk premium on BBB corporate bond rates (Corporates-Canada Spread, 1980-2001),18,2. Effect of Liquidity on interest rates Liquidity. Ability to buy or sell an asset quickly and in large volume without substantially affecting the assets price. Corporate bonds vs. Canada bonds Which ones are more liquid? Spread? Assume initially corporate bonds and Canada bonds are equally liquid, ceteris paribus. a) Which event (s) would decrease the liquidity of corporate bonds? Why? b) What will the effect be on interest rates of corporate bonds and Canada bonds? c) What will happen to the risk (liquidity) premium of corporate bonds? Draw their respective graphs (demand and supply curves of Corporates and Canada bonds).,19,3. Tax Considerations How does taxation affect the interest rate (YTM) on bonds? Government bonds that pay no taxes yield lower interest rates (e.g., U.S. municipal bonds or munis). Munis are advantageous for high tax-bracket investors. Example: Suppose Charlie White (a US investor) has 2 alternatives to invest his savings (say $1,000) invest a $1,000 face value muni that sells for $,1000, with coupon payments of $80. 2) invest a $1,000 face value taxable bond that sells for $1,000 and has a coupon payment of $120. The tax-bracket is 35%. a) Which option should he choose? Why? b) Suppose Jane Red is faced with similar options but her tax-bracket is 30%. What option would be best for her? c) Does it matter to know the maturity of the bonds to obtain their YTM?,20,5.2 Term Structure of Interest Rates (TSIR) The TSIR refers to the relationship between YTM and term to maturity for bonds of same risk class. The Yield Curve is the graphical representation of the TSIR. The Yield Curve shape can be a) Upward-sloping Long Term is Short Term is b) Flat Long term is = Short Term is c) Downward-sloping (inverted yield curve) LT is ST is,21,Reasons of Upward sloping Yield curve (High yields on long term bonds) Example: Inflation Short term interest rates are are expected to increase in the future due to inflation. Remember, interest rates (nominal) = real interest rates + expected inflation. What the Bank of Canada should do? Reasons of Downward sloping yield curve?,22,Term Structure of Interest Rates (Yield curves),YTM,Time to Maturity,Time to Maturity,Time to Maturity,Time to Maturity,YTM,23,Theories of the Term Structure of Interest Rates,Empirical Facts of Yield Curves YTMs of bond of different maturities move together over time If ST is rates are low Yield curve is upward sloping Usually yield curves slope upward Theories to explain above facts A) Pure Expectations Theory B) Market Segmentation Theory C) Liquidity Premium Theory,24,A) Pure Expectations Theory It asserts that YTMs are determined solely by expectations of future short-term interest rates. For Example: Upward-sloping Long Term is Short Term is average of future ST rates is expected current short term rates Downward-sloping Long Term is Short Term is average of future ST rates is expected current short term rates Flat Long Term is = Short Term is average of future ST rates is expected = current short term rates,25,Expected holding-period yields (HPY) on bonds of all maturities (with same risk) ought to be about equal, that is: 1. HPY(1-year bond) = HPY (2-year bond) = = HPY (n-year bond) 2. If we know the one-year HPY(commonly called yield) on two bonds of n-1, and n maturities, we can obtain the market expectation of the future short-term interest rate on year n (also called forward rate).,Implications of Expectations Theory,26,Example - If one-year bonds offer an 8% annual yield (return) and the principal and interest are reinvested at 10% at the end of first year while - two-year bonds have an YTM (i, or annual yield, or commonly called yield*) of 8.995%, both bonds must have same holding period yield (HPY), that is: *In practice yield refers to one-year interest rate. 1. Two-year HPY for both types of bonds Two-year HPY of 1-year bonds = (1+0.08)(1+0.1)-1 = 0.188 or 18.8% Two-year HPY of 2-year bonds =(1.08995)(1.08995)-1 = 0.188 or 18.8% 2. One-year HPY (commonly called yield) yield of 1-year bonds = (1+0.08)(1+0.1)1/2- 1 = (1.188)0.5 1 = 0.08995 or 8.995% yield of 2-year bonds = 8.995% (given) If it is not given you can obtain it from Two-year HPY of 1-year bonds Yield of 2-year bonds = (1+two-year HPY of 1-year bonds)1/2 -1 = (1.188)1/2 1 = 0.08995 or 8.995%. 3. The expected year two interest rate, i2, (or forward rate) is obtained as follows (1+ yield of one year bonds)1 (1+i2) = (1+yield of two years bonds)2 (1+i2) = (1+ yield of two years bonds)2/(1+yield of one year bonds)1 = (1.08995)2/1.08-1 = 1.0999-1 = 9.999 10%,27,Generalizing 1. One-year HPY (or yield) for 1-year bonds reinvested T periods (at t+1 rate) Yield of 1-year bonds = (1+i1) (1+i2) + (1+iT )1/T-1 Based on previous example T=2 HPY (1-year bonds) =(1+0.08)(1.1)1/2 1 =0.08995 or 8.995 2. One-year HPY for n-year bonds (usually given) If it is not given, it can be obtained from the n-year HPY for 1-year bonds reinvested each year, as follows Yield of n-year bonds = (1+ n-year HPY of one-year bonds)1/n 1 Based on the example of previous slide Yield of 2-year bonds = (1+ two-year HPY of 1-year bonds)1/2 1 = (1.188)1/2 1 = 0.08995 or 8.995%. 3. Expected year n interest rate, in, (or forward rate) It is obtained as follows: (1+ yield of n-1 year bonds)n-1 (1+in) = (1+ yield of n-year bonds)n (1+in) = (1+yield of n-year bonds)n / (1+ yield of n-1 year bonds)n-1 in = (1+yield of n-year bonds)n / (1+ yield of n-1 year bonds)n-1 1 Based on previous example the expected year 2 interest rate (or forward rate) is (1+i2) = (1+ yield of two years bonds)2/(1+yield of one year bonds)1 = i2 = (1.08995)2/1.08-1 = 1.0999-1 = 9.999 10%,28,Solve the following problems Assume the Expectations Theory holds 1. a) Determine the One-year HPY (or yield, assumed annual) for 1-year bonds reinvested 3 periods such as the expected interest rates are 5, 6 and 7 percent, for years 1, 2 and 3, respectively. b) Determine the yield for 3-year bonds. 2. Determine the three-year HPY for 3-year bonds that have yields to maturity (or yields, assumed annual) of 5.9968% Assume that two-year maturity bonds offer yields (assumed annual) of 5.4988%, and three-year bonds have yields of 5.9968 %. Determine the expected one-year interest rate (forward rate) for the third year. What does this tell you about the monetary policy to purse by the Bank of Canada?,29,B) Market Segmentation Theory This theory holds that long-and short-term maturity bonds are traded in essentially distinct or segment markets (bonds are not perfect substitutes) The trading of long-term borrowers and lenders determine rates on long-term bonds. Similarly, the trading of short-term borrowers and lenders determine rates on short-term bonds. Various equilibrium rates (according to maturity of bonds) Their explanation of upward sloping yield curve? A:? This view of the market is not supported by empirical facts. It does not explain the shape of the yield curve (for low and high short term interest rates) and why yields on bonds of different maturities tend to move together (See Figure 5, p. 117,Mishkin et al.),30,31,C) Liquidity Premium Theory The theory that investors demand a risk premium on longterm bonds. The risk premium required to hold longer term bonds is called liquidity premium Investors and firms are willing to hold these bonds. Why? A: Yield curve will be upward sloping even in the absence of any expectations of future increases in rates. If the liquidity preference theory is valid, the forward rate of interest is not a good estimate of market expectations of future interest rates. Why? A:,32,Pure Expectations Theory Yield Curve,Liquidity Premium Theory Yield Curve,Interest Rate,Years to Maturity,Relationship between the Expectations Theory and the Liquidity Premium Theory,Liquidity Premium,5,10,15,20,25,30,0,33,What theory explains better the TSIR? The Liquidity premium theory explains better the empirical facts such as 1. That interest rates on different maturity bonds move together over time. 2. That yield curves tend to be upward sloping when short-term interest rates are low and to be inverted when short-term interest rates are high. 3. It explains that yield curves typically slope upward by recognizing that the liquidity premium rises with a bonds maturity (because of investors preferences for short-term bonds).,34,In summary,The liquidity premium theory predicts the behaviour of future short term interest rates by looking at the slope of the yield curve: 1. A steeply rising yield curve indicates that ST is are expected to rise in the future 2. A moderately rising yield curve indicates that ST is are not expected to rise or fall much in the future. 3. A flat yield curve, indicates that ST is are expected to fall moderately in the future. 4. An inverted yield curve, indicates that ST is are expected to fall sharply in the future.,35,Yield curves and the markets expectations