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1、Part TwoFundamentals of Financial MarketsChapter 3What Do Interest Rates Mean and What Is Their Role in Valuation?Chapter PreviewInterest rates are among the most closely watched variables in the economy. They affect economic decision of business and households.They directly affect our everyday live
2、s and have important consequence for the health of the economy. 3Copyright 2009 Pearson Prentice Hall. All rights reserved.Chapter PreviewIn this chapter, we will develop a better understanding of interest rates. We examine the terminology and calculation of various rates, and we show the importance
3、 of these rates in our lives and the general economy. Topics include:Measuring Interest RatesReal and Nominal Interest RatesInterest Rates and ReturnsInterest-Rate Risk and Duration4Copyright 2009 Pearson Prentice Hall. All rights reserved.Measuring Interest Rate:Types of Credit InstrumentsSimple Lo
4、anDiscount BondCoupon BondFixed Payment Loancommerical loans to busniessInstallment loans and mortgages5Copyright 2009 Pearson Prentice Hall. All rights reserved.Interest Rate:Simlpe Loan TermSimple loan1. The amount of funds the lender provides to the borrower.1.The date the loan must be repaid; 2.
5、the Loan Term is from initiation to maturity date.1. The cash amount that the borrower must pay the lender for the use of the loan principal.1.The interest payment divided by the loan principal;2.The percentage of principal that must be paid as interest to the lender.Loan PrincipalMaturity DateInter
6、est PaymentSimple Interest Rate6Copyright 2009 Pearson Prentice Hall. All rights reserved.Present Value Concept: Simple Loani=10%7Copyright 2009 Pearson Prentice Hall. All rights reserved.Present Value IntroductionThe term present value (PV) can be extended to mean the PV of a single cash flow or th
7、e sum of a sequence or group of cash flows. A dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today. Because you could invest the dollar in a savings account that earns interest and have more than a dollar in one year.8Copyright 2009 Pearson Prenti
8、ce Hall. All rights reserved.Present Value Different debt instruments have very different streams of cash payments to the holder (known as cash flows), with very different timing. All else being equal, debt instruments are evaluated against one another based on the amount of each cash flow and the t
9、iming of each cash flow.This evaluation, where the analysis of the amount and timing of a debt instruments cash flows lead to its yield to maturity or interest rate, is called present value analysis.9Copyright 2009 Pearson Prentice Hall. All rights reserved.Yield to MaturityYield to maturity = inter
10、est rate that equates present value of cash flows received from a debt instrument with its value todayYield to maturity is the most accurate measure of interest rates, because the concept behind the calculation of the yield to maturity makes good economic sense.10Copyright 2009 Pearson Prentice Hall
11、. All rights reserved.Simple LoanSimple Loans require payment of one amount which equals the loan principal plus the interest at the maturity date.Simple Loan Interest Rate (PV=100,FV=110, n=1)11Copyright 2009 Pearson Prentice Hall. All rights reserved.Fixed-Payment Loan Fixed-Payment Loans are loan
12、s where the loan principal and interest are repaid in several payments, often monthly, in equal dollar amounts over the loan term. Installment Loans, such as auto loans and home mortgages are frequently of the fixed-payment type.12Copyright 2009 Pearson Prentice Hall. All rights reserved.Fixed-Payme
13、nt Loan Fixed Payment Loan (PV=1000, C=85.81，n=25)13Copyright 2009 Pearson Prentice Hall. All rights reserved.Fixed-Payment Loan You decide to purchase a new home and need a 100000 mortgage. You take out a loan from the bank that has an interest rate of 7%. What is the yearly payment to the bank to
14、pay off the loan in 20 years?14Copyright 2009 Pearson Prentice Hall. All rights reserved.Coupon Bond To calculate the yield to maturity for a coupon bond,follow the same strategy used for the fixed-payment loan: Equate todays value of the bond with its present value.The present value of the bond is
15、calculated as the sum of the present values of all the coupon payments plus the present value of the final payment of the face value of the bond.15Copyright 2009 Pearson Prentice Hall. All rights reserved.Yield to Maturity: BondsCoupon Bond (F=1000, Coupon rate = 10% = C/F,n=10)16Copyright 2009 Pear
16、son Prentice Hall. All rights reserved.Relationship Between Price and Yield to MaturityThree interesting facts in Table 3-11.Price and yield are negatively related2.When bond is at par, yield equals coupon rate3.Yield greater than coupon rate when bond price is below par value17Copyright 2009 Pearso
17、n Prentice Hall. All rights reserved.Perpetuity/ConsolPerpetuity/Consol: Fixed coupon payments of $C forever18Copyright 2009 Pearson Prentice Hall. All rights reserved.Current Yield Current yield (CY) is just an approximation for YTM easier to calculate. However, we should be aware of its properties
18、:1.If a bond has a long maturity, then CY is a good approximation.2.A change in the current yield always signals change in same direction as yield to maturity19Copyright 2009 Pearson Prentice Hall. All rights reserved.Discount BondThe yield-to-maturity calculation for a discount bond is similar to t
19、hat for the simple loan.One-Year Discount Bond (P = $900, F = $1000)20Copyright 2009 Pearson Prentice Hall. All rights reserved.Quantitative Problems1.Calculate the present value of a 1000 zero-coupon bond with five years to maturity if the yield to maturity is 6%?2.Consider a coupon bond that has a
20、 1000 par value and a coupon rate of 10%. The bond is currently selling for 1150 and has eight years to maturity. What is the bonds yield to maturity? 21Copyright 2009 Pearson Prentice Hall. All rights reserved.3.What is the price of a perpetuity that has a coupon of 50 per year and a yield to matur
21、ity of 2.5%? If the yield to maturity doubles, what will happen to its price?4.You are willing to pay 15625 now to purchase a perpetuity that will pay you and your heirs 1250 each year, forever, starting at the end of this year. If your required rate of return does not change, how much would you be
22、willing to pay if this were 20-years, annual payment, ordinary annuity instead of a perpetuity?Quantitative Problems22Copyright 2009 Pearson Prentice Hall. All rights reserved.Distinction Between Real and Nominal Interest RatesThis interest rate reflects the true cost of borrowing more accurately,Wh
23、en the real rate is low, there are greater incentives to borrow and less to lendex ante real interest rate/ ex post real interest rateInterest rate that is adjusted by substracting expected changes in the price level(inflation)Fisher equation/Fisher Effect 23Copyright 2009 Pearson Prentice Hall. All
24、 rights reserved.Distinction Between Real and Nominal Interest Rates (cont.)If i = 5% and e = 0% thenIf i = 10% and e = 20% then，24Copyright 2009 Pearson Prentice Hall. All rights reserved.U.S. Real and Nominal Interest RatesSample of current rates and indexeshttp:/ 2009 Pearson Prentice Hall. All r
25、ights reserved.Misery Index26Copyright 2009 Pearson Prentice Hall. All rights reserved.Quantitative ProblemsAssume you just deposited 1000 into a bank account. The current real interest rate is 2%, and inflation is expected to be 6% over the next year. What nominal rate would you require from the ba
26、nk over the next year? How much money will you have at the end of one year？If you are saving to buy a stereo that currently sells for 1050, will you have enough to buy it?27Copyright 2009 Pearson Prentice Hall. All rights reserved.Distinction Between Interest Rates and ReturnsRate of Return: we can
27、decompose returns into two pieces:where = current yield, and= capital gains.28Copyright 2009 Pearson Prentice Hall. All rights reserved.Quantitative Problems1.A 10-year, 7% coupon bond with a face value of 1000 is currently selling for 871.65. Compute your rate of return if you sell the bond next ye
28、ar for 880.10.2. You have paid 980.30 for an 8% coupon bond with a face value of 1000 that matures in five years. You plan on holding the bond for one year. If you want to earn a 9% rate of return on this investment, what price must you sell the bond for?29Copyright 2009 Pearson Prentice Hall. All r
29、ights reserved.Key Facts about the Relationship Between Rates and Returns30Copyright 2009 Pearson Prentice Hall. All rights reserved.Maturity and the Volatility of Bond ReturnsKey findings from Table 3-21.Only bond whose return = yield is one with maturity = holding period2.For bonds with maturity h
30、olding period, i P implying capital loss3.Longer is maturity, greater is price change associated with interest rate change4.Longer is maturity, more return changes with change in interest rate5.Bond with high initial interest rate can still have negative return if i 31Copyright 2009 Pearson Prentice
31、 Hall. All rights reserved.Maturity and the Volatility of Bond Returns: Interest RiskConclusion from Table 3-2 analysis1.Prices and returns more volatile for long-term bonds because have higher interest-rate riskThe riskiness of an assets return that results from interest-rate changes2. No interest-
32、rate risk for any bond whose maturity equals holding periodThe price at the end of the holding period is already fixed at the face value, the change in interest rates can then have no effect on the price at the end of the holding period for these bonds.32Copyright 2009 Pearson Prentice Hall. All rig
33、hts reserved.Reinvestment Risk 1.Occurs if hold series of short bonds over long holding period2.interest rate at which reinvest uncertain3.Gain from i , lose when i Reinvestment risk occurs because the proceeds from the short-term bond need to be reinvested at a future interest rate that is uncertai
34、n. 33Copyright 2009 Pearson Prentice Hall. All rights reserved.Bonds are subject to reinvestment riskThe term to maturity the holding period2200820072006 The return on a bond = the yield to maturityWhen the holding period=the maturity134Copyright 2009 Pearson Prentice Hall. All rights reserved.Durat
35、ion: Measuring Interest-Rate RiskThe fact that two bonds have the same term to maturity does not mean that they have the same interest-rate risk. A bond with a longer term to maturity has a larger change in its price and hence more interest rate riskExample: Calculate the rate of capital gain or los
36、s in one year on a 10-year zero-coupon bond for which the interest rate has increased from 10% to 20%. The bond has a face value of 1000.The coupon bond makes payments earlier than the zero-coupon bond, so the coupon bond has shorter effective maturity and less interest-rate risk.35Copyright 2009 Pe
37、arson Prentice Hall. All rights reserved.Key Facts about the Relationship Between Rates and Returns36Copyright 2009 Pearson Prentice Hall. All rights reserved.Duration: Measuring Interest-Rate RiskBecause a zero-coupon bond makes no cash payments before the bond matures, it makes sense to define its
38、 effective maturity as equal to its actual term to maturity.A coupon bond is equivalent to a set of zero-coupon discount bonds, the effective maturity of a coupon bond can be measured by summing up the effective maturity of each zero-coupon bond.Effective maturity of a debt secutity, the average lif
39、etime of a debt securitys stream of payments37Copyright 2009 Pearson Prentice Hall. All rights reserved.Duration: Measuring Interest-Rate RiskA 10-year 10% coupon bond with 1000 face value has cash payments identical to the following set of zero-coupon bonds:A 100 one-year zero-coupon bond(which pay
40、s the equivalent of the 100 coupon payment made by the 1000 10-year 10% coupon bond at the end of one year)A 100 two-year zero-coupon bond(which pays the equivalent of the 100 coupon payment at the end of two years)012345679810100100010010010010010010010010010038Copyright 2009 Pearson Prentice Hall.
41、 All rights reserved.To get the effective maturity of this set of zero-coupon bonds, we would want to sum up the effective maturity of each zero-coupon bond.The duration of this set of zero-coupon bonds is the weighted average of the effective maturities of the individual zero-coupon bonds, with the
42、 weights equaling the proportion of the total value represented by each zero-coupon bond. Duration: Measuring Interest-Rate Risk39Copyright 2009 Pearson Prentice Hall. All rights reserved.Calculating Durationi =10%, 10-Year 10% Coupon Bond40Copyright 2009 Pearson Prentice Hall. All rights reserved.F
43、ormula for DurationKey facts about duration1.All else equal, when the maturity of a bond lengthens, the duration rises as well2.All else equal, when interest rates rise, the duration of a coupon bond fall3.All else equal, the higher is the coupon rate on the bond, the shorter is the duration of the
44、bond.41Copyright 2009 Pearson Prentice Hall. All rights reserved.Calculating Durationi =10%, 10-Year 10% Coupon Bond42Copyright 2009 Pearson Prentice Hall. All rights reserved.Calculating Durationi = 20%, 10-Year 10% Coupon Bond43Quantitative ProblemsCalculate the duration of a 1000,6% coupon bond w
45、ith three years to maturity. Assume that all market interest rate are 7%.44Copyright 2009 Pearson Prentice Hall. All rights reserved. The duration of a portfolio of securities is the weighted-average of the durations of the individual securities, with the weights equaling the proportion of the portf
46、olio invested in eachFormula for Duration45Copyright 2009 Pearson Prentice Hall. All rights reserved.A manager of a financial institution is holding 25% of a portfolio in a bond with a five-year duration and 75%in a bond with a 10-year duration. What is the duration of the portfolio?Formula for Dura
47、tionThe duration of the portfolio is :46Copyright 2009 Pearson Prentice Hall. All rights reserved.Quantitative ProblemsThe Duration of a 100 million portfolio is 10 years. 40 million in new securities are added to the portfolio, increasing the duration of the portfolio to 12.5 years. what is the dur
48、ation of the 40 million in new securities?47Copyright 2009 Pearson Prentice Hall. All rights reserved.Quantitative ProblemsA bank has two 3-year commercial loans with a present value of 70 million. The first is a 30 million loan that requires a single payment of 37.8 million in three years, with no
49、other payments till then. The second loan is for 40 million.It requires an annual interest payment of 3.6 million. The principal of 40 million is due in three years.What is the duration of the banks commercial loan portfolio?48Copyright 2009 Pearson Prentice Hall. All rights reserved.Duration and In
50、terest-Rate RiskDuration is a particularly useful concept because it provides a good approximation for how much the security price changes for a given change in interest rates, particularly when interest-rate changes are small.49Copyright 2009 Pearson Prentice Hall. All rights reserved.Calculating D
51、urationi =10%, 10-Year 10% Coupon Bond50Copyright 2009 Pearson Prentice Hall. All rights reserved.Duration and Interest-Rate Riski 10% to 11%:Table 3-3, 10% coupon bond51Copyright 2009 Pearson Prentice Hall. All rights reserved.Calculating Durationi = 20%, 10-Year 10% Coupon Bond52Duration and Inter
52、est-Rate Riski 20% to 21%:Table 3-4, coupon bond, DUR = 5.72 years53Copyright 2009 Pearson Prentice Hall. All rights reserved.The greater is the duration of a security, the greater is the percentage change in the market value of the security for a given change in interest ratesDuration and Interest-
53、Rate Risk Therefore, the greater the duration of a security, the greater its interest-rate risk54Copyright 2009 Pearson Prentice Hall. All rights reserved.Quantitative ProblemsConsider a 1000,6% coupon bond with three years to maturity. Calculate the expected price change if the interest rate drop f
54、rom 7% to 6.75% using the duration approximation.Calculate the actual price change using discounted cash flow.55Copyright 2009 Pearson Prentice Hall. All rights reserved.Quantitative Problems. Consider a bond that promises the following cash flows. The required discount rate is 12%.Year01234Promised
55、 Payments 160170180230 You plan to buy this bond, hold it for 2.5 years, and then sell the bond.a.What total cash will you receive from the bond after the 2.5 years? Assume that periodic cash flows are reinvested at 12%.b.If immediately after buying this bond, all market interest rates drop to 11% (
56、including your reinvestment rate), what will be the impact on your total cash flow after 2.5years? How does this compare to part (a)?c.Assuming all market interest rates are 12%, what is the duration of this bond?56Copyright 2009 Pearson Prentice Hall. All rights reserved.Chapter SummaryMeasuring In
57、terest Rates: We examined several techniques for measuring the interest rate required on debt instruments.The Distinction Between Real and Nominal Interest Rates: We examined the meaning of interest in the context of price inflation.The Distinction Between Interest Rates and Returns: We examined what each means and how they should be viewed for asset valuation.57Copyright 2009 Pearson Prentice Hall. All rights reserved.
