米什金金融市場課件

1、Part IIFundamentals of Interest RatesChapter ThreeUnderstanding Interest Rates3Chapter PreviewnWe examine the terminology and calculation of various rates, and we show the importance of these rates in our lives and the general economy. Topics include:qMeasuring Interest RatesqThe Distinction Between

2、 Real and Nominal Interest RatesqThe Distinction Between Interest Rates and Returns43.1 Measuring Interest RatesnSince interest rates are among the most closely watched variables in the economy, it is imperative that what exactly is meant by the phrase interest rates is understood. nIn this chapter,

3、 we will see that a concept known as yield to maturity (YTM,到期收益率) is the most accurate measure of interest rates.53.1.1 Present Value IntroductionnDifferent debt instruments have very different streams of cash payments to the holder (known as cash flows), with very different timing. nAll else being

4、 equal, debt instruments are evaluated against one another based on the amount of each cash flow and the timing of each cash flow.nThis 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 ana

5、lysis. Interest Rates as Exchange RatesnPresent value is the concept based on the commonsense notion that a dollar of cash flow paid to you one year from now is less valuable to you than a dollar paid to you today.nInterest rate is the “exchange rate” between present value and future value.

6、 Concept of Present ValueSimple loan of $1Year123n$1.10 $1.21 $1.33 1(1+i)nPV of future $1=$11+in Four Types of Credit InstrumentsnSimple LoannFixed Payment LoannCoupon BondnDiscount Bond93.1.2 Simple loan (簡單貸款)nSimple loan is a loan, in which the lender provides the borrower with a

7、n amount of funds, which must be repaid to the lender at the maturity date along with an additional payment for the interest. Simple Loan: Yield to Maturity（到期收益率）nYield to maturity = interest rate that equates todays value with present value of all future paymentsnSimple Loan (one year loa

8、n for principal $100, on maturity creditor will be paid $110 (P+I)：$100 $110 1 ii $110 $100$100$10$100 .10 10%113.1.3 Fixed-payment loan (分期固定支付貸款)nFixed-payment loans are also called fully amortized loans, in which the lender provides the borrower with an amount of funds, which must be repaid by ma

9、king the same payment every period (such as a month), consisting of part of the principal and interest for a set number of years. : Fixed Payment Loans: Yield to MaturityFixed Payment Loan (i = 12%)$1000 $1261 i$1261 i2$1261 i3 .$1261 i25LV FP1 iFP1i2FP1 i3.FP1 inNote: LV = Loan Value; FP=

10、Fixed Payment A Mortgage Payment Table (Figure 3-1)143.1.4 Coupon Bond (息票債券)nA coupon bond pays the owner of the bond a fixed interest payment (coupon payment) every year until the maturity date, when a specified final amount (face value or par value) is repaid. Coupon Bonds: Yie

11、ld to MaturityCoupon Bond (Coupon rate = 10% = Coupon/Face value)P $1001 i$1001 i2$1001 i3 .$1001 i10$10001 i10P C1 iC1 i2C1 i3 .C1 inF1 inConsol (無期限債券): Fixed coupon payments of $C foreverP Cii CP A Bond Table (Figure 3-2)Coupon rate = 10% = C/F173.1.5 A Discount BondnA discount bond, als

12、o called a zero-coupon bond, is bought at a price below its face value (at discount), and the face value is repaid at the maturity date. Discounted Bonds (貼現(xiàn)債券): Yield to MaturityOne-Year Discount Bond (P = $900, F = $1000)$900 $10001 ii $1000 $900$900 .11111.1%i F PP Relationship

13、Between Price and Yield to MaturitynThree interesting facts in Table 3-11.When bond is at par, yield equals coupon rate2.Price and yield are negatively related3.Yield greater than coupon rate when bond price is below par value203.1.6 Current Yield (本期收益率)nCurrent yield is the approximation to descri

14、be interest rate on long-term bonds, including a perpetuity (永續(xù)年金), which is also called as a consol(無到期日債券) , a perpetual bond with no maturity date and no repayment of principal that makes fixed coupon payments of $c forever.icCPC=yearly payment; P= Price of the bond Two Characteristics

15、of Current YieldnCY is better approximation to yield to maturity, nearer price is to par and longer is maturity of bond;nChange in current yield always signals change in same direction as yield to maturity22Bond Page of the Newspaper233.2 Nominal and Real Interest Rates (名義利率與實(shí)際利率)nSo far our discus

16、sion has not taken account of the effects of inflation on the cost of borrowing.nThe interest rate which makes no allowance for inflation is called Nominal Interest Rate.nThe interest rate which is adjusted by eliminating expected changes in the price level (inflation), is called Real Interest Rate.

17、243.2.1 Fisher Equation nFisher equation states that the nominal interest rate equals the real interest rate plus the expected rate of inflation. nReal interest rate:ir i e253.2.2 Distinction Between Real and Nominal Interest RatesnIf i = 5% and e = 0% thenir 5% 0% 5%ir 10% 20% 10%If i = 10% and e =

18、 20% then263.2.3 Conclusion of Fisher EquationnReal interest rate more accurately reflects true cost of borrowing;nWhen real rate is low, greater incentives to borrow and less to lend273.2.4 U.S. Real and Nominal Interest RatesFigure 3-3: Real and Nominal Interest Rates (Three-Month Treasury Bill),

19、19532001Sample of current rates and indexeshttp:/ Interest Rate and ReturnnBecause of the possible fluctuation on the price of a bond, the return of a bond is not the same as its interest rate in most of the cases.29RET C Pt1 PtPt ic gwhere icCPt current yieldg pt1 PtPt capital gain3.3.1 Distinction

20、 Between Interest Rates and ReturnsnRate of Return = Current yield + Capital gain303.3.2 Key Facts in the Relationship Between Rates and ReturnsThe above data can be calculated by Equation 3, or by financial calculator: e.g. the 1st one, N=30-1, PMT=100, FV=1000, I/Y=20, CPT(PV) =502.53(4)313.3.3 Ma

21、turity and the Volatility of Bond Returns (期限與債券回報(bào)率的波動(dòng))Conclusion from Table 3-2 (P58) analysis：nWhen studying the affect from a change in interest rate, we talk about the expected price or future value of bonds;nPrices and returns more volatile for long-term bonds because have higher interest-rate

22、risk;nNo interest-rate risk for any bond whose maturity equals holding period. On maturity, the bond is repaid in cash and therefore, the change in interest rate does not affect its value.323.3.4 Key findings from Table 2nOnly bond whose return = yield is one with maturity = holding period (期限等于持有期，

23、P+I will be repaid in cash in one year);nFor bonds with maturity holding period, i P , implying capital loss;nLonger is maturity, greater is price change associated with interest rate change;nLonger is maturity, more return changes with change in interest rate;nBond with high initial interest rate c

24、an still have negative return if i 333.3.4 Reinvestment Risk (再投資風(fēng)險(xiǎn))nIf an investors holding period is longer than the term to maturity of the bond, the investor is exposed to a type of interest-rate risk called reinvestment risk.nThere exist re-inverment risk if the proceeds from the short-term bon

25、d need to be reinvested；ni at which reinvest is uncertain；nGain from i , lose when i nExample on P60-Chapter end-343.4 Duration(久期) and Interest-Rate RisknWhen interest rates change, a bond with a longer term to maturity has a larger change in its price and hence more interest rate risk than a bond

26、with a shorter term to maturity.nTo have more precisely information on the actual capital gain or loss that occur when interest rate changes by a certain amount, we need to calculate Duration.nDuration is the average lifetime of a debt securitys stream of payments.353.4.1 Interest Rate Risk on Diffe

27、rent BondsnTwo bonds with same term to maturity can have different interest rate risk (P61).nThe following example.3 Example (1)nBond 1: 10-year zero-coupon bond, interest rate rise from 10% to 20%, the effect on rate of capital gain (g)? year one: N=10, I/Y=10, PMT=0, FV=1000 PV=385.54 year

28、 two: N=9, I/Y=20, PMT=0, FV=1000 PV=193.81g=(193.81-385.54)/385.54=-49.7%Rate of return=-49.7+0(coupen received）=-49.7% 3 Example (2)nBond 2: 10-year bond, initial current yield 10%, initial price $1000, interest rate rise from 10% to 20%, the effect on rate of capital gain (g)? year one: P

29、V=1000(price first year) year two: N=9, I/Y=20, PMT=100, FV=1000 PV=596.90 (price second year)g=(596.90-1000)/1000=-40.3%Rate of return=-40.3+10%（coupen received） =-30.3% Table 2 on P58(line 3)383.4.2 Calculating DurationnFrederick Macaulay invented the concept of duration, to calculate the duration

30、 or effective maturity on any debt security.nMacaulay realizsed that he could measure the effective maturity of a coupon bond by recognizing that a coupon bond is equivalent to a set of zero-coupon dicount bonds, as shown in the Timeline on P62.nThe duration calcuation is shown on P63.3 Calc

31、ulating Duration (P63) i = 20%, 10-Year 10% Coupon Bond40 Particulars on CalculationnColumn (3): the PV of each of the zero-coupon bonds when the interest rate is 10%;nColumn (4): divide each of these PV by $1000, the total PV of the set of zero-coupen bonds (also the real PV of this 10% inte

32、rest rate coupon bond), to get the percentage of the total value of all the bonds that each bond represents, or so called the weight;nColumn (5): time each of these weights by the relative number of years (1)*(4) and we get the weighted maturities (the years for each of the effective payments) . Add

33、ing up allthe weighted maturities, we obtain the duration of the 10% 10-year coupon bond.nDuration is a weighted average of the maturities of the each payments.41DURtCPt1 itt1nCPt1 itt1n Formula for DurationnDUR=Duration；nt=years until cash payment is made；nCPt =cash payment (P+I) at time t;n

34、i=interest rate;nn=years to maturity of the security.Practice calculating duration on basis of data in Table 3 on P63 with financial calculator, assuming interest rate rises from 10% to 20% (compare your result with Table 4 on P65).423.4.3 Key facts about durationnAll else equal, when the maturity o

35、f a bond lengthens, the duration rises as well;nAll else equal, when interest rates rise, the duration of a coupon bond fall;nThe higher is the coupon rate on the bond, the shorter is the duration of the bond;nDuration is also useful in measuring the duration of a portfolio: the duration of a portfo

36、lio of securities is the weighted-average of the durations of the individual securities, with the weights equaling the proportion of the portfolio invested in each. Example 9 on P64.433.4.4 Duration and Interest-Rate RisknDuration is useful to measure interest-rate risk. nIt provides a good approxim

37、ation(近似值), particularly when interest rate changes are small, for how much the security price changes for a given change in interest rates.4 Formula for Measuring Interest-Rate Risk by duration%P DURi1iWhere %P=(Pt+1 Pt)/ Pt =percentage change in the price of the security from t to t+1 = rate of capital gain;DUR = durationi=interest rate4 Example 1 (P66):Assuming that i 10% to 11%, nCalculate the price change with the 10% coupon bond, on Table 3 (P63):%P 6.760.011 0.10%P 0.0615 6.15%The result tells that the rise in interest rate from 10% to 11%, w