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1、计算Term structureExpectations theory: int=it+it+1e+it+2e+it+n-1enLiquidity premium theory: int=it+it+1e+it+2e+it+n-1en+lntBecause of people preferred short- term bonds, there is a larger liquidity premium as the term to maturity lengthens. (上升图)Yield curves tend to have an especially steep upward slo
2、pe. (下降图）Yield curves will not tend to have a steep downward slope, and maybe will slope upward.Stock pricing modelOne-Period Valuation Model： P0=Div11+ke+P11+ke P0=the current price of the stock Div1=the dividend paid at the end of year 1. ke=the required return on investments in equity. P1=the pri
3、ce at the end of the first period.Generalized Dividend Valuation Model： P0=t=1Dt1+ketGordon Growth Model： P0=D01+g(ke-g)=D1(ke-g) D0=the most recet dividend paid. g=the expected constant growth rate in dividends.Interest-Rate RiskA change in its interest rate: percent change in market value of secur
4、ity-persentage-point change in interest rateduration in yearsA1：The assets fall in value by $8 million(=$100 million-2%4 years)while the liabilities fall in value by $10.8 million(=$90 million-2%6 years). Because the liabilities fall in value by $2.8 million more than the assets do, the net worth of
5、 the bank rises by $2.8 million. The interest-rate risk can be reduced by shortening the maturity of the liabilities to a duration of 4 years or lengthening the maturity of the assets to a duration of 6 years. Alternatively, you could engage in an interest-rate swap, in which you swap the interest e
6、arned on your assets with the interest in another banks assets that have a duration of 6 years.A2: The gap is $10 million ($30 million of rate-sensitive assets minus $20 million of rate-sensitive liabilities). The change in bank profits from the interest rate rise is +$0.5 million (5%$10 million); t
7、he interest rate risk can be reduced by increasing rate-sensitive liabilities to $30 million or by reducing rate-sensitive assets to $20 million. Alternatively, you could engage in an interest rate swap in which you swap the interest in $10 million of rate-sensitive assets for the interest on anothe
8、r banks $10 million of fixed-rate assets.The Money MultiplierM is money supply. MB is the monetary base. M=mMBc = C/D = currency ratioe = ER/D = excess reserves ratioC is currency. ER is excess reserves. D is checkable deposits.r is the required reserve ratio. D=1r+e+cMB M=1+cr+e+cMB m=1+cr+e+c问答Pre
9、sent Value: A dollar paid to you one year from now is less valuable than a dollar paid to you today.Yield to Maturity and the Bond Price for a Coupon Bond: have 3 facts.1.When the coupon bond is priced at its face value, the yield to maturity equals the coupon rate.2.The price of a coupon bond and t
10、he yield to maturity are negatively related; that is, as the yield to maturity rises, the price of the bond falls. AS the yield to maturity falls, the price of the bond rises.3.The yield to maturity is greater than the coupon rate when the bond price is below its face value.Yield to Maturity(到期收益率):
11、1.The interest rate that equates the present value of cash flow payments received from a debt instrument with its value today. 2.Also called internal rate of return. 3.Most accurate measure of i.Rate of Return: The payment to the owner plus the change in value expressed as a fraction of the purchase
12、 price. RET=CPt+Pt+1-PtPtRET=return from holding the bond from time t to t+1. Pt=price of bond at time t Pt+1=price of the bond at time t+1C=coupon payment CPt=current yield=ic Pt+1-PtPt=rate of capital gain=gRate of Return and Interest Rates: 1.The return equals the yield to maturity only if the ho
13、lding period equals the time to maturity.2.A rise in interest rates is associated with a fall in bond prices, resulting in a capital loss if time to maturity is longer than the holding period.3.The more distant a bonds maturity, the greater the size of the percentage price change associated with an
14、interest-rate change.4.The more distant a bonds maturity, the lower the rate of return that occurs as a result of an increase in the interest rate.5.Even if a bond has a substantial initial interest rate, its return can be negative if interest rates rise.Real and Nominal Interest Rates: 1.Nominal in
15、terest rate makes no allowance for inflation.2.Real interest rate is adjusted for changes in price level so it more accurately reflects the cost of borrowing.3.Ex ante real interest rate is adjusted for expected changes in the price level.4.Ex post real interest rate is adjusted for actual changes i
16、n the price level.4 Factors of Asset Demand: An asset is a piece of property that is a store of value, such as money ,bond, stocks, and houses.1.Wealth: the total resources owned by the individual, including all assets2.Expected Return: the return expected over the next period on one asset relative
17、to alternative assets3.Risk: the degree of uncertainty associated with the return on one asset relative to alternative assets4.Liquidity: the ease and speed with which an asset can be turned into cash relative to alternative assetsTheory of Asset Demand:1.The quantity demanded of an asset is positiv
18、ely related to wealth2.The quantity demanded of an asset is positively related to its expected return relative to alternative assets3.The quantity demanded of an asset is negatively related to the risk of its returns relative to alternative assets4.The quantity demanded of an asset is positively rel
19、ated to its liquidity relative to alternative assetsThe Structure of Interest Rates风险结构：Bonds with the same maturity have different interest rates due to: Default risk违约风险, Liquidity流动性, Tax considerations所得税因素.1. Default risk: probability that the issuer of the bond is unable or unwilling to make i
20、nterest payments or pay off the face value.Conclusion: a bond with default risk will always have a positive risk premium, and an increase in its default risk will raise the risk premium. 具有违约风险的债券通常具有正的风险溢价，而违约风险的增长将会提高风险溢价水平。2. Liquidity: the relative ease with which an asset can be converted into
21、cashCost of selling a bond3. Income tax considerations Interest payments on municipal bonds are exempt from federal income taxes. Term Structure of Interest Rates 利率的期限结构 ：Bonds with identical risk, liquidity, and tax characteristics may have different interest rates because the time remaining to ma
22、turity is different.3个现象：1.Interest rates on bonds of different maturities move together over time2.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 inverted3.Yield curv
23、es almost always slope upward3个理论：（后拓）1.Expectations theory explains the first two facts but not the third2.Segmented markets theory explains fact three but not the first two3.Liquidity premium theory combines the two theories to explain all three factsGap and Duration Analysis:Gap analysis: The sen
24、sitivity of bank profits to changes in interest rates can be measured more directly using gap analysis, in which the amount of rate-sensitive liabilities is subtracted from the amount of rate-sensitive assets.GAP= rate-sensitive assets rate-sensitive liabilitiesDuration analysis: An alternative meth
25、od for measuring interest-rate risk, called duration analysis, examines the sensitivity of the market value of the banks total assets and liabilities to changes in interest rates.Financial Derivatives(4个金融衍生品)Forward contracts: Agreements by two parties to engage in a financial transaction at a futu
26、re (forward) point in time.Financial Futures Contracts: Similar to an interest-rate forward contract but differs in ways that overcome some of the liquidity and default problems.Options: Contracts that give the purchaser the option (right) to buy or sell the underlying financial instrument at a spec
27、ified price (exercise or strike price) within a specific period of time (term to expiration).Swaps: Financial contracts that obligate each party to the contract to exchange a set of payments (not assets) it owns for another set of payments owned by another party.Pricing Option Premiums（factors affec
28、ting the price of option premiums）1. The higher the strike price, everything else being equal, the lower the premium on call (buy) options and the higher the premium on put (sell) options.2. The greater the term to expiration, everything else being equal, the higher the premiums for both call and pu
29、t options.3. The greater the volatility of prices of the underlying financial instrument, everything else being equal, the higher the premiums of both call and put options.如何规避利率的风险？套期保值Hedging：Engage in a financial transaction that reduces or eliminates risk.Long position= buying of a security with
30、 the expectation that the asset will rise in value. Short position= agree to sell securities at future date.Hedging risk involves engaging in a financial transaction that offsets a long position by taking an additional short position, or offsets a short position by taking an additional long position
31、.Tools of Monetary Policy1. Open market operations: Affect the quantity of reserves and the monetary base.Advantages: The Fed has complete control over the volume. Flexible and precise. Easily reversed. Quickly implemented. 2. Discount rate policy: Affect the monetary base.Advantages and Disadvantag
32、es: Used to perform role of lender of last resort：Important during the subprime financial crisis of 2007-2008. Cannot be controlled by the Fed; the decision maker is the bank. Discount facility is used as a backup facility to prevent the federal funds rate from rising too far above the target. 3. Re
33、serve requirements: Affect the money multiplier.Disadvantages: No longer binding for most banks.Can cause liquidity problems.Increases uncertainty for banks.(The policy of changing reserve requirement is no longer used in the US.)拓The Liquidity Preference Framework: Keynesian model that determines t
34、he equilibrium interest rate in terms of the supply of and demand for money. There are two main categories of assets that people use to store their wealth: money and bonds.Total wealth in the economy=Bs-Bd=Ms-MdIf the market for money is in equilibrium (Ms=Md), then the bond market also in equilibri
35、um (Bs=Bd).Expectations TheoryThe interest rate on a long-term bond will equal an average of the short-term interest rates that people expect to occur over the life of the long-term bond.Buyers of bonds do not prefer bonds of one maturity over another; they will not hold any quantity of a bond if it
36、s expected return is less than that of another bond with a different maturity.Bond holders consider bonds with different maturities to be perfect substitutes.Segmented Markets TheoryBonds of different maturities are not substitutes at all.The interest rate for each bond with a different maturity is
37、determined by the demand for and supply of that bond.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).Liquidity premium th
38、eoryThe 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 partial (not perfect) substitutes.