计算计算 Term structure Expectations theory:=+ + 1+ + 2+ + +( 1) Liquidity premium theory:=+ + 1+ + 2+ + +( 1) + Because 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 slope. (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：0=1(1 + )+1(1 + )0= 1= 1.= .1= Generalized Dividend Valuation Model：0= = 1(1 + )Gordon Growth Model：0=0(1 + )( )=1( ).0= = . Interest-Rate Risk A change in its interest rate: percent change in market value of securitypersentage-point change in interest rateduration in yearsA1：The assets fall in value by $8 million(=$100 million)while the liabilities fall 2% 4 in value by $10.8 million(=$90 million). Because the liabilities fall in value by 2% 6 $2.8 million more than the assets do, the net worth of 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 earned 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); the 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 another banks $10 million of fixed-rate assets. The Money Multiplier M is money supply. MB is the monetary base. = c = C/D = currency ratio e = ER/D = excess reserves ratio C is currency. ER is excess reserves. D is checkable deposits. r is the required reserve ratio. =1 + + =1 + + + =1 + + + 问答问答Present 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 the 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(到期收益率到期收益率): 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 price. = + + 1 RET=return from holding the bond from time t to t+1.=price of bond at time t=price of the bond at time t+1 + 1C=coupon payment=current yield= =rate of capital gain=g + 1 Rate of Return and Interest Rates: 1.The return equals the yield to maturity only if the holding 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 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 interest 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 in the price level.