计算
Term structure
Expectations theory:
i nt =i t +i t+1e +i t+2e +⋯+i t+(n−1)
e n
Liquidity premium theory:
i nt =i t +i t+1e +i t+2e +⋯+i t+(n−1)
e n +l nt
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 model
One -Period Valuation Model ：
P 0=Div 1
(1+k e )+P
1(1+k e ) P 0=the current price of the stock
Div 1=the dividend paid at the end of year 1.
k e =the required return on investments in equity.
P 1=the price at the end of the first period .
Generalized Dividend Valuation Model ：
P 0=∑D t
(1+k e )t ∞t=1
Gordon Growth Model ：
P 0=D 0×(1+g )
(k e −g)=D 1
(k e −g)
D 0=the most recet dividend paid .
g =the expected constant growth rate in dividends.
Interest -Rate Risk
A change in its interest rate:
percent change in market value of security≈−persentage -point change in interest rate×duration in years
A1：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 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 bank’s 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 bank’s $10 million of fixed -rate assets.
The Money Multiplier
M is money supply.
MB is the monetary base.
M=m×MB
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.
D=1
r+e+c
×MB
M=1+c
r+e+c
×MB
m=1+c
r+e+c
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):
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.
RET=C
P t +P t+1−P t
P t
RET=return from holding the bond from time t to t+1. P t=price of bond at time t
P t+1=price of the bond at time t+1
C=coupon payment
C
P t
=current yield=i c
P t+1−P t
P t
=rate of capital gain=g
