货币金融学 米什金 期末重点总结

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 =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 durati on 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

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 bond’s maturity, the greater the size of the percentage price change associated with an interest-rate change.

4.The more distant a bond’s 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.

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 assets

2.Expected Return: the return expected over the next period on one asset relative to alternative assets

3.Risk: the degree of uncertainty associated with the return on one asset relative to alternative assets

4.Liquidity: the ease and speed with which an asset can be turned into cash relative to alternative assets

Theory of Asset Demand:

1.The quantity demanded of an asset is positively related to wealth

2.The quantity demanded of an asset is positively related to its expected return relative to alternative assets

3.The quantity demanded of an asset is negatively related to the risk of its returns relative to alternative assets

4.The quantity demanded of an asset is positively related to its liquidity relative to alternative assets

The 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 interest 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 cash

Cost of selling a bond

3. 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 maturity is different.

3个现象：

1.Interest rates on bonds of different maturities move together over time

2.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 inverted

3.Yield curves almost always slope upward

3个理论：（后拓）

1.Expectations theory explains the first two facts but not the third

2.Segmented markets theory explains fact three but not the first two

3.Liquidity premium theory combines the two theories to explain all three facts

Gap and Duration Analysis:

Gap analysis: The sensitivity 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 liabilities

Duration analysis: An alternative method for measuring interest-rate risk, called duration analysis, examines the sensitivity of the market value of the bank’s 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 future (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 specified 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 affecting 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 put 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 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.

Tools of Monetary Policy

1. Open market operations: Affect the quantity of reserves and the monetary base. Advantages: ①The Fed has complete control over the volume. ②Flexible and precise. ③Easily reversed. ④Quickly implemented.

2. Discount rate policy: Affect the monetary base.

Advantages and Disadvantages: ①Used to perform role of lender of last resort：Important during the subprime financial crisis of 2007-2008. ②Cannot be controlled by the Fed; the decision maker is the bank. ③Discount facility is used as a backup facility to prevent the federal funds rate from rising too far above the target.

3. Reserve requirements: Affect the money multiplier.

Disadvantages: ①No longer binding for most banks.②Can cause liquidity problems.③Increases 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 the 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=B s-B d=M s-M d

If the market for money is in equilibrium (M s=M d), then the bond market also in equilibrium (B s=B d).

Expectations Theory

The 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 its 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 Theory

Bonds of different maturities are not substitutes at all.

The interest rate for each bond with a different maturity is 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 theory

The 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.