《微观经济学》清华大学-ju-imicro-Ch11PPT精品文档16页

Arbitrage in Bonds
A bond pays a fixed stream of payments of $x per year, no matter the interest rate paid by banks.
At an initial equilibrium the rate-of-return to holding a bond must be R = r’, the initial bank interest rate.
Chapter Eleven
Asset (资产)Markets
Main Issue
No Arbitrage(套利) Condition
Assets
An asset is a commodity that provides a flow of services over time.
E.g. a house, or a computer. A financial asset provides a flow of
(1 - t)rb = re I.e. after-tax rates-of-return are equal.
Assets with Consumption Returns
The example of house A=appreciation T=implicit rental rate P=initial investment h=(T+A)/P=total rate of return h=(T+A)/P=r
Arbitrage (套利)
Arbitrage is trading for profit in commodities which are not used for consumption.
E.g. buying and selling stocks, bonds, or stamps.
No uncertainty all profit opportunities will be found. What does this imply for prices over time?
Arbitrage
The price today of an asset is p0. Its price tomorrow will be p1. Should it be sold now?
rb is the before-tax rate-of-return of a taxable asset.
re is the rate-of-return of a tax exempt asset.
t is the tax rate. The no-arbitrage rule is:
(1r)p0.
Arbitrage
When is not selling best? When
( 1 R ) p 0 ( 1 r ) p 0 .
I.e. if the rate-or-return to holding the
asset Rr the interest rate, then
The rate-of-return from holding the
asset is I.e.
R p1 p0 p0
(1 R )p 0 p 1 .
Arbitrage
Sell the asset now for $p0, put the money in the bank to earn interest at rate r and tomorrow you have
If the bank interest rate rises to r” > r’ then r” > R and the bond should be sold.
Sales of bonds lower their market prices.he asset.
And if Rr then ( 1 R ) p 0 ( 1 r ) p 0
so sell now for $p0.
Arbitrage
If all asset markets are in equilibrium
then Rrfor every asset.
money over time -- a security.
Assets
Typically asset values are uncertain. Incorporating uncertainty is difficult at this stage so we will instead study assets assuming that we can see the future with perfect certainty.
today’s price. Equivalently,
p0

p1 1r
.
I.e. today’s price is the present-value
of tomorrow’s price.
Arbitrage in Bonds
Bonds “pay interest”. Yet, when the interest rate paid by banks rises, the market prices of bonds fall. Why?
Financial Intermediaries
Banks, brokerages etc. – facilitate trades between people with different levels of impatience – patient people (savers) lend funds to impatient people (borrowers) in exchange for a rate-of-return on the loaned funds. – both groups are better off.
Hence, for every asset, today’s price p0 and tomorrow’s price p1 satisfy
p 1 (1 r)p 0 .
Arbitrage
p 1(1 r)p 0
I.e. tomorrow’s price is the future-value of