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
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,
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?
The rate-of-return from holding the
asset is
I.e.
R p p
p
1 0
0
( ),1 0 1R p p
Arbitrage
Sell the asset now for $p0,put the
money in the bank to earn interest at
rate r and tomorrow you have
( ),1 0? r p
Arbitrage
When is not selling best? When
I.e,if the rate-or-return to holding the
asset the interest rate,then
keep the asset.
And if then
so sell now for $p0.
( ) ( ),1 10 0R p r p
R r?
R r?
( ) ( )1 10 0R p r p
Arbitrage
If all asset markets are in equilibrium
then for every asset.
Hence,for every asset,today’s price
p0 and tomorrow’s price p1 satisfy
R r?
p r p1 01( ),
Arbitrage
p r p1 01( )
I.e,tomorrow’s price is the future-value of
today’s price,Equivalently,
p p r0 11,
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?
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.
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.
Taxation of Asset Returns
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:
(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
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.
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
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,
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?
The rate-of-return from holding the
asset is
I.e.
R p p
p
1 0
0
( ),1 0 1R p p
Arbitrage
Sell the asset now for $p0,put the
money in the bank to earn interest at
rate r and tomorrow you have
( ),1 0? r p
Arbitrage
When is not selling best? When
I.e,if the rate-or-return to holding the
asset the interest rate,then
keep the asset.
And if then
so sell now for $p0.
( ) ( ),1 10 0R p r p
R r?
R r?
( ) ( )1 10 0R p r p
Arbitrage
If all asset markets are in equilibrium
then for every asset.
Hence,for every asset,today’s price
p0 and tomorrow’s price p1 satisfy
R r?
p r p1 01( ),
Arbitrage
p r p1 01( )
I.e,tomorrow’s price is the future-value of
today’s price,Equivalently,
p p r0 11,
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?
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.
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.
Taxation of Asset Returns
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:
(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
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.
