Chapter Eleven

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Chapter Eleven

• Asset Markets

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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.

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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.

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Selling An Asset

• Q When should an asset be sold?
• When its value is at a maximum?
• No. Why not?

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Selling An Asset

• Suppose the value of an asset changes with time
  according to

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Selling An Asset
Value
Years
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Selling An Asset
Maximum value occurs when
That is, when t 50.
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Selling An Asset
Value
Max. valueof 24,000is reachedat year 50.
Years
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Selling An Asset

• The rate-of-return in year t is the income earned
  by the asset in year t as a fraction of its value
  in year t.
• E.g. if an asset valued at 1,000 earns 100 then
  its rate-of-return is 10.

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Selling An Asset

• Q Suppose the interest rate is 10. When should
  the asset be sold?
• A When the rate-of-return to holding the asset
  falls to 10.
• Then it is better to sell the asset and put the
  proceeds in the bank to earn a 10 rate-of-return
  from interest.

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Selling An Asset
The rate-of-return of the asset at time t is
In our example,
so
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Selling An Asset
The asset should be sold when
That is, when t 10.
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Selling An Asset
Value
Max. valueof 24,000is reachedat year 50.
slope 0.1
Years
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Selling An Asset
Value
Max. valueof 24,000is reachedat year 50.
slope 0.1
Sell at 10 yearseven though theassets value
isonly 8,000.
Years
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Selling An Asset

• What is the payoff at year 50 from selling at
  year 10 and then investing the 8,000 at 10 per
  year for the remaining 40 years?

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Selling An Asset

• What is the payoff at year 50 from selling at
  year 10 and then investing the 8,000 at 10 per
  year for the remaining 40 years?

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Selling An Asset
So the time at which an asset should besold is
determined by
Rate-of-Return r, the interest rate.
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Arbitrage

• 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?

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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 isI.e.

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Arbitrage

• Sell the asset now for p0, put the money in the
  bank to earn interest at rate r and tomorrow you
  have

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Arbitrage

• When is not selling best? WhenI.e. if the
  rate-or-return to holding the asset
  the interest rate, then keep the asset.
• And if thenso sell now for p0.

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Arbitrage

• If all asset markets are in equilibrium then
  for every asset.
• Hence, for every asset, todays price p0 and
  tomorrows price p1 satisfy

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Arbitrage
I.e. tomorrows price is the future-value
oftodays price. Equivalently,
I.e. todays price is the present-valueof
tomorrows price.
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Arbitrage in Bonds

• Bonds pay interest. Yet, when the interest
  rate paid by banks rises, the market prices of
  bonds fall. Why?

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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 gt r then
  r gt R and the bond should be sold.
• Sales of bonds lower their market prices.

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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.

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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.