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Chapter Eleven

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Chapter Eleven

Asset Markets

- 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.

- 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.

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

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

Value

Years

Maximum value occurs when

That is, when t = 50.

Value

Max. valueof $24,000is reachedat year 50.

Years

- 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%.

- 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.

The rate-of-return of the asset at time t is

In our example,

so

The asset should be sold when

That is, when t = 10.

Value

Max. valueof $24,000is reachedat year 50.

slope

= 0.1

Years

Value

Max. valueof $24,000is reachedat year 50.

slope

= 0.1

Sell at 10 yearseven though theasset’s value isonly $8,000.

Years

- 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?

- 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?

So the time at which an asset should besold is determined by

Rate-of-Return = r, the interest rate.

- 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?

- 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.

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

- 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.

- 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

I.e. tomorrow’s price is the future-value oftoday’s price. Equivalently,

I.e. today’s price is the present-valueof tomorrow’s price.

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

- 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.

- 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.

- 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.