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# Chapter Eleven PowerPoint PPT Presentation

Chapter Eleven. Asset Markets. 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.

Chapter Eleven

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## Chapter Eleven

Asset Markets

### 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.

### Selling An Asset

• Q: When should an asset be sold?

• When its value is at a maximum?

• No. Why not?

### Selling An Asset

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

Value

Years

### Selling An Asset

Maximum value occurs when

That is, when t = 50.

### Selling An Asset

Value

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

Years

### 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%.

### 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.

### Selling An Asset

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

In our example,

so

### Selling An Asset

The asset should be sold when

That is, when t = 10.

### Selling An Asset

Value

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

slope

= 0.1

Years

### Selling An Asset

Value

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

slope

= 0.1

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

Years

### 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?

### 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?

### Selling An Asset

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

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

### 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?

### 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.

### Arbitrage

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

### 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.

### 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

### Arbitrage

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.

### 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.

### 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.