Chapter Eleven Asset Markets

Assets u An asset is a commodity that provides a flow of services over time. u E.g. a house, or a computer. u A financial asset provides a flow of money over time -- a security.

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

Selling An Asset u Suppose the value of an asset changes with time according to

Selling An Asset Value Years

Selling An Asset Maximum value occurs when That is, when t = 50.

Selling An Asset Value Years Max. value of $24,000 is reached at year 50.

Selling An Asset u 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. u E.g. if an asset valued at $1,000 earns $100 then its rate-of-return is 10%.

Selling An Asset u Q: Suppose the interest rate is 10%. When should the asset be sold? u A: When the rate-of-return to holding the asset falls to 10%. u 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 Years Max. value of $24,000 is reached at year 50. slope = 0.1

Selling An Asset Value Years Max. value of $24,000 is reached at year 50. Sell at 10 years even though the asset’s value is only $8,000. slope = 0.1

Selling An Asset u 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 u 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 be sold is determined by Rate-of-Return = r, the interest rate.

Arbitrage u Arbitrage is trading for profit in commodities which are not used for consumption. u E.g. buying and selling stocks, bonds, or stamps. u No uncertainty  all profit opportunities will be found. What does this imply for prices over time?

Arbitrage u The price today of an asset is p 0. Its price tomorrow will be p 1. Should it be sold now? u The rate-of-return from holding the asset is I.e.

Arbitrage u Sell the asset now for $p 0, put the money in the bank to earn interest at rate r and tomorrow you have

Arbitrage u When is not selling best? When I.e. if the rate-or-return to holding the asset the interest rate, then keep the asset. u And if then so sell now for $p 0.

Arbitrage u If all asset markets are in equilibrium then for every asset. u Hence, for every asset, today’s price p 0 and tomorrow’s price p 1 satisfy

Arbitrage I.e. tomorrow’s price is the future-value of today’s price. Equivalently, I.e. today’s price is the present-value of tomorrow’s price.

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

Arbitrage in Bonds u A bond pays a fixed stream of payments of $x per year, no matter the interest rate paid by banks. u At an initial equilibrium the rate-of-return to holding a bond must be R = r’, the initial bank interest rate. u If the bank interest rate rises to r” > r’ then r” > R and the bond should be sold. u Sales of bonds lower their market prices.

Taxation of Asset Returns u r b is the before-tax rate-of-return of a taxable asset. u r e is the rate-of-return of a tax exempt asset. u t is the tax rate. u The no-arbitrage rule is: (1 - t)r b = r e u I.e. after-tax rates-of-return are equal.

Financial Intermediaries u 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.