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.

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 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 t = t-t 2 t t = 0 (t - 10)(t - 110) = 0 So sell when t = 10

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 (in principle) better off.