Selling an Asset: When and Why?

1. Chapter Eleven Asset Markets

2. 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.

3. Selling An Asset • Q: When should an asset be sold? • When its value is at a maximum? • No. Why not?

4. Selling An Asset • Suppose the value of an asset changes with time according to

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

6. Selling An Asset Value Max. valueof $24,000is reachedat year 50. Years

7. 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%.

8. 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.

9. Selling An Asset The rate-of-return of the asset at time t is In our example, so

10. Selling An Asset The asset should be sold when 1000 - 20t = -100 +100t-t2 t2 - 120t +1100 = 0 (t - 10)(t - 110) = 0 So sell when t = 10

11. 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

12. 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?

13. 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?

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

15. 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?

16. 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.

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

18. 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.

19. 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

20. 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.

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

22. 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.

23. 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.

24. 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 (in principle) better off.