Bond Prices Was the price paid in the auction for Taylor’s 99-year zero-coupon bond reasonable? Define notation again: F = face value (in dollars) R = coupon (in dollars) i = yield (in percent) P = price (in dollars)

Arbitrage Reasoning Compare rates of return in two similar markets If there is a difference, funds will move from one market to the other Hence, in equilibrium rates of return will equalize

Use arbitrage reasoning to determine the bond price when these are two alternatives Buy a bond 1-year maturity F = $100 R = $5 Put funds in a bank for one year interest rate at bank equals 5 percent (.05)

Compare rates of return Bond ( P)/P Bank Account.05

Rates of return must be equal Thus ( P)/P = = 1.05P P = 100 Simply solve for the bond price P as shown on the left

What if the interest rate at the bank changes? To 10 percent Now we have ( P)/P = = (1 +.10)P P = 105/1.10 P = 95 To 3 percent Now we have ( P)/P = = (1 +.03)P P = 105/1.03 P = 102

In general the price of a one year bond will be determined by (R + F - P)/P = i P = (R + F)/(1+i)

The same reasoning applies to longer maturity bonds: Two-year bonds: P = R/(1+i) + (R+F)/(1+i) 2 n-year bonds P = R/(1+i) + R/(1+i) 2 + R/(1+i) 3 + … + (R+F)/(1+i) n for zero coupon bonds (R = 0) so that P = F/(1+i) n

Price of a 99-year zero at different interest rates

Risk and Asset Pricing People are risk averse (at least when the amounts are big) Consider purposeful choice again, this time between more risky and less risky choices

Two Choices XYZ stock rate of return Case 1: -2% or 10% –(4 + or - 6) Case 2: 2% or 14% –(8 + or - 6) Case 3: 3% or 15% –(9 + or - 6) Bank account rate of return Case 1: 4% Case 2: 4% Case 3: 4%

Thus, risk averse people are willing to take on risk if they are paid for it This has implications for the prices on the market More risky assets should have a higher expected rate of return

Diversification A diversified portfolio is less risky than any single asset But some systematic risk will remain

Efficient Market Hypothesis stock prices change rapidly in response to new information, this eliminates profit opportunities quickly

Problems caused by separation of ownership from management asymmetric information –stockholders have less info than the managers creates moral hazard –example: wasteful use of corporate jet creates adverse selection –example: too many high-risk firms choose equity financing remedies: Profit sharing or hostile takeovers