Capital Markets

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Capital Markets II
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Bond Prices

• Was the price paid in the auction for Taylors
  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)

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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

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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)

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Compare rates of return

• Bond
• (5 100 - P)/P

• Bank Account
• .05

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Rates of return must be equal

• Thus
• (5 100 - P)/P .05
• 105 1.05P
• P 100

• Simply solve for the bond price P as shown on the
  left

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What if the interest rate at the bank changes?

• To 10 percent
• Now we have (5 100 - P)/P .10
• 105 (1 .10)P
• P 105/1.10
• P 95

• To 3 percent
• Now we have (5 100 - P)/P .03
• 105 (1 .03)P
• P 105/1.03
• P 102

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In general the price of a one year bond will be
determined by (R F - P)/P i
P (R F)/(1i)
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The same reasoning applies to longer maturity
bonds

• Two-year bonds
  P R/(1i) (RF)/(1i)2
• n-year bonds
  P R/(1i) R/(1i)2 R/(1i) 3
  (RF)/(1i) n
• for zero coupon bonds (R 0) so that P
  F/(1i) n

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Price of a 99-year zero at different interest
rates
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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

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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

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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

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Diversification

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

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Efficient Market Hypothesis

• stock prices change rapidly in response to new
  information,
• this eliminates profit opportunities quickly

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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

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