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Capital Markets

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Two-year bonds: P = R/(1 i) (R F)/(1 i)2 ... for zero coupon bonds (R = 0) so that P = F/(1 i) n ... stock prices change rapidly in response to new information, ... – PowerPoint PPT presentation

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Title: Capital Markets


1
Capital Markets II
2
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)

3
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

4
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)

5
Compare rates of return
  • Bond
  • (5 100 - P)/P
  • Bank Account
  • .05

6
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

7
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

8
In general the price of a one year bond will be
determined by (R F - P)/P i
P (R F)/(1i)
9
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

10
Price of a 99-year zero at different interest
rates
11
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

12
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

13
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

14
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15
Diversification
  • A diversified portfolio is less risky than any
    single asset
  • But some systematic risk will remain

16
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17
Efficient Market Hypothesis
  • stock prices change rapidly in response to new
    information,
  • this eliminates profit opportunities quickly

18
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

19
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