# Capital Markets - PowerPoint PPT Presentation

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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
• 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