Chapter 15

							                                          Chapter 15
                   Arbitrage Pricing Theory, Option Pricing Theory,
                                    and Capital Budgeting
                                           Questions
15-1. As noted in Chapter 14, the set of assumptions necessary to justify CAPM are both
lengthy and unrealistic. In contrast, the basic assumptions about investor behavior necessary
to justify arbitrage pricing are that investors like wealth and dislike risk. The basic
assumption about markets is that markets are efficient in that two identical streams of benefits
cannot sell at different prices.
15-2. If there is only one factor and the portfolio with unitary sensitivity to that factor is the
market portfolio, then APT reduces to CAPM.
15-3. The only priced factor is linear relationship between security returns and returns for the
market portfolio.
15-4. There is not general agreement as to the priced factors. Factors that have been
identified include industrial production or return on the market portfolio, changes in the risk
premium, the slope of the yield curve, and unanticipated inflation.
15-5. The quantity of the analysis is a problem with this method. For example, 30
simultaneous equations need to be solved for a 30-year project.
15-6. a) Option: A contract giving the holder the right to buy or sell an asset for a
predetermined price.
b) Call option: An option to buy an asset.
c) Put option: An option to sell an asset.
d) European option: An option that can be exercised only on the expiration date.
e) American option: An option that can be exercised at any time prior to its expiration date.
f) Exercise: The buying and selling of an asset as provided for in the option contract.
g) Exercise price: The price at which the asset can be bought or sold, as stated in the option
contract.
h) Striking price: Same as exercise price.
i) Exercise date: The actual date on which the option is exercised.
15-7. Total risk determines how much the price of the underlying security might change
before the option expires. The value of an option is directly related to the amount by which
the price of the underlying asset might change.
15-8. A stock is considered to be a call option on the firm itself, because the stockholders can
either acquire the firm by paying off the debt or simply turn the firm over to the creditors if it
is worth less than the amount owed. Therefore, the bondholders can be viewed as having
purchased the firm and then selling an option on it.
15-9. Option pricing models treated in this book rest on the assumptions that the financial
markets are frictionless, with no transaction costs and with information freely available to all,
that there are no restrictions on short sales, that there are no dividends or cash distributions
prior to maturity, and that there are no opportunities to earn a risk-free rate of return above the
risk-free rate. The Black-Scholes model for European options is based on the additional
assumptions that the risk-free rate remains constant over time, that assets are traded
continuously, and that asset returns obey a stationary stochastic process over time which


                                                1
results in asset returns being lognormally distributed for any finite period. Of course, a
European option cannot be exercised until its expiration date.
15-10. The Black-Scholes model tends to underprice options on low-variance stocks and
overprice options on high-variance stocks.
15-11. Managers can be viewed as having an option, which pays off only if the company is
successful. If the payoff is of a fixed amount, managers will be discouraged from taking
risks. If managers are to have interests similar to those of shareholders, they can be given an
interest in equity rather than a fixed payoff so that the value of their option will closely
coincide with the value of the shareholders' investment.
15-12. a. The leasing of the minivan is like own a put option on the van. With a put option
you are allowed to sell the van to the writer (in this case the auto company) at the end of the
option (or lease in this case). An outright purchase does not have this right to sell. The risk
of a lower sale price in the used car market is passed to the writer of the option or lease (the
auto company in this case).
         b. This would be a put option.
         c. Since you would probably not be allowed to return the van until the end of the
lease, this would be similar to a European option. European option can only be exercised at
the end of the option life.
         d. From the customer's point of view, these leases were to their benefit. The reverse
is true for the auto company.

15-13. a. When you purchase a CMO you are buying a bond and simultaneously selling a
call option on this bond. If rates increase, you will lose value because of the fixed nature of
the bond. If rates decrease, you will lose because the investor will refinance and return the
principal which can only be reinvested at lower rates.
        b. These securities are probably inappropriate for the elderly unless the time is taken
to explain the embedded option and only then if the expected return compensates for the
additional risk.
        c. The selling of these securities to market participants who do not understand the
             embedded option would be considered unethical.
15-14. Translation risk is the risk that reported income will flutuate because of fluctuating
         exchange rates. Translation risk is the risk that actual cash flows will flutuate because
         of fluctuating exchange rates.
15-15. Currency futures can be used to eliminate rate risk for a known future need for
         currency.
         Currency options can be used to manage exchange rate risk when there is an uncertain
         future need for a currency.
         Swaps can be used when there are no option contracts available.
15-16. This can be a case where the manager is expending the shareholder’s money to reduce
            a balance sheet exposure that is not important from the shareholder’s perspective.




                                                2
                                               Problems

15-1. Ka=.06 + 1.5(.10 - .06) + .5(0.08 -.06)+.5(0.7 -.06)   + .75(.07 - .06)8
  = .06 + .06 + .01 + .02 + .0025 = 14.25%

Kb=.06 + .5(.10 - .06) + 2(.08 -.06) + 2(.07 - .06)
  + .25(.07 - .06)
 = .06 + .02 + .04 + .02 + .0025 = 14.25%

15-2. Factor 1
 1a + .5c + 0c = 1
 .5a + 756 + 1.25c = 0
   a +b + c     =1
Solving a = -1, b = 4, and c = -2

Factor 2
 1a + .5b + 0c = 0
.5a + .75b + 1.25 c = 1
a+b+c            =1
Solving, a = -1, b = 2, and c = 0

15-3. E(Rfactor 1) = -1(.12) + 4(.10) -2(.10) = 8%
E(Rfactor 2) -1(.12) + 2(.10) + 0     = 8%

15-4.       K = .06 + 1.5(.08 - .06) + -.5(.08 - .06) = 8%




                                                3