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					Some Answers & Explanations

            Test#2-A
          Winter 2001
    FINC434 - Prof: David Eagle
            (a) Exercising Now:
                 Time 0                          time 0        tax basis
                                   Price #shares tax situation              cash flow
                  current              $6 85,000 $510,000          $510,000
                  exercise price       $3 85,000 $255,000                    ($255,000)
                  taxable income @ 35%              $255,000
                  less taxes                        ($89,250)                 ($89,250)


Problem 1         Time 2
                                                    $165,750                 ($344,250)




                                     Price
                  proceeds from sale     16      85,000 $1,360,000                      $1,360,000
                  less tax basis                         ($510,000)
                  capital gains @ 20%                     $850,000
                  less taxes                             ($170,000)                      ($170,000)
                                                          $680,000                      $1,190,000

                  profit on investment                                                   $845,750 (ANSWER to part (a)

            (b) Exercising in two years:

                  Time 2
                                       Price
                  proceeds from sale $16         85,000 $1,360,000
                  exercise price           $3    85,000 $255,000
                  taxable income @ 35%                  $1,105,000
                  less taxes                             ($386,750)
                  profit on investment                    $718,250 = cash flow at time 2              (ANSWER to part (b)

            (c) NPV ( exercising now)
                 relevant discount rate =              9%

                                                time      cash flows PV(cash flows)
                                                        0 ($344,250) $ (344,250)
                                                        2 $1,190,000 $ 1,001,599
                                                                     $   657,349 = NPV                (ANSWER to part (c)



            (d) NPV (exercising two years from now)
                 relevant discount rate =       5% (when compared to option of exercising now)

                                                time        cash flows PV(cash flows)
                                                        2     $718,250 $   651,474
                                                                       $   651,474

            (e) Exercising now (but just barely)

            (f)   The risk of exercising now may be less than the 9% rrr indicates because
                  the company may let us rescind our stock purchase.
           Problem 6

           interest  principal total
Tranch 1      $7,215 $ 13,355 $20,570
Tranch 2      $7,215              $7,215
Tranch 3      $7,215              $7,215
Z Tranch                              $0
                                 $35,000
              Question 7
The appraisal value would have to be less
than the cost of the house for this not to be a
conforming loan.
                         Question 8


                     PV       because the discount rate is higher
       r

                     prepayments                 duration                   PV

Since the value of the PO is the present value of the future principal
payments, its value will go up. Note: as long as there is no default, the
PO will receive the same amount of principal payments. It is just a
question of when thoses payments will come and what the discount
rate will be that we should use to compute PV.
                  Question 9
If the market interest rate increases from 7.3% to 10%, the
prepayments on the 7% fixed-rate mortgages will decrease.
Prepayments from refinancing will almost disappear
because homeowners would be refinancing with higher
interest rates. Some prepayments will nevertheless
continue because some people will still be selling their
homes. However, people considering selling their homes
and moving up to a bigger home will become more
reluctant to do so, because they would be replacing their
7% mortgage with a 10% one.
                  Problem 10
When the market interest rate decreases
from 5.5% to 4.7%, the prepayment of 7%
fixed-rate mortgages will increase because
more people will choose to refinance their
mortgages at the lower rate.
Note: The payments that people are required to make on
these fixed-rate mortgages stays the same unless the
prepay. As a result, the lower market interest rate does not
decrease people’s monthly payment unless they
refinance..
             Essay #11
See Quiz #9 and Chapter 9 in the Crash
Book.
                                  Question 12.
                                                    (c) The futures sold will result in a $15,750 profit.
         (a) buy stock and sell                            (1275-1212)*250
         stock index futures. For                      The stock bought will result in an $8750 loss.
         each future contract they                         (1212-1247)*250
         sell at 1275, they should                     The overall profit will be $7000.
         buy $311,750 worth of                             (15,750-8750)
         the stock in the S&P500
         (1247*250)                                 (d) The futures sold will result in a $8250 loss.
                                                           (1275-1308)*250
(b) The futures sold will result in a $1250 loss.      The stock bought will result in an $15,250 profit.
       (1275-1280)*250                                     (1308-1247)*250
   The stock bought will result in an $8250 profit.    The overall profit will be $7000.
       (1280-1247)*250                                     (15,250-8250)
   The overall profit will be $7000.
      (8250-1250)

          Note that the expiration value of S&P 500 stock index futures contract is
          now based on the opening S&P 500 on expiration day, not the closing.
            Question 13
See Chapter 7 in the Crash Book
Remember that index arbitrage is a subset
of program trading, but it does not mean the
same as program trading.


       Question 14: D
                      Question 15
• Suppose that there would be more hedgers wanting to buy T-bond futures
  than hedgers wanting to sell T-bond futures if the futures price of the T-
  bond equaled the expected price of the T-bond at expiration. Therefore,
  in order to induce speculators to fill the gap, the futures price would need
  to be greater than the expected expiration price of the T-bond. As the
  expiration of this futures contract approaches, the difference between the
  futures prices and the expected price at expiration would diminish. On
  the other hand, suppose instead that there would be more hedgers wanting
  to sell T-bond futures than hedgers wanting to buy T-bond futures if the
  futures price equaled the expected price of the T-bond at expiration.
  Therefore, in order to induce speculators to fill the gap, the futures price
  would need to be less than the expected expiration price of the T-Bond.
  As the expiration of this futures contract approaches, the difference
  between the futures prices and the expected price at expiration would
  diminish.
            Question 16
According to Van Horne, interest rate swaps
are marked to market now.
                          Question 17
Buying a stock index futures contract at 1300 is the same as buying $325,000 worth of
stock. If the S&P 500 increases, you will gain the same whether you bought the SIF or
the stock. For example, if the S&P 500 increases to 1367, then the stock should now be
worth $341,750, which is a gain of $16,750. If you had bought stock index futures your
cash settlement would be $16,750.

On the other hand, if the S&P 500 decreases you will lose the same regardless whether
you bought stock index futures or the stock. For example, if the S&P 500 decreases to
1175, then the stock should now be worth $293,750 which is a loss of $31,250. This is
also the loss you would get if you had bought SIF.

Selling a stock index futures contract at 1300 is equivalent to selling $325,000 worth of
stock short. If the S&P 500 increases, you will lose money regardless whether you sold
stock index futures or stock. For example if the S&P 500 increases to 1367, the short
seller of stock would lose $16,750 and so would the seller of the futures contract.

On the other hand, if the S&P 500 decreases you will gain regardless whether you sold
stock index futures or stock. For example, if the S&P 500 decreases to 1175, the short
seller of stock will gain $31,250 and so will the seller of the futures contract.
                       Question 18
            $20                                C

          $15                                    B

          $10
           $5
                                                A
                  80    90   100   110   120   market price
           -$5                                  at expiration

         -$10
         -$15
          -$20



buying stock and buying stock index futures also have profit-
loss graphs like C.
This is the basis for put-call parity (See Appendix A of
Chapter 10 in Van Horne).

				
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