# Answers – Problem Set 3

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```					                             Answers – Problem Set 3
(f02aps3mb – 10/11/02)

Problem 1a.         In general, a speculator earns a profit if he or she buys low and sells high. In
particular, the maximum profit attainable on a single December 2002 Mexican Peso contract
during intraday trading at the Chicago Mercantile Exchange on 10/2/02 would have been
\$
earned if the speculator had bought the contract at the daily low price of 0.09680             and
MXN
\$
sold the contract at the daily high price of 0.09845        . Since the standard size of a
MXN
Mexican Peso futures contract traded at the CME is MXN500,000, the total paid for the
           \$ 
Pesos bought would have been  0.09680               MXN500 ,000  \$48 ,400 , while the total
         MXN 
            \$ 
received for the Pesos sold would have been  0.09845              MXN500 ,000  \$49,225 .
        MXN 
Thus, the maximum profit earnable during October 2nd trading on a single December 2002
Mexican Peso contract was \$49,225 – \$48,400 = \$825.

Problem 1b.         Similarly, the maximum profit attainable on a single March 2003 Mexican
Peso contract during intraday trading at the Chicago Mercantile Exchange on 10/2/02
would have been earned if the speculator had bought the contract at the daily low price of
\$                                                              \$
0.09530          and sold the contract at the daily high price of 0.09585      . The total paid
MXN                                                             MXN
            \$ 
for the Pesos bought would have been  0.09530               MXN500 ,000  \$47,650 , and the
          MXN 
            \$ 
total received for the Pesos sold would have been  0.09585             MXN500 ,000  \$47,925 .
          MXN 
Thus, the maximum profit earnable during October 2nd trading on a single March 2003
Mexican Peso contract was \$47,925 – \$47,650 = \$275.

Problem 1c.            In order to achieve the maximum profit attainable on a single March 2003
Mexican Peso contract during intraday trading at the Chicago Mercantile Exchange on
10/2/02, a speculator would have had to sell, or go short, when the price was at its daily high
\$                                                                                 \$
of 0.09585              , and buy, or go long, when the price was at its daily low of 0.09530         .
MXN                                                                               MXN
Since the daily low occurred at the open, observe that it would have been necessary to
establish the long position at the open. And since the daily high occurred neither at the open nor
at the close, it must have occurred at some point after the open but prior to the close. Thus,
attainment of maximum profit would have required the long position established at the open
to be reversed with a subsequent short at the moment after the open but prior to the close when March
2003 Mexican Pesos reached their daily high. Consequently, we reveal as false the assertion
that the speculator needed to “go short at the open and reverse this position with a long at

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an appropriate point prior to the close” in order to earn maximum profit from a single
March 2003 Mexican Peso contract.

Problem 2a.        See the diagram illustrated on the page that follows.

Problem 2b.        See the diagram illustrated two pages hence.

Problem 2c.        See the diagram illustrated three pages hence.

Problem 2d.        See the diagram illustrated four pages hence.

Problem 2e.        See the diagram illustrated five pages hence.

Problem 2f.        As shown in the diagram illustrated for Problem 2d, the maximum
¢
possible loss incurred on the long December British Pound strap equals 6.12 . This equals
£
the sum of the prices of two calls and one put. Since the standard British Pound option
contract traded at the Chicago Mercantile Exchange has size £62,500, this maximum
        \$
possible loss translates to  0.0612 £62,500  \$3,825 . And as shown in the illustration for

        £
Problem 2e, the maximum possible loss incurred on the long December British Pound strip
¢
is 5.88 . This equals the sum of the prices of one call and two puts. Given a standard British
£
Pound option contract of size £62,500, this translates to a maximum total loss of
         \$                                                     ¢
 0.0588 £62,500  \$3,675 . So whether we express it on a
                                                                 basis or on a total \$ basis,
         £                                                     £
the maximum possible loss on the long December British Pound strap exceeds the
maximum possible loss on the long December British Pound strip. Thus, we reveal the
statement under scrutiny in this problem as true.

Problem 2g.       As shown in the diagram illustrated for Problem 2d, the window of
exchange rates within which the long December British Pound strap incurs losses is
¢
bounded below by an exchange rate of 149 .88 and bounded above by an exchange rate of
£
¢
159 .06 . Thus, the window of exchange rates within which the long December British
£
¢         ¢        ¢
Pound strap incurs losses is 159 .06  149 .88  9.18 wide.
£         £        £

Similarly, as shown in the diagram illustrated for Problem 2e, the window of exchange rates
within which the long December British Pound strip incurs losses is bounded below by an

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¢                                                   ¢
exchange rate of 153 .06 and bounded above by an exchange rate of 161 .88 . Thus, the
£                                                   £
window of exchange rates within which the long December British Pound strip incurs losses
¢         ¢       ¢
is 161 .88  153 .06  8.82 wide.
£         £       £

¢         ¢
Since 9.18     8.82 , the width of the window in which the long December British Pound
£         £
strap incurs losses exceeds the width of the window in which the long December British
Pound strip incurs losses, and we affirm the statement under scrutiny here as true.

Problem 2h.      To see where the long December British Pound straddle and the long
December British Pound strap are equally profitable, observe that

1 Call + 1 Put = 2 Calls + 1 Put 
0 = 1 Call

Thus, the exchange rate at which the long December British Pound straddle and the long
December British Pound strap are equally profitable is the exchange rate at which one long
December British Pound call earns zero. In the diagram illustrated for Problem 2a, the long
¢
December British Pound call breaks even at an exchange rate of 158 .12 . This result
£
reappears in the diagram shown on the page that follows, where the long December British
¢
Pound straddle intersects the long December British Pound strap at 158 .12 , the same
£
exchange rate where the long December British Pound call crosses the horizontal axis.

Problem 2i.     Similarly, to observe where the long December British Pound straddle and
the long December British Pound strip are equally profitable, observe that

1 Call + 1 Put = 1 Call + 2 Puts 
0 = 1 Put

Thus, the exchange rate at which the long December British Pound straddle and the long
December British Pound strip are equally profitable is the exchange rate at which one long
December British Pound put earns zero. In the diagram illustrated for Problem 2b, the long
¢
December British Pound put breaks even at an exchange rate of 154 .12 . This result
£
reappears in the diagram shown two pages hence, where the long December British Pound
¢
straddle intersects the long December British Pound strip at 154 .12 , the same exchange
£
rate where the long December British Pound put crosses the horizontal axis.

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