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Homework Assignment #1 – (150 points total) Econ 351 –Fall 2015 –PLEASE STAPLE, DUE, Friday 9/18/2015 AT THE
BEGINNING OF CLASS: NO LATE HWS ACCEPTED.
YOU MUST USE THIS AS A TEMPLATE – HIT ENTER TO MAKE SPACE FOR YOUR ANSWERS Please be a neat as
possible, especially with graphs and please show all work or points will be taken off.
1) (50 points total) Use the three tables below to answer the following questions
Table 1
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Table 2
Table 3
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a) (5 points) Suppose we play a long straddle by purchasing one 537.5 call option and one 537.5 put option at Table 1 and close both
positions on Table 2. Calculate the profit/loss AND rate of return.
COST: 983 + 1314 = $ 2,297
close: REV: 249 + 2538 = $2,787 profit = $490 return = 21.3%
b) (5 points) Suppose instead that we waited and closed at Table 3, calculate the profit/loss and rate of return.
COST: 983 + 1314 = $ 2,297
close: REV: 11 + 120 = $131 LOSS = $2,166 return = - 94%
c) (5 points) Why is your 537.5 call option so much cheaper in Table 3 as compared to Table 1? The word probability needs to be in
your answer.
The call in Table 3 is set to expire where in Table 1, it has more time to maturity and thus, has a much higher probability of getting
in the money. Note that the call is closer to the money in table 3 so that answer gets 100% off!
d) (5 points) Suppose your friend played a short straddle by writing one 537.5 call option and one 537.5 put option at Table 1 and
closed both positions on Table 2. Calculate the profit or loss. Does your answer relate to any of your answers above? What is this
principle referred to as? Explain.
REV: 983 + 1314 = $ 2,297 close: COST: 249 + 2538 = $2,787 LOSS = $490 YES - the answer is the opposite of the player of the
long straddle as in part a). This is what we call a zero sum game.
e) (5 points) Assuming the spot of Google is frozen at its value on Table 1 until expiration, plot the evolution of the premium on your
537.5 put starting from the conditions at Table 1 through expiration.
f) (25 points for a correct and completely labeled graph) We are now going to graph the profit functions for the long and short straddle
as above where we opened up the positions at Table 1. Identify the profit / loss for both players for one point, let's call it point B,
with the spot at expiration as it is in Table 2: spot = $510.66 (there are two points B's, one for the player of short straddle and one for
the player of long straddle). Be sure to include the math as to how you calculated the payoffs for each player (at Point B) and
prove that this is indeed a zero sum game! Be sure to label the break even points (there are two of them!). Also, be sure to label
which profit function represents the long straddle and which profit function represents the short straddle.
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MATH FOR POINT B. THE PUT IS $26.84 IN THE MONEY SO WE, PLAYING THE LONG STRADDLE, WILL MAKE A
PROFIT OF $2,684 MINUS $2,297 = 387. OUR FRIEND COLLECTED $2,297 WRITING BOTH OPTIONS BUT HAS TO BUY
BACK THE PUT FOR $2,684 FOR A LOSS OF $387.
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2. (50 points total)
a) (5 points) Suppose we play a strangle by buying a 542.5 call and a 527.5 put on Table 1 and close at Table 2. Calculate the profit or
loss AND rate of return.
COST: 801 + 848 = $ 1,649 Close Table 2 REV: 205 + 2,648 = $2, 853...... Profit = $1,204.... Return = 73%.
b) (25 points) We are now going to graph the profit functions for the strangle for both the buyer and writer of the strangle above where
both players opened up the positions at Table 1. We are only going to plot the profit / loss for both players for one point on each profit
function, let's call them points B, with the spot at expiration as it is in Table 2: spot = $510.66 (there are two points B's, one for buyer
of the strangle and one for the writer of the strangle). Be sure to include the math as to how you calculated the payoffs for each
player and prove that this is indeed a zero sum game! Be sure to label the break even points (there are two of them!).
Player of long strangle - TC = 801 + 848 = $1,649; Exercise put - buy low @ spot = 100 x 510.66 = $51,066
TC = $52,715 TR: Sell @ strike = 100 x 527.50 = 52,750....profit = $35
Player of short strangle - collect premiums = $1,649 - honor put by buying High @ strike - costs = 100 x 527.50 = $52,750
Sell low at spot: 100 x 510.66 = $51,066 TR = $1,649 + $51,066 = $52,715 Total Costs = $52,750 LOSS = $35
c) (5 points) There are two breakeven points on your graph for the player of the long strangle. Pick the larger of the two and explain
exactly how this is indeed the breakeven point assuming importantly that the player of the long strangle is going to exercise the
option that is in the money. Please go through the total costs and total revenue like we did in class numerous times.
FOR LONG STRANGLE: COST OF OPTIONS: $1,649 - EXERCISE CALL (BUY LOW @ STRIKE = 100 X $542.5 = $54,250
TC = $1,649 + $54,250 = $55,899 TR : SELL @ SPOT = 100 X 558.99 = $55,899
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d) (5 points) Similar to your answer in c) above, using the same breakeven point, assuming again that the player of the long strangle is
going to exercise the option that is in the money at this breakeven point, explain how the player of the short strangle is also going to
breakeven. Please go through the total costs and revenue as you did above, but this time, for the player of the short strangle.
FOR SHORT STRANGLE: COLLECT PREMIUMS: $1,649 - BUY HIGH AT SPOT = 100 X $558.99 = $55,899
HONOR CALL BY SELLING @ STRIKE = 100 X $542.50 = $54,250 TR = $54,250 + $1,649 - $55,899
e) (10 points) The Table below is from September 12, 2015 that contains information about calls and puts that have already expired
(they expired on 9/11). The ‘last’ columns for all the 8 options are wrong. Please enter the correct last sale price to the left of the
existing and wrong last sale price for all 8 options (in parentheses). Note, the spot at expiration for NFLX = $97.51.
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3) (50 points total)
a) (5 points) Suppose you are bearish on Google and you decide to short 100 shares of Google at Table 1 and close (cover) your short
position at Table 2. Calculate your profit or loss showing all work.
COLLECT 100 X $532.21 = $53,521 BUY BACK LOW @ $ 510.66 PROFIT = $53,521 - $51,066 = $2,455
b) (5 points) Suppose you are bearish on Google and you decide to buy ten 537.5 puts at Table 1 and close your position at Table 2.
Calculate your profit or loss and rate of return.
10 X 1314 = $13,140 SELL TABLE 2: 10 X 2528 = $25,380 PROFIT = $12,240: return = 93.15%
c) (5 points) Suppose you are bearish on Google and you decide to write (sell) 10 537.5 calls at Table 1 and close your position at
Table 2. Calculate your profit or loss showing all work and rate of return.
COLLECT 10 X 983 = $9,830 BUY BACK 10 X 249 = $2,490 PROFIT = $7,340
d) (10 points) In the space below, graph the profit function of the ten 537.5 put options assuming you purchased them at Table 1. In
this case we only consider one scenario and that is that the spot of Google at expiration is as it is at Table 2. Label this as point B on
your diagram. On your diagram make sure you include the breakeven point along with identifying the in, at, and out of money areas
on your graph.
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e) (10 points) In the space below, graph the profit function of the ten 537.5 call options that you wrote assuming that you wrote them
at Table 1. In this case we only consider one scenario and that is that the spot of Google at expiration is as it is at Table 2. Label this as
point B on your diagram. On your diagram make sure you include the breakeven point.
f) (5 points) Suppose you played a short straddle on Google by writing one 537.5 call and one 537.5 put at
Table 1 and close at Table 3. Calculate your profit or loss.
COLLECT 983 + 1314 = 2297 BUY BACK 11 + 120 = 131: PROFIT = $2,166
g) (10 points) Suppose that someone with a really good 'crystal ball' told you that the spot price of Google was
going to stay as it is at Table 3 until expiration. Would you be better off closing as you did in part f) above or
would it be better to wait until expiration and close your short straddle then. Please be very specific with
numbers and the intuition. This question is worth 10 points!
THE CALL THAT IS SELLING FOR $11 IN TABLE 3 IS OUT OF MONEY SO IT WILL BE WORTHLESS
IF WE WAIT - THE PUT IS $1.14 IN THE MONEY SO IT WILL BE WORTH EXACTLY $114 AT
EXPIRATION.
IF WE WAIT, WE SAVE $11 ON CALL AND $6 ON PUT - PROFIT $17 HIGHER = $2,183
INTUITION - IF WE FREEZE THE SPOT UNTIL EXPIRATION ALL IS GREAT BECAUSE WE
COLLECT WHATEVER TERM PREMIUM THERE IS IN THE CALL ($11) AND THE PUT ($6).
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