exam 2, fall 2013 answer key

8/10/2019 Exam 2, Fall 2013 Answer Key

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NAME: ___________________________________

ACE 428 Commodity Futures & Options

Fall 2013

ANSWER KEY FOR Exam #2, Versions A/C/E 120 Points Possible

There are 12 (twelve) pages in this exam make sure you have all the pages before you begin.

Write your name at the top of this page

Write your answers in the spaces provided below each question.

If you need additional room for calculations or other work, you can use the back side of these

pages.

Feel free to draw pictures or diagrams to help explain or think about your answers.

If you take apart this exam booklet, be sure to re-assemble and staple it with the pages in the

correct order when you submit your completed exam.

* * * * *

Short Answer Questions (17 points total)

Please answer the following questions clearly and concisely. A word or phrase is OK if that isall it takes to answer the question. If you provide a longer answer, only the first 2 sentences ofyour answer for each part of the question will be graded.

QUESTION 1 (3 points)

Name 3 of the 4 components of time value.

ANY 3 of the following:

Time to expiration

Volatility

Distance between strike price and market price

Interest rates

QUESTION 2 (1 point)

What is the maximum profit on any short option position?

Premium (received at the beginning)


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ACE 428 Exam #2A/C/E ANSWER KEYPage 2


What is the maximum profit on any long option position?

Option ITM; change in premium between purchase and sale/exercise/expiration

OR

Option ITM; gain in intrinsic value minus loss of time valueOR

Unlimited for long call; finite for long put because futures price cant go below zero

(may be other correct answers)


As the market price moves closer to the strike price of an in-the-money option, what happens tothe premium (all other things constant)?

Premium decreases (because option is moving out of the money)


What would be an appropriate trading strategy if you expect volatility to decrease?

Anything short volatility (short premium) short put, short call, etc.Short straddle

Short strangle


Suppose that the futures price closed limit-down, but at the close of trading the premium for a$150 put is $4.62 and the premium for a $150 call is $4.42. If there had not been any daily price

limits, what would have been the underlying futures price?

Futures price = Call premium Put premium + Strike

= $4.42 $4.62 + $150 = $0.20 + $150 = $149.80


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Name 4 ways that swaps differed from futures prior to Dodd-Frank.

ANY 4 of the following:

OTC, not exchange traded

Customized, not standardized Always cash settled, not physically

delivered

No regular settlements or mark-to-

market

No margins or margin calls

Not fungible

Not regulated No price transparency

No netting out of positions

No clearing house or recording agency

(may be other correct answers)


Suppose that a put option has a delta of -.678. Use this information to answer the following 4questions:

a)

What is the probability that the option will expire worthless?

.322 = 1 ABS(-.678)

b) If the underlying futures price changes by $1.00, how much would the put premium change?

$.678 = .678 x $1.00

c) If you use these put options in a hedge that requires 500 short futures contracts, how manyoptions would you need to buy (rounded to the nearest whole option contract)?

737 = 500 (.678)

d)

What is the delta of a call option with the same strike price as this put option?

+.322 = 1 ABS (-.678)


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Suppose that the Federal Reserve announces a change in policy that will allow interest rates torise. What will this do to option premiums?

Decrease option premiums (inverse relationship)

PROBLEM 1 (46 points)

Note: This is a two-part problem. Both parts use the information provided in the box

below. However, the answers for Part A do not depend on the answers for Part B and the

answers for Part B do not depend on the answers for Part B.

* * * * *

Suppose you are a candy manufacturer and need to manage the price you pay for sugar, which isan important ingredient and your biggest expense. Your board of directors wont let you gounhedged, so you always have used futures contracts for your hedges. Last winter you learnedthat there is a worldwide oversupply of sugar, and because this oversupply could drive down theprice of sugar you decide that hedging with options instead of futures might be a good idea.Since this is your first time using options, you decide to run an experiment and try severaldifferent hedging strategies. You run this experiment for 8 months, from February 1 to October1, using October futures and options contracts.

You use a standard futures hedge as the experiments control or benchmark against which all

option hedging result will be compared. Your basis is zero, and between February 1 andOctober 1 prices fell from 23 cents to 17 cents. Here are your futures hedging results:

Date Cash Futures Basis

Feb [Short at 20 cents] Long October at 20 cents $0

Oct Long at 17 cents Short October at 17 cents $0

Gain/Loss +3 cents -3 cents $0

Net Price Paid for Sugar = 20 cents

Two of the option hedges you use in your experiment are an at-the-money put option and an at-the-money call option, each with a 20-cent strike price.


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A. Construct a hedge using an October 20-cent put option. The premium in February is 1.55cents and the premium in October is 3.15 cents. (4 points)

Date Cash October 20-cent Put

Long or Short? Price? Long or Short? Premium?

Feb [Short at 20 cents] ___ Short___ Put at 1.55 cents

Oct Long at 17 cents ___Long___ Put at 3.15 cents

Gain/Loss +3.00 cents -1.60 cents

Net Price Paid for Sugar = 18.60 cents = 17 cents cash + 1.60 cents option loss

(show your work)

1) Calculate the difference between the net price paid for sugar with the put option hedgeand the net price paid for sugar with the futures hedge (Hint: See the information in thebox above), and write that difference in the space below. Compared with the futureshedge, did the put option hedge make you better off or worse off? What type of cashprice trend would have caused the put option hedge to give its best results? (3 points)

1.40 cents = 20 cents with futures hedge 18.60 cents with put option hedge

Better off (by 1.40 cents)

Stable or Rising prices (put option would have expired worthless and seller wouldhave kept the full premium)

2) You also are interested in knowing the sensitivity of your put option hedging results tochanging sugar prices. Looking back, if the board of directors had allowed you to gounhedged you would have had a zero gain/loss on the futures/options side of the hedge.You also know that the standard futures hedge had a 3-cent loss on the futures/optionsside of the hedge. Using these results as the best-case and worst-case scenarios:

a.

What put premium and what futures price at expiration would have given you a zerogain/loss on the option side of your put option hedge, so that you would have realizedthe full 3-cent gain on the cash side? (2 points)

For zero gain/loss, need October premium on put = 1.55 cents

20-cent strike 1.55 cents = 18.45 cents


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b. What put premium and what futures price at expiration would have given you a 3-cent loss on the option side of your put option hedge, so that you would have lost theentire 3-cent gain on the cash side? (2 points)

For 3-cent loss, need October premium on put = 1.55 + 3.00 = 4.55 cents

20-cent strike 4.55 cents = 15.45 cents

3) Use the steps below to calculate the change in intrinsic value on your put option positionbetween February and October (5 points)

a. Intrinsic value in February: 0 (at-the-money so there is no intrinsic value)

b. Intrinsic value in October: 3 cents = 20 cents strike 17 cents futures

c. Change in intrinsic value: 3 cents

d.

Is this a profit (+) or loss (-) to you as the hedger? Explain your answer.

Loss (-)

Sold option at 0 intrinsic value and bought option at 3 cents

Option sellers dont benefit from gain in intrinsic value

(other answers possible)

4)

Use the steps below to calculate the change in time value on your put option positionbetween February and October: (5 points)

a. Time value in February: 1.55 cents = 1.55 premium 0 intrinsic value

b. Time value in October: 0.15 cents = 3.15 premium 3 intrinsic value


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c.

Change in time value: 1.40 cents

d.

Is this a profit (+) or loss (-) to you as the hedger? Explain your answer

Profit (+)

Sold option at 1.55 cents time value and bought at 0.15

Option sellers benefit from time value erosion


5)

Use your answers from Section 3) and Section 4) above to explain your put optionhedging results. (1 point)

Losses from change in intrinsic value (-3 cents) > gains from change in time value

(+1.40 cents)

B.Next, construct a hedge using an October 20-cent call option. The premium in February is1.06 cents and the premium in October is 0.01 cents. (3 points)

Date Cash October 20-cent Call

Long or Short? Price? Long or Short? Premium?

Feb [Short at 20 cents] ___ Long___ Call at 1.06 cents

Oct Long at 17 cents ___Short___ Call at 0.01 cents

Gain/Loss +3.00 cents -1.05 cents

Net Price Paid for Sugar = 18.05 cents = 17 cents cash + 1.05 cents option loss

(show your work)


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1) Calculate the difference between the net price paid for sugar with the call option hedgeand the net price paid for sugar with the futures hedge (Hint: See the information in thebox above), and write that difference in the space below. Compared with the futureshedge, did the call option hedge make you better off or worse off? What type of cashprice trend would have caused the call option hedge to give its best results? (3 points)

1.95 cents = 20 cents with futures hedge 18.05 cents with put option hedge

Better off (by 1.95 cents)

Rising prices (call option would have moved into the money)

2)

You also are interested in knowing the sensitivity of your call option hedging results tochanging sugar prices. Looking back, if the board of directors had allowed you to go

unhedged you would have had zero gain/loss on the futures/options side of the hedge.You also know that the standard futures hedge had a 3-cent loss on the futures/optionsside of the hedge. Using these results as the best-case and worst-case scenarios:

a. What call premium and what futures price at expiration would have given you a zerogain/loss on the option side of your call option hedge, so that you would have realizedthe full 3-cent gain on the cash side? (2 points)

For zero gain/loss, need October premium on put = 1.06 cents

20-cent strike + 1.06 cents = 21.06 cents

b. What call premium and what futures price at expiration would have given you a 3-cent loss on the option side of your call option hedge, so that you would have lost theentire 3-cent gain on the cash side? (2 points)

For 3-cent loss, need October premium on put = 1.06 + 3.00 = 4.06 cents

20-cent strike + 4.06 cents = 24.06 cents


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3) Use the steps below to calculate the change in intrinsic value on your call option positionbetween February and October (3 points)

a) Intrinsic value in February: 0 (at-the-money so there is no intrinsic value)

b) Intrinsic value in October: 0 (out-of-the-money so there is no intrinsic value)

c) Change in intrinsic value: 0 cents

4) Use the steps below to calculate the change in time value on the call option betweenFebruary and October: (5 points)

a)

Time value in February: 1.06 cents = 1.06 premium 0 intrinsic value

b) Time value in October: 0.01 cents = 0.01 premium 0 intrinsic value

c) Change in time value: 1.05 cents

d) Is this a profit (+) or loss (-) to you as the hedger? Explain your answer

Loss (-)

Bought option at 1.06 cents time value and sold at 0.01 cents time value

Option buyers dont benefit from time value erosion


5)

Use your answers from Section 3) and Section 4) above to explain your call optionhedging results. (1 point)

Option losses entirely due to change in time value (-1.05 cents)


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Suppose that you decide to speculate using one of the option spreads that we discussed in class.You expect December live cattle futures will move lower in the next few weeks from the currentlevel of $133, so you decide to use a bear call spread involving the purchase of a $135 call at apremium of $0.30 and the sale of a $131 call at a premium of $2.70.

A. Complete the payoff table below (25 points)

Futures

Price

Gross

Profit on

$135 Call

Premium

for

$135 Call

Net

Profit on

$135 Call

Gross

Profit on

$131 Call

Premium

for

$131 Call

Net

Profit on

$131 Call

Total

Profit on

Bear Call

Spread

$129 0 -$0.30 -$0.30 0 +$2.70 +$2.70 +$2.40

$131 0 -$0.30 -$0.30 0 +$2.70 +$2.70 +$2.40

$133 0 -$0.30 -$0.30 -$2 +$2.70 +$0.70 -$0.40$135 0 -$0.30 -$0.30 -$4 +$2.70 -$1.30 -$1.60

$137 +$2 -$0.30 +$1.70 -$6 +$2.70 -$3.30 -$1.60

B. Use the data in the payoff table to plot a payoff diagram on the grid on the next page, with 3separate lines showing:

The net profits on the $135 call

The net profits on the $131 call, and

The total profit on the bear call spread

You will not be graded on your artistic ability, but your payoff diagram should show eachline with the proper shape and drawn to scale over a range of futures prices from $129 to$137 and a range of profits from -$4 to +$4. (3 points).

C. December live cattle options expire in approximately 2 weeks, on December 6. Calculate thetime value today for the $135 call option, and explain how you obtained this answer. (2points)

$0.30

Out of the money (no intrinsic value), so premium is all time value


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D. Suppose the December futures price remains at $133. What will be the premium for the$131 call option at expiration? How much time value erosion will have occurred betweennow and then? (2 points)

$2 (the intrinsic value)

$2.70 - $2 intrinsic value = $0.70

$4.00

$3.00

$2.00

$1.00

$0.00

$1.00

$2.00

$3.00

$4.00

$129 $131 $133 $135 $137


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In our Homework #6 trading exercise at the Margolis Lab, we saw how a refinery can influenceits profit margin by managing the price of the input (crude oil) and the price of the outputs(gasoline and heating oil). We also saw in class how cash positions can be substituted for futurespositions and combined with options to create ceilings and floors on profits.

Suppose that you are responsible for the pricing and risk management on all gasoline producedby a refinery; the crude oil and heating oil are handled by other traders. At current pricerelationships, the refinery needs $2.60 to break even on gasoline; the market price is currently$2.66. You are concerned about the losses that would occur if the price turns lower, but youdont want to miss out on better profits if the price moves higher. You decide to combine therefiners cash gasoline position with a gasoline option and create a synthetic cash-option positionthat puts a floor under gasoline profits.

Your manager has given you permission to use the following December gasoline options, all ofwhich have a premium of $0.04:

Long $2.66 Call

Short $2.66 Call

Long $2.66 Put

Short $2.66 Put

First, circle the option you will use to put a floor under the refinerys gasoline profits. (1 point)

Then complete the table below to show the refinerys profits at expiration using a synthetic floor.(24 points)

Gasoline

Price

Gross Profit

on Option

Option

Premium

Net Profit on

Option

RefineryProfit Based

on Cash

Gasoline

Price

Refinery

Profit With

Synthetic

Floor

$2.54 .12 -.04 .08 -.06 .02

$2.58 .08 -.04 .04 -.02 .02

$2.62 .04 -.04 .00 .02 .02

$2.66 .00 -.04 -.04 .06 .02

$2.70 .00 -.04 -.04 .10 .06

$2.74 .00 -.04 -.04 .14 .10

END OF EXAM 2

exam 2, fall 2013 answer key

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