exam 2, spring 2013 answer key

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

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NAME: ___________________________________

ACE 428 Commodity Futures & Options

Spring 2013

ANSWER KEY FOR Exam #2, Version A 113 Points Possible

There are 11 (eleven) 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 thesepages.

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 thecorrect order when you submit your completed exam.

* * * * *Short Answer Questions (25 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: The following exchange is from the Trading Places clip we viewed in classthe Wednesday before Spring Break:

President of the Exchange: Margin call, gentlemen. You know the rules, all accountsmust be settled at the end of the day, without exception.

Randolph Duke: You know perfectly well we do not have $394 million in cash!

President of Exchange: Oh, I am sorry. [To his assistant] Put the Dukes' seats on theExchange up for sale and seize all holdings and property of Mortimer and RandolphDuke.

Mortimer Duke: This is an outrage! I demand an investigation! A Duke has been sittingon this Exchange ever since it was founded!

[Randolph Duke collapses in shock]

A. What direction did the Dukes expect orange juice prices to move following the USDAreport? What was their market position long or short? (2 points)

Higher (up)

Long


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ACE 428 Exam #2A ANSWER KEYPage 2

B. What direction did orange juice prices actually move following the USDA report, andresulted in the margin call? (1 point)

Lower (down)

C. By receiving a margin call, were the Dukes trading futures or options? How do you knowthis? (2 points)

Futures

No margins or margin calls with long options

D.

When a margin call occurs, can the exchange actually sell a traders seat (exchangemembership) and seize a traders other assets to cover the shortfall, or is this just a case ofHollywood storytelling? (1 point)

Yes, the exchange can do all these things

QUESTION 2: When an option expires out of the money, what does the option buyer receive?Does the option buyer have a profit, a loss, or is it unclear? How much is the option buyers

profit or loss? (3 points)

Receives nothing

Loss

Premium paid at the outset

QUESTION 3: When an option expires in the money, what does the option seller receive?Does the option seller have a profit, a loss, or is it unclear? How much is the option sellers

profit or loss? (3 points)

Receives a losing futures position at the strike price

Unclear (depends on premium received versus loss on futures position)

Difference between the premium received and the loss on the futures position

assigned at exercise


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QUESTION 4: Answer the following questions on option premiums.

A. How would an option premium change (increase or decrease) if there is an increase involatility? Explain your answer in terms of the probability that the option will be exercised.How much would the premium change a lot or a little? Give an example of an option

trading strategy that would profit from an increase in volatility. (4 points)

Increase

More volatility means a greater chance that the option will move (deeper) in the

money and be exercised

A lot

Anything long premium

B. How would an option premium change (increase or decrease) if there is an increase ininterest rates? How much would the premium change a lot or a little? (2 points)

Decreases

A little

C. How would an option premium change (increase or decrease) if there is a decrease in thenumber of days to expiration? Explain your answer in terms of the probability that the optionwill be exercised. Give an example of an option trading strategy that would profit from adecrease in the time to expiration. (3 points)

Decrease

Fewer days to expiration means a lesser chance that the option will move

(deeper) in the money and be exercised

Anything short premium


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QUESTION 5: One of our homework assignments used linear regression to find the best way tohedge a commodity, even when the futures contract is for a different commodity than thecommodity being hedged.

A. What does the Hedge Ratio measure? What statistic from linear regression is used for the

Hedge Ratio? (2 points)

Number of futures contracts Quantity of cash commodity (measured in futures

contracts) OR Percentage of cash commodity covered by futures

Slope term (coefficient)

B. What does Hedging Effectiveness measure? What statistic from linear regression is used forHedging Effectiveness? (2 points)

Percentage of price risk eliminated by the hedge

Coefficient of variation (R-squared)

PROBLEM 1 (14 points)

On Friday, April 12, June crude oil futures settled at $91.61; the June $95 put option settled atpremium of $4.33 with a delta of -0.7201

A. Calculate the time value and intrinsic value. (2 points)

Intrinsic value = $3.39 = $95 - $91.61

Time value = $0.94 = $4.33 - $3.39

B. Is this option in-the-money, at-the-money, or out-of-the-money? Why? (2 points)

In the money

Strike price > Futures price; has intrinsic value

C. If you are long this option, would it make economic sense to exercise it now? Why or whynot? (2 points)

Yes

Has intrinsic value (in of the money)


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D. What is the probability that this option will expire in the money? (1 point)

.7201 or 72.01%

E. If the crude oil futures price goes up 10 cents per barrel, how much would the premium onthe option change? Which way would the premium change (up or down)? (2 points)

-.07201 or -7.2 cents

Goes down

F. What would be the delta of a June $95.00 call option? (1 point)

Delta = +.2799 = 1 ABS (-.7201), using [ABS (put delta) + call delta = 1]

G. How many June $95 put options (rounded to the nearest whole number) would be needed toobtain similar performance (within a narrow price range and short time frame) as 50 shortJune crude oil futures contracts? Should these put options be long or short? (2 points)

69 put options 69.4348 = -50 -.7201 = Number of futures Delta

Long options, because long puts are analogous to short futures

H. Suppose that on May 16 the day when the June options expire the June crude oil futuresprice is $93.00. What would be the premium for the June $95 put option at expiration? Howmuch time value erosion would have occurred since April 12? (2 points)

$2.00 = intrinsic value; time value at expiration = 0

$0.94 = all of the time value on April 12


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Show how you would create a synthetic long call for natural gas, selecting the futures andoptions you need from the following list:

Long futures at $4.38

Short futures at $4.38 Long $4.40 call at a premium of $0.12

Short $4.40 call at a premium of $0.12

Long $4.40 put at a premium of $0.15

Short $4.40 put at a premium of $0.15

A. Circle the two items from this list that you will use to create a synthetic long call. (2 points)

B. Complete the payoff table below. (25 points)

Futures

Price

Profit on

Futures

Position

Value of

Option

Position at

Expiration

Premium for

Option

Position

Profit on

Option

Position

Combined

Profit on

Futures &

Option

Positions

$4.20 -$0.18 +$0.20 -$0.15 +$0.05 -$0.13

$4.30 -$0.08 +$0.10 -$0.15 -$0.05 -$0.13

$4.40 +$0.02 $0 -$0.15 -$0.15 -$0.13

$4.50 +$0.12 $0 -$0.15 -$0.15 -$0.03

$4.60 +$0.22 $0 -$0.15 -$0.15 +$0.07

C. Use the data in the payoff table to plot a payoff diagram on the grid on the next page, with 3separate lines showing the profits at expiration for:

The natural gas futures position

The natural gas option position

The synthetic long call

You will not be graded on your artistic ability, but your payoff diagram should:

Show each line with the proper shape and drawn to scale (6 points)

Be properly labeled to show which axis is the profit and which axis is the underlyingfuture price (2 points)

Cover the range of future prices from $4.20 to $4.60 (1 point)


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PROBLEM 3 (4 points)Using the put-call parity formula, calculate the missing values in the table below:

Commodity Futures Call Premium Strike Price Put Premium

Apr Feeder Cattle 149.80 4.42 150.00 4.62

May Rice 1566.00 34.75 1600.00 68.75

Feb Butter 171.00 5.00 176.00 10.00

May Lumber 333.8 37.9 300.1 4.2

$0.20

$0.15

$0.10

$0.05

$0.00

$0.05

$0.10

$0.15

$0.20

$0.25

$4.20

$4.30

$4.40

$4.50

$4.60

Profit

FuturesPrice

Synthetic

Long

Call

SyntheticLongCall

LongCashat$4.28

Long$4.40Putat$0.15


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Earlier we looked at a jewelry manufacturer who buys gold and hedged those purchases withfutures. Now we want to compare the results from hedging with futures to the results fromhedging with options.

The jewelry manufacturer knows that it will need to buy a large quantity of gold during thesummer for making holiday gift items. The cash price in February, when it is making itspurchasing plans, is $1,520, and the manufacturer expects the price to move higher betweenFebruary and July. However, the jewelry manufacturer does not have the ability to buy the cashgold in February, so it hedges by buying July futures at a price of $1,520. When July arrives, theJuly futures price is $1,585 and the cash price is $1,585.

For simplicity, we will assume the basis is unchanged at zero. Here are the jewelrymanufacturers results using a futures hedge:

Date Cash Futures Basis

Feb Short at $1,520 Long July at $1,520 $0

July Long at $1,585 Short July at $1,585 $0

Gain/Loss -$65 +$65 $0

Net Price Paid for Gold= $1,520

A. Construct a hedge using a July $1,520 call option. The premium in February is $76 and thepremium in July is $66. (6 points)

Date Cash July $1520 Call

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

Feb Short at $1,520 ___ Long___ Call at $76

July Long at $1,585 ___Short___ Call at $66

Gain/Loss -$65 -$10

Net Price Paid for Gold = $1,595

(show your work)= $1,585 cash price in July + $10 option loss OR

= $1,520 cash price in Feb + $65 cash price increase from Feb to July + $10 option loss


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For the hedge using the call option:

1) Calculate the difference between the net price paid for gold with the call option hedge tothe price that the manufacturer would have paid in July without hedging. Did the calloption hedge make the manufacturer better off or worse off? (2 points)

$10 = $1,595 with call option hedge - $1,585 cash price in July

Worse off (by $10)

2) Use the steps below to calculate the change in intrinsic value on the call option betweenFebruary and July (4 points)

a)

Intrinsic value in February: $0

b)

Intrinsic value in July: $65 = $1,585 futures price - $1,520 strike price

c) Change in intrinsic value: $65

d) Is this a profit (+) or loss (-) to the hedger? Profit (+)

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

a) Time value in February: $76 = $76 - $0

b) Time value in July: $1 = $66 - $65

c) Change in time value: $75

d) Is this a profit (+) or loss (-) to the hedger? Loss (-)

4) Use your answers from Part 2 and Part 3 to explain the jewelry manufacturers call optionhedging results. (1 point)

Loss in time value > Gain in intrinsic value, so call option hedge wasnt effective


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B.Next, construct a hedge using a July $1,520 put option. The premium in February is $76 andthe premium in July is $1 (one dollar). (6 points)

Date Cash July $1520 Put

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

Feb Short at $1,520 ___ Short___ Put at $76

July Long at $1,585 ___Long___ Put at $1

Gain/Loss -$65 +$75

Net Price Paid for Gold = $1,510

(show your work)

= $1,585 cash price in July - $75 option gain OR= $1,520 cash price in Feb + $65 cash price increase from Feb to July - $75 option gain

For the hedge using the put option:

1) Calculate the difference between the net price paid for gold with the put option hedge tothe price that the manufacturer would have paid in July without hedging. Did the putoption hedge make the manufacturer better off or worse off? (2 points)

$75 = $1,510 with put option hedge - $1,585 cash price in July

Better off (by $75)

2) Use the steps below to calculate the change in intrinsic value on the put option betweenFebruary and July (4 points)

a) Intrinsic value in February: $0

b) Intrinsic value in July: $0

c)

Change in intrinsic value: $0

d) Is this a profit (+) or loss (-) to the hedger? Any answer OK


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3) Use the steps below to calculate the change in time value on the put option betweenFebruary and July: (4 points)

a) Time value in February: $76 = $76 - $0

b)

Time value in July: $1 = $66 - $65

c) Change in time value: $75

d) Is this a profit (+) or loss (-) to hedger: Profit (+)

5) Use your answers from Part 2 and Part 3 to explain the jewelry manufacturers put optionhedging results. (1 point)

No change in intrinsic value, but time value erosion benefits an option seller, so put

option hedge was effective

END OF EXAM #2

exam 2, spring 2013 answer key

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