Homework Exercise 7 – Derivatives

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Homework
Exercise 7 – Derivatives

1) On June 21, 2011, the GE’s stock closed at
$18.81 per share. The accompanying table
lists the prices for GE’s exchange-traded options. Using this data, calculate the payoff and the
profit for each of the following September expiration options, assuming that at
the September expiration the value of
the stock was $17.72.

a) Call option X = $17

b) Put option x
= $17

c) Call option x = $19

d) Put option x
= $19

e) Call option x
= $15

f) Put option x
= $21

2. It is mid July. You believe that Walmart stock which is
currently priced at $53.00 will appreciate significantly over the next several
months. A long-term equity call option
(LEAPS) with an expiry in mid January and a strike price of $52.50 is available
at a price of $2.50. You have $10,600 to
invest. You consider 4 alternatives:

a) Use your entire amount of funds to buy the
stock outright

b) Use the entire amount to purchase the stock
on margin. Assume that the minimum
margin requirement is 50% and that you will pay 7% (annually) on borrowed
funds.

c)
Use the entire amount of funds to buy LEAPS call options with the January
expiry date.

d)
Buy options for 200 shares and use the
rest of the money to buy government bills paying 1% per year. (hence figure on
6 months of interest).

For
simplicity ignore any brokerage charges Calculate the net gain or loss from
each strategy as of mid January assuming that the price of stock is:

Gain / Loss from Investment in Walmart

Investment Strategy

Stock Price in Mid January

$45

$50

$55

$60

Stock
Outright

Stock
on Margin

All
Options

Options
& Bills

3) One of the financial instruments that
attracted so much hostile fire in the analysis of the recent financial crisis
were “Synthetic Collateralized Debt Obligations” (synthetic cdos) which used
“synthetic debt” as its collateral.
Describe how you could use a combination of risk free investments and
derivatives to create the same pay-off / risk profile as if you were holding
a corporate bond, say for IBM. Explain how the pay-off / risk profile is the
same (a) if the company remains afloat and pays all of its debt obligations on
time or (b) if the company defaults on its debt obligations.

4) A stock is currently priced at $50. The risk
free interest rate is 10% per year. What
is the value of a call option on the stock with a strike price of $45 due in one
year?

a) Using the Binomial valuation approach, assume
that at the end of one year the value of the stock could either have increased
to $60 or decreased to $40.

b) Using the Black-Scholes model, assume that
the annual volatility (standard deviation) of the stock price is 25%.

5) On June 29, 2010 the S&P 500 stood at
1308.44. The one year futures price on
the index was 1278.7. The 1 year risk
free rate was 0.238%. Using the
Spot-Futures Parity relationship, calculate the annualized expected dividend
yield from the S&P 500 Index.

6) Futures contracts for copper are traded on
the COMEX exchange. The standard
contract is 25000 pounds. The initial
margin is $5738 per contract and the maintenance margin is $4250 per
contract. The 6 month futures price is
$4.321 per pound. The spot price today
is $4.204. What will be the annualized rate of
return for an investor purchasing copper futures under the following spot
prices at maturity?

Spot Price at Maturity

$4.25

$4.30

$4.35

$4.40

Spot Value of 1 contract at Maturity

Futures price of 1 contract (today)

Net Gain / Loss

6 month rate of return

Annualized Rate of Return

7) Joan Tam, CFA, believes she has identified an arbitrage
opportunity for a commodity as indicated by the following information:

Current
Spot Price: $120

Futures
Price (1 Year): $125

Interest
Rate (1 Year): 8%

Initial
Margin to purchase Futures $7.50

a) Describe the strategy and transactions that
Joan should use to take advantage of this arbitrage opportunity.

b) Calculate the arbitrage profit

c) Verify the arbitrage profit by calculating the
initial cash flows (when the transactions are entered into) and the profits for
each of the spot prices at time T indicated below:

Initial Cash Flow

Spot Price at Time T

116

120

124

128

132


GE
Exchange Traded Options

.wsj.com/public/quotes/main.html?symbol=GE”>Gen El ( GE )

.wsj.com/mdc/public/page/2_3044-Opt_L_G-Opt_C_GEN_EL.html#priceftnt”>Underlying stock price*: 18.81

Expiration

Strike

Call

Put

Option Price (Last)

Volume

Open

Interest

Option Price (Last)

Volume

Open

Interest

Dec

10

0.08

217

3322

Sep

13

870

0.06

20

6070

Dec

13

0.15

8

2114

Jul

14

4.6

29

827

204

Jul

15

3.7

1

1

0.02

210

15799

Sep

15

4

1

1280

13893

Dec

15

4

1

409

0.3

380

3581

Jul

16

542

0.03

222

3347

Aug

16

597

0.12

191

1932

Sep

16

3.04

353

1919

0.2

375

78449

Dec

16

250

0.49

690

4915

Jul

17

1.95

86

2503

0.06

124

11300

Aug

17

2.08

25

1150

0.23

362

21499

Sep

17

2.18

349

4196

0.34

1089

29426

Dec

17

2.45

15

479

0.72

105

16755

Jul

18

0.99

3537

7192

0.17

11672

26979

Aug

18

1.3

626

4138

0.41

1773

12694

Sep

18

1.38

376

12832

0.58

2698

40944

Dec

18

1.79

120

2683

1.03

2594

10423

Jul

19

0.35

36899

61396

0.53

9103

32734

Aug

19

0.65

2031

16488

0.78

3856

21731

Sep

19

0.77

4565

25395

0.96

101

64748

Dec

19

1.22

274

7206

1.51

1046

13989

Jul

20

0.06

4781

22943

1.19

222

19283

Aug

20

0.25

4649

28705

1.47

15

17267

Sep

20

0.38

4856

31045

1.56

32

36015

Dec

20

0.76

962

11433

2.06

67

9845

Jul

21

0.01

169

25400

2.15

20

2592

Aug

21

0.08

348

10613

1990

Sep

21

0.15

786

24122

2.41

509

9623

Dec

21

0.45

2224

11789

2.87

1

1250

Jul

22

0.01

1318

9329

592

Aug

22

0.03

195

3487

3.18

1

1189

Dec

22

0.24

909

7256

948

Sep

22.5

0.04

417

34725

3.75

4

20599

Jul

23

3399

4.21

2

904

Aug

23

0.02

25

1712

441

Dec

23

0.12

590

12298

977

Sep

24

0.02

118

7820

1069

Dec

24

0.07

20

3177

5.35

1

1454

Aug

25

92

6.4

10

Sep

25

7223

6.36

186

1088

Dec

25

0.04

250

5511

602

Sep

30

2756

11.35

76

1240

*Underlying stock price represents listed exchange price only. It may
not match the composite closing price.

Source: Wall Street
Journal

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