# Homework Exercise 7 – Derivatives

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Investment
Analysis & Portfolio Management

717 OL

Homework
Exercise 7 – Derivatives

1) On June 21, 2011, the GEâ€™s stock closed at
\$18.81 per share. The accompanying table
lists the prices for GEâ€™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:

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 â€œSynthetic Collateralized Debt Obligationsâ€ (synthetic cdos) which used
â€œsynthetic debtâ€ 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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