Investment Analysis & Portfolio Management
AD 717 OL
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.
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Investment Analysis & Portfolio Management AD 717 OLHomework E.docx
1. Investment Analysis & Portfolio Management
AD 717 OL
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
2. 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
3. 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%.
4. 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
5. 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:
