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An investor makes the following transactions in calls on a stock: (1) buys one call with a premium of $3.50 and exercise price of $20, (2) buys one call with a premium of $1.00 and exercise price of $25, and (3) sells two calls with a premium of $2.00 each and an exercise price of $22.50. What is (are) the breakeven price(s)?

A) $21 only.

B) $21 and $26.

C) $20.50 and $24.50.

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The transaction describes a butterfly spread. The total amount spent on purchasing the calls was $3.50 + $1.00 = $4.50 and the total amount received from the sale of the calls was $2 + $2 = $4 so the investor is - $.50 from the purchase and sale of the calls. The first exercise price on one of the calls purchased is $20 so the stock price would have to go up to $20.50 to reach the first breakeven point. At $22.50, the two written calls and the purchased call with the higher strike price will all expire worthless, while the call with the strike price of $20 will be exercised for a profit of $2.50. The total transaction will result in a profit of (+$2.50 + 4.00 - 4.50 = 2). The second breakeven price is $24.50. At this price, the two written calls will breakeven ($2 loss + $2 premium = 0 for each call), the call with the $20 strike price will be exercised for a profit of $1.00 ($4.50 gain - $3.50 premium), and the call with the $25 strike price will expire worthless, resulting in the loss of the $1.00 premium. At a price of $24.50, the total of the transactions will be zero (+$4.00 – 4.00 + 1.00 – 1.00 = 0).

optiix

Dennis Austin works for O’Reilly Capital Management and manages endowments and trusts for large clients.
The fund invests most of its portfolio in S&P 500 stocks, keeping some cash to facilitate purchases and withdrawals.
The fund’s performance has been quite volatile, losing over 20 percent last year but reporting gains ranging from 5 percent to 35 percent over the previous five years.
O’Reilly’s clients have many needs, goals, and objectives, and Austin is called upon to design investment strategies for their clients. Austin is convinced that the best way to deliver performance is to, whenever possible, combine the fund’s stock portfolio with option positions on equity.

Given the following scenario:

• Performance to Date: Up 3%

• Client Objective: Stay positive

• Austin's scenario: Low stock price volatility between now and end of year.

Which is the best option strategy to meet the client's objective?

A) Bull call.

B) Protective put.

C) Long butterfly.

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Long butterfly is the choice as this combination produces gains should stock prices not move either up or down, while not producing much in loss if prices are volatile. None of the other positions produce gains should stock prices not move much. The protective put guards against falling prices, the bull call limits losses and gains should prices move, and the 2:1 ratio spread gains should prices move up.

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Given the following scenario:

• Performance to Date: Up 16%

• Client Objective: Earn at least 15%

• Austin's scenario: Good chance of large gains or large losses between now and end of year.

Which is the best option strategy to meet the client's objective?

A) Long butterfly.

B) Short straddle.

C) Long straddle.

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Long straddle produces gains if prices move up or down, and limited losses if prices do not move. Short straddle produces significant losses if prices move significantly up or down. Long Butterfly also produces losses should prices move either up or down. The condor is similar to the long butterfly, although the gains for no movement are not as great.

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Given the following scenario:

• Performance to Date: Up 16%

• Client Objective: Earn at least 15%

• Austin's scenario: Good chance of large losses between now and end of year.

Which is the best option strategy to meet the client's objective?

A) Long put options.

B) Short call options.

C) Long call options.

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Long put positions gain when stock prices fall and produce very limited losses if prices instead rise. Short calls also gain when stock prices fall but create losses if prices instead rise. The other two positions will not protect the portfolio should prices fall.

optiix

Assume that the current price of a stock is $100. A call option on that stock with an exercise price of $97 costs $7. A call option on the stock with the same expiration and an exercise price of $103 costs $3. Using these options what is the profit for a long bull spread if the stock price at expiration of the options is equal to $110?

A) -$2.

B) $2.

C) $6.

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The buyer of a bull spread buys the call with an exercise price below the current stock price and sells the call option with an exercise price above the stock price. Therefore, for a stock price of $110 at expiration of the options, he gets a payoff $13 from his long position and a payoff of -$7 from his short position for a net payoff of $6. The cost of the strategy is $4. Hence the profit is equal to $2.

optiix

Which of the following best explains put-call parity?

A) No arbitrage requires that using any three of the four instruments (stock, call, put, bond) the fourth can be synthetically replicated.

B) No arbitrage requires that only the underlying stock can be synthetically replicated using at the money call and put options and a zero coupon bond with a face value equal to the strike price of the options.

C) A stock can be replicated using any call option, put option and bond.

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A portfolio of the three instruments will have the identical profit and loss pattern as the fourth instrument and therefore the same value by no arbitrage. So the fourth security can be synthetically replicated using the remaining three.

optiix

In 30 days, a firm wishes to borrow $15 million for 90 days. The borrowing rate is LIBOR plus 250 basis points. The current LIBOR is 3.8%. The firm buys an interest-rate call that matures in 30 days with a notional principal of $15 million, 90 days in underlying, and a strike rate of 4%. The call premium is $4,000. What is the maximum effective annual rate the firm can anticipate paying?

A) 0.0687.

B) 0.0671.

C) 0.0603.

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First we compute the implied net amount to be borrowed after the cost of the call:

$ 14,995,979 = $15,000,000 − $4,000 × (1 + (0.038 + 0.025) × (30 / 360))

The most the firm will expect to pay is the rate associated with the strike rate: 4% plus the 250 basis-point spread equals 6.5%. This gives the nominal cost of the loan:

$243,750 = $15,000,000 × 0.065 (90 / 360)

The highest effective annual rate is:

0.0687 = ($15,243,750 / $14,995,979)(365/90) − 1

optiix

In 90 days, a firm wishes to borrow $10 million for 180 days. The borrowing rate is LIBOR plus 200 basis points. The current LIBOR is 4%. The firm buys an interest-rate call that matures in 90 days with a notional principal of $10 million, 180 days in underlying, and a strike rate of 4.1%. The call premium is $9,000. What is the effective annual rate of the loan if at expiration LIBOR = 4%?

A) 0.0619.

B) 0.0787.

C) 0.0637.

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The call option is out-of-the-money. The implied net amount to be borrowed after the cost of the call is:

$9,990,865 =$10,000,000 - $9,000 × (1 + (0.04+0.02) × (90/360))

For LIBOR = 0.04 at expiration, the dollar cost is:

$300,000 = $10,000,000 × 0.06 × (180/360)

The effective annual rate is:

0.0637 = ($10,300,000 / $9,990,865)(365/180) - 1

optiix

In 60 days, a bank plans to lend $10 million for 180 days. The lending rate is LIBOR plus 200 basis points. The current LIBOR is 4.5%. The bank buys an interest-rate put that matures in 60 days with a notional principal of $10 million, days in underlying of 180 days, and a strike rate of 4.3%. The put premium is $4,000. What is the effective annual rate of the loan if at expiration LIBOR = 4.1%?

A) 0.0648.

B) 0.0640.

C) 0.0619.

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The effective amount the bank parts with or “lends” at time of the loan is:

$10,004,043 = $10,000,000 + $4,000 × (1 + (0.045 + 0.02) × (60/360))

If LIBOR at maturity equals 4.1%, the payoff of the put would be:

payoff = ($10,000,000) × [max(0, 0.043 – 0.041) × (180/360)

payoff = $10,000

The dollar interest earned is:

$305,000=$10,000,000 × (0.041 + 0.02) × (180/360), and
EAR = [($10,000,000 + $10,000 +$305,000) / ($10,004,043)](365/180) - 1
EAR = 0.0640 or 6.40%

optiix

A firm purchases a collar with floor rate of 3% and a cap rate of 4.4%. The cap and floor have quarterly settlement and a notional principal of $10 million. The maximum outflow and inflow the buyer can expect on a given settlement is (assume equal settlement periods):

A) $110,000 and maximum inflow = $140,000.

B) $75,000 and maximum inflow = $140,000.

C) $75,000 and maximum inflow = infinite.

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Given the possible answers, this must be a collar consisting of a short floor and long cap. The firm’s maximum outflow would occur from the floor when the reference rate is zero: $10,000,000 × (0.03 − 0) / 4 = $75,000. Although interest rates cannot go to infinity, there is no upper limit on what the owner can expect from the cap. Thus “infinite” is the best answer.

optiix

Which of the following is equivalent to a pay-fixed interest rate swap?

A) Buying a cap and selling a floor.

B) Buying a cap and selling an interest rate collar.

C) Selling a cap and buying a floor.

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A pay-fixed interest rate swap has the same payoffs as a long position in the corresponding interest rate collar (with the strike rate equal to the swap fixed rate).

optiix

A firm purchases a one-year cap with a strike rate of 4%, a notional principal of $3 million, and semiannual settlement. The reference rate at the initiation of the cap is 5%, falls to 4.5% at the next settlement and then to 4% one year after the cap’s initiation. The total payoffs (without discounting) over the maturity of the swap would be:

A) $22,792.

B) $25,500.

C) $7,583.

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Since the number of days is not given for each period, approximate it with 182 in the first period and 183 in the second period. Remember that payments are made in arrears.

First payoff = $ 15,167 = $3,000,000 × max(0, 0.05 – 0.04) × (182/360).
Second payoff = $7,625 = $3,000,000 × max(0, 0.045 – 0.04) × (183/360)
Total = $22,792 = $7,625 + $ 15,167