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# Multiple choice questions on options

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1. Answer questions 1-4 about insuring a portfolio identical to the S&P 500 worth \$12,500,000 with a 3-month horizon. The risk-free rate is 7%. Three-month t-bills are available at a price of \$98.64 per \$100 face value. The S&P 500 is at 385. Puts with an exercise price of 390 are available at a price of 13. Calls with an exercise price of 390 are available at a price of 13.125. Round off your answers to the nearest integer.
What is the minimum value of the insured portfolio?

1. 12,091,709
2. 16,672,344
3. 12,244,898
4. 12,500,000
5. 13,375,000

2. If the S&P 500 ends up at 401, determine the upside capture.

1. 96%
2. 96.7%
3. 100%
4. 99.3%
5. 94%

3. If the insured portfolio consisted entirely of calls and t-bills, how many would be used?

1. 19,143 calls and 124,176 t-bills
2. 31,397 calls and 122,449 t-bills
3. 933,238 calls and 2,547 t-bills
4. 31,407 calls and 119,977 t-bills
5. 32,468 calls 32,468 t-bills

4. If the insured portfolio were dynamically hedged with stock index futures, how many futures would be used? The call delta is .52 and the continuous risk-free rate is 5.48%. Each futures has a multiplier of 500 and a price of 388.65.

1. 60
2. 64
3. 32
4. none are correct
5. 30

5. If the stock price is currently 36, the exercise price is 35 and the stock ends up at 44, the value of an asset-or-nothing option at expiration is:

1. 35
2. 8
3. 9
4. none are correct
5. 44

6. Which of the following statements is correct about cash-or-nothing options?

1. they must be priced by the binomial model
2. none are correct
3. they have lower upside gains and lower downside losses than ordinary options
4. they are equivalent to short positions in asset-or-nothing options
5. they are subject to no credit risk

7. A contingent-pay option is replicated by which of the following combinations?

1. long an ordinary call and long an equity forward
2. long an ordinary call and long an ordinary put
3. long an ordinary call and short an asset-or-nothing call
4. long an ordinary call and long a risk-free bond
5. long an ordinary call and short a cash-or-nothing call

8. A lookback call option provides the right

1. to insure a stock against loss.
3. none are correct.
4. to buy the stock at its lowest price over the option's life.
5. to change the stock on which the option is written

9. Which of the following is a path-independent option

1. an up-and-out call option
2. a standard European call option
3. a fixed strike Asian call option
4. an American put option
5. none are correct

10. Weather derivative payoffs can be based on each of the following variables except

1. inches of snowfall
2. sunshine
3. total value of insurance claims
4. temperature above a given level
5. temperature below a given level

#### Solution Preview

1. Answer questions 1-4 about insuring a portfolio identical to the S&P 500 worth \$12,500,000 with a 3-month horizon. The risk-free rate is 7%. Three-month t-bills are available at a price of \$98.64 per \$100 face value. The S&P 500 is at 385. Puts with an exercise price of 390 are available at a price of 13. Calls with an exercise price of 390 are available at a price of 13.125. Round off your answers to the nearest integer.
What is the minimum value of the insured portfolio?
1. 12,091,709
2. 16,672,344
3. 12,244,898
4. 12,500,000
5. 13,375,000

N= Number of shares = Number of put = Value of portfolio / (Stock price + Put price)
12,500, 000 / (385+ 13) = 31,407.03
Minimum Value = N x Exercise Price of the Put option= 31,407.03 x \$390
= \$ 12,248,741
This is close to the answer choice 3. 12,244,898 but not exactly equal (there is a 0.03% difference)
This may be due to the fact that the values of call and put options have been interchanged in the problem. If we interchange the values, we get an exact answer.
N= Number of shares = Number of put = Value of portfolio / (Stock price + Put price)
12,500, 000 / (385+ 13.125) = 31,397.17
Minimum Value = N x Exercise Price of the Put option= 31,397.17 x \$390
= \$ 12,244,898

2. If the S&P 500 ends up at 401, determine the upside capture.
1. 96%
2. 96.7%
3. 100%
4. 99.3%
5. 94%