Question 1

If the hedge ratio for a stock call is 0.70, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

The hedge ratio for a put option is the negative of the hedge ratio for a call option with the same expiration date and exercise price. Therefore, if the call's hedge ratio is 0.70, the put's hedge ratio would be -0.30.

Question 2

If the hedge ratio for a stock call is 0.30, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

The answer of If the hedge ratio for a stock...

Question 3

An American call-option buyer on a nondividend-paying stock will

Accepted Answer

The option buyer will never exercise the call early because there is no advantage to doing so. By waiting until expiration or closer to expiration, the buyer can capitalize on any further stock price appreciation without forfeiting any remaining time value of the option. Exercising early would only result in giving up this time value.

Question 4

A $1 decrease in a call option's exercise price would result in a(n) __________ in the call option's value of __________ one dollar.

Accepted Answer

The answer of A $1 decrease in a call option's...

Question 5

If the hedge ratio for a stock call is 0.50, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

The hedge ratio for a put option is simply the negative value of the hedge ratio for a call with the same characteristics, so the hedge ratio for the put in this case would be -0.50.

Question 6

Portfolio A consists of 400 shares of stock and 400 calls on that stock.Portfolio B consists of 500 shares of stock.The call delta is 0.5.Which portfolio has a higher dollar exposure to a change in stock price?

Accepted Answer

Portfolio B has a higher dollar exposure to a change in stock price because it has 500 shares of stock, while Portfolio A has only 400 shares of stock. The call delta is 0.5, which means that each call option has an exposure of 0.5 shares of stock. Therefore, Portfolio A has an exposure of 400 + (400 * 0.5) = 600 shares of stock, while Portfolio B has an exposure of 500 shares of stock.

Question 7

A put option is currently selling for $6 with an exercise price of $50.If the hedge ratio for the put is -0.30, and the stock is currently selling for $46, what is the elasticity of the put?

Accepted Answer

The answer of A put option is currently selling for...

Question 8

Higher dividend-payout policies have a __________ impact on the value of the call and a __________ impact on the value of the put compared to lower dividend-payout policies.

Accepted Answer

Higher dividend-payout policies decrease the value of a call option because dividends reduce the stock price when they are paid out, making it less likely that the call will be in the money. Conversely, higher dividends increase the value of a put option, as the reduction in stock price makes it more likely that the put will be in the money.

Question 9

A put option on the S&P 500 Index will best protect a portfolio

Accepted Answer

A put option on the S&P 500 Index will best protect a portfolio that corresponds to the S&P 500 because it provides a hedge against a decline in the overall market, rather than just the performance of individual stocks or bonds. Protecting a specific stock, bonds or a combination of stocks may not be as effective as protecting against a broader market downturn.

Question 10

Which one of the following variables influences the value of call options? I) Level of interest rates
II) Time to expiration of the option
III) Dividend yield of underlying stock
IV) Stock price volatility

Accepted Answer

All four variables influence the value of call options. The level of interest rates affects the cost of carrying positions, time to expiration impacts the time value component of an option, dividend yield influences the underlying stock price projections, and stock price volatility affects the option's potential for profit.

Question 11

A portfolio consists of 800 shares of stock and 100 calls on that stock.If the hedge ratio for the call is 0.5, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

Hedge ratio = 0.5
This means that for every 1 share of stock, the portfolio needs to hold 0.5 calls.
So, for 800 shares of stock, the portfolio needs 400 calls.
Total number of options = 100
So, to reach the required number of calls, the portfolio is short 300 calls.
Now, to calculate the dollar change in the value of the portfolio in response to a $1 decline in the stock price, we can use the following formula:
Dollar change in portfolio value = (number of shares * change in stock price) + (number of options * hedge ratio * change in stock price * 100)
= (800 * -1) + (400 * 0.5 * -1 * 100)
= -800 - 20000
= -$20800
Therefore, the dollar change in the value of the portfolio in response to a $1 decline in the stock price is -$20800, which is equivalent to a decline of $26 per share.

Question 12

Which one of the following variables influences the value of put options? I) Level of interest rates
II) Time to expiration of the option
III) Dividend yield of underlying stock
IV) Stock price volatility

Accepted Answer

All four variables influence the value of put options. Interest rates affect the cost of carrying positions, time to expiration impacts the probability of the option ending in the money, dividend yield can affect the underlying stock price, and stock price volatility influences the likelihood of price movements that could make the option valuable.

Question 13

Relative to European puts, otherwise identical American put options

Accepted Answer

American put options give the holder the right to exercise the option at any time before expiration, whereas European put options can only be exercised at expiration. This added flexibility of the American put option makes it more valuable than a European put option, all else being equal. Therefore, American puts are more valuable than European puts.

Question 14

A portfolio consists of 400 shares of stock and 200 calls on that stock.If the hedge ratio for the call is 0.6, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

The answer of A portfolio consists of 400 shares of...

Question 15

A portfolio consists of 225 shares of stock and 300 calls on that stock.If the hedge ratio for the call is 0.4, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

The dollar change in the portfolio due to a $1 decline in the stock price can be calculated by considering the impact on both the shares and the calls. The 225 shares would lose $225 in value (225 shares * -$1 per share). The 300 calls, with a hedge ratio (delta) of 0.4, would gain in value because they are calls on the stock, and their value moves inversely to the stock price. The gain from the calls would be 300 calls * 0.4 * $1 = $120. Therefore, the net change in the portfolio value would be -$225 (from the shares) + $120 (from the calls) = -$105. However, since this option is not available, the calculation must be revisited. The correct calculation is: The loss from the shares is straightforward, -$225. For the calls, the hedge ratio indicates how much the value of the calls would change for a $1 change in the stock price. Since the calls are on the stock, a decline in the stock price would actually decrease the value of the calls, not increase it as previously stated. Therefore, the correct calculation for the calls' part is actually a loss: 300 calls * 0.4 * -$1 = -$120. Adding this to the loss from the shares gives a total change of -$225 (from the shares) - $120 (from the calls) = -$345.

Question 16

Portfolio A consists of 500 shares of stock and 500 calls on that stock.Portfolio B consists of 800 shares of stock.The call delta is 0.6.Which portfolio has a higher dollar exposure to a change in stock price?

Accepted Answer

The answer of Portfolio A consists of 500 shares of...

Question 17

A portfolio consists of 100 shares of stock and 1500 calls on that stock.If the hedge ratio for the call is 0.7, what would be the dollar change in the value of the portfolio in response to a $1 decline in the stock price?

Accepted Answer

The hedge ratio for the call is 0.7, meaning that for every 1 share of stock, there are 0.7 calls. Therefore, the number of shares effectively covered by the call option is:

0.7 x 1500 = 1050

The total number of shares in the portfolio, taking into account the covered shares, is:

100 + 1050 = 1150

If the stock price declines by $1, then the total loss in the value of the portfolio would be:

1150 x $1 = $1150

Therefore, the answer is C, a decrease in value of $1150.

Question 18

If the hedge ratio for a stock call is 0.60, the hedge ratio for a put with the same expiration date and exercise price as the call would be

Accepted Answer

The hedge ratio for a put option is typically negative, and it can be calculated as -1 + the hedge ratio for the call option. Therefore, if the hedge ratio for the call is 0.60, the hedge ratio for the put would be -1 + 0.60 = -0.40. Therefore, the correct choice is D.

Question 19

Lower dividend-payout policies have a __________ impact on the value of the call and a __________ impact on the value of the put compared to higher dividend-payout policies.

Accepted Answer

Lower dividend-payout policies mean that the company is retaining more earnings to reinvest back into the company, which increases the expected future value of the company, resulting in higher stock prices. Therefore, lower dividend-payout policies have a positive impact on the value of the call option. On the other hand, lower dividends reduce the potential value of the put option, as investors are less likely to exercise their option and sell the stock at a higher price, as there is a lower likelihood of a significant decline in price due to the company reinvesting earnings. Therefore, lower dividend-payout policies have a negative impact on the value of the put option.

Question 20

Portfolio A consists of 600 shares of stock and 300 calls on that stock.Portfolio B consists of 685 shares of stock.The call delta is 0.3.Which portfolio has a higher dollar exposure to a change in stock price?

Accepted Answer

Portfolio B has a higher dollar exposure to a change in stock price because it has more shares of stock. The call delta is a measure of how much the option's price will change for a given change in the stock price. In this case, the call delta is 0.3, which means that the option's price will increase by $0.30 for every $1 increase in the stock price. However, Portfolio A has more calls than shares, so it will have a higher exposure to changes in the option's price.

Quiz 21: Option Valuation