Stock Options and Portfolios Quiz

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Questions and Answers

Consider a stock that will have a value of either 22 or 14 one year from now. If the risk-free rate is 5%, what is the ratio of shares to short call options with an exercise price of 18 for a portfolio that will have the same value at expiration regardless of the stock price at the end of the year?

0.53
0.50 (correct)
0.48

One method of valuing a call option with a one-period binomial model involves:

Discounting the average call value at expiration by the risk-free rate.
Using the probabilities of an up-move and a down-move to get the expected value of the payment at expiration.
Finding a combination of the call option and the underlying that will have the same value regardless of the price of the underlying at expiration. (correct)

We can use the risk-free rate to value an option with a one-period binomial model because:

Options investors are risk-neutral, on average.
Combining put and call options in specific ratio can produce a risk-free future payment.
Combining options with the underlying asset in a specific ratio will produce a risk-free future payment. (correct)

In order to value an option with a one-period binomial model, three things an analyst would need to know are:

The risk-free rate, the volatility of the price of the underlying, and the current asset price. (A) Signup and view all the answers

Consider a European call option and put option that have the same exercise price, and a forward contract to buy the same underlying asset as the two options. An investor buys a risk-free bond that will pay, on the expiration date of the options and the forward contract, the difference between the exercise price and the forward price. According to the put-call-forward parity relationship, this bond can be replicated by:

Writing the call option and buying the put option. (C) Signup and view all the answers

A synthetic European put option includes a short position in:

The underlying asset. (C) Signup and view all the answers

A fiduciary call is a portfolio that is made up of:

A call option and a bond that pays the exercise price of the call at option expiration. (A) Signup and view all the answers

An investor calculates that the premium of a European put option is less than its value based on put-call parity. In exploiting this arbitrage opportunity, the investor is most likely to:

Sell the call option. (B) Signup and view all the answers

Using put-call parity, it can be shown that a synthetic European call can be created by a portfolio that is:

Long the stock, long the put, and short a pure discount bond that pays the exercise price at option expiration. (B) Signup and view all the answers

Which of the following portfolios has the same future cash flows as a protective put?

Long call option, long risk-free bond. (C) Signup and view all the answers

Which of the following instruments is a component of the put-call-forward parity relationship?

The present value of the forward price of the underlying asset. (C) Signup and view all the answers

The relationship referred to as put-call-forward parity states that at time = 0, if there is no arbitrage opportunity, the value of a call at X on an asset that has no holding costs or benefits plus the present value of X is equal to:

The value of a put option at X plus the present value of the forward contract price. (C) Signup and view all the answers

The value of a put option at expiration is most likely to be increased by:

A higher exercise price. (A) Signup and view all the answers

A call option that is in the money:

Has an exercise price less than the market price of the asset. (B) Signup and view all the answers

At expiration, exercise value is equal to time value for:

An out-of-the-money call or an out-of-the-money put. (C) Signup and view all the answers

Which of the following statements about long positions in put and call options is most accurate? Profits from a long call:

Are positively correlated with the stock price and the profits from a long put are negatively correlated with the stock price. (B) Signup and view all the answers

Which of the following will increase the value of a call option?

An increase in volatility. (A) Signup and view all the answers

An option's intrinsic value is equal to the amount the option is:

In the money, and the time value is the market value minus the intrinsic value. (A) Signup and view all the answers

An increase in the riskless rate of interest, other things equal, will:

Increase call option values and decrease put option values. (A) Signup and view all the answers

Flashcards

How to determine the ratio of shares to short call options for a risk-free portfolio?

The ratio of shares to short call options needed to create a portfolio that provides a risk-free payoff at expiration, regardless of the stock price.

What is the one-period binomial model?

A method of valuing a call option that utilizes the probabilities of an up-move and a down-move in the stock price to calculate the expected value of the call option at expiration.

What is the risk-free rate?

The rate of return that investors expect to earn on a risk-free investment, such as a U.S. Treasury bond.

How can we derive the value of an option using the one-period binomial model?

The ability to replicate a portfolio's payoff using a combination of options and the underlying asset. This ensures that the portfolio's value remains the same regardless of the price of the underlying at expiration.