Question 1

You are managing a stock portfolio with a value of $50,000,000 and a beta of 1.15. The S&P 500 index is trading at 1,120. If the delta of the options is-0.48, how can you hedge your portfolio using put options?
A) buy 1,070 contracts
B) sell 1,130 contracts
C) sell 1,070 contracts
D) sell 1,095 contracts
E) buy 1,130 contracts

Accepted Answer

To hedge a $50,000,000 portfolio with a beta of 1.15 using put options with a delta of -0.48, you need to calculate the number of contracts required to achieve a neutral position. The formula to calculate the number of contracts is: (Portfolio Value * Portfolio Beta) / (Option Delta * S&P 500 Index Value * 100). Plugging in the values: ($50,000,000 * 1.15) / (-0.48 * 1,120 * 100) = 1,070.09 contracts. Since you can't buy a fraction of a contract, you round to the nearest whole number, which is 1,070 contracts. Therefore, you would buy 1,070 put option contracts to hedge the portfolio.

Question 2

All else the same, an increase in the volatility of the underlying stock will __________ the price of a call option and __________ the price of a put option.
A) increase; increase
B) increase; decrease
C) decrease; decrease
D) decrease; increase
E) not affect; not affect

Accepted Answer

An increase in the volatility of the underlying stock increases the price of both call and put options because higher volatility increases the potential for movement in the stock price, which increases the value of having an option.

Question 3

An implied standard deviation can be computed by using the directly observable Black-Scholes-Merton option pricing variables plus an option price and solving the Black-Scholes-Merton formula for
A) Beta
B) Vega
C) Sigma
D) Rho
E) Gamma

Accepted Answer

The Black-Scholes-Merton formula can be used to calculate the implied standard deviation (sigma) of an option by using the observable variables (stock price, strike price, time to expiration, risk-free interest rate, and option price). Therefore, the correct choice is C) Sigma.

Question 4

A rising MVX implies
A) a relatively stable stock market
B) investors having heightened fears for the future
C) the options traded on the Montreal Exchange are in-the-money
D) no risk of market turmoil
E) the options traded on the Montreal Exchange are out-of-the-money

Accepted Answer

MVX is the Montreal Exchange Volatility Index, which measures the implied volatility of option prices on the Montreal Exchange. A rising MVX indicates that investors are willing to pay more for options to protect their investments, meaning they are anticipating increased market fluctuations and heightened fears for the future. Therefore, option prices are likely to be higher, and investors are willing to pay more for the protection options provide.

Question 5

Hedging a long position in a stock is best accomplished by
A) Selling a put
B) Buying a put
C) Selling a call
D) Buying a call
E) Doing nothing

Accepted Answer

Buying a put option will allow the investor to profit from a decline in the stock's price, thereby reducing the potential loss on the long position.

Question 6

You manage a stock portfolio with a beta of 0.90 and a market value of $250 million. S&P 500 index call options with a delta of 0.53 are available at a strike price of 1,100. If the index is currently trading at 1,084, how many call options should you write?
A) 3,705
B) 3,859
C) 3,534
D) 3,916
E) 4,102

Accepted Answer

The answer of You manage a stock portfolio with a...

Question 7

All else the same, an increase in the risk-free rate will __________ the price of a call option and __________ the price of a put option.
A) increase; increase
B) increase; decrease
C) decrease; decrease
D) decrease; increase
E) not affect; not affect

Accepted Answer

An increase in the risk-free rate will increase the cost of carrying the underlying asset and therefore decrease the present value of an option’s exercise price. This will decrease the price of a call option as the exercise price is more expensive, but it will increase the price of a put option as the exercise price is less expensive.

Question 8

The Black-Scholes-Merton model assumes __________ volatility.
A) stochastic
B) high
C) low
D) constant
E) random

Accepted Answer

The Black-Scholes-Merton model assumes constant volatility. This means that the volatility of the underlying asset doesn't change over time, which is a simplifying assumption that makes the model easier to use. However, in reality, volatility can and does change.

Question 9

An increase in the price of the underlying stock will __________ the price of a put option because put option delta is always __________.
A) increase; negative
B) decrease; negative
C) decrease; positive
D) increase; positive
E) not affect; equal to one

Accepted Answer

As the price of the underlying stock increases, the value of the put option decreases. This is because the put option gives the holder the right to sell the stock at a predetermined price, and if the current stock price is higher than the predetermined price, then it is not profitable for the holder to exercise the option. Put option delta is always negative, as the value of the option decreases as the stock price increases.

Question 10

Which of the following is/are the same for a call option and a put option?
I. Rho
II. Theta
III. Beta
IV Vega
A) I only
B) II only
C) II and IV only
D) I and III only
E) I, II and IV only

Accepted Answer

Rho and Beta are not the same for call and put options. Theta and Vega are the same for both call and put options. Therefore, option C is the best choice as it includes only the common characteristics of call and put options.

Question 11

The risk-free rate used in the Black-Scholes-Merton model is the:
A) 30-day Treasury bill.
B) 90-day Treasury bill.
C) 1-year Treasury bill.
D) 10-year Treasury bond.
E) Treasury bill with the same maturity as the option.

Accepted Answer

The risk-free rate used in the Black-Scholes-Merton model should be the Treasury bill with the same maturity as the option. This reflects the fact that the risk-free rate should be consistent with the time frame of the option being valued. Other choices such as the 30-day or 90-day Treasury bill may not accurately reflect the time horizon of the option. The 1-year or 10-year Treasury rates are also not appropriate as they are not directly related to the option's maturity. Therefore, E is the best choice.

Question 12

The S&P 500 is currently trading at 1,040. Call options with a strike price of 1,075 and a delta of 0.25 are available. If you want to hedge portfolio with a value of $300 million and a beta of 1.10, how many options should you write?
A) 12,843
B) 12,503
C) 12,692
D) 12,386
E) 12,279

Accepted Answer

To hedge the portfolio, calculate the number of options using the formula: (Portfolio Value * Beta) / (Option Delta * Strike Price). This gives (300,000,000 * 1.10) / (0.25 * 1,075) = 12,692 options.

Question 13

Which of the following inputs for the Black-Scholes-Merton model is not directly observable?
A) The risk-free rate.
B) The strike price.
C) The time to maturity.
D) The standard deviation.
E) The dividend yield.

Accepted Answer

The standard deviation is not directly observable and must be estimated from historical data or implied volatility.

Question 14

A call option that sells for $7.18 has a delta of 0.63. If the stock price decreases by $1.50, what is your estimate of the new call price?
A) $6.86
B) $6.24
C) $6.55
D) $6.37
E) $6.64

Accepted Answer

The answer of A call option that sells for $7.18...

Question 15

The change in a put option's price in response to a 1% increase in interest rates is approximately equal to
A) Rho
B) B.-1 * rho
C) 0.01 * rho
D) 0.01 * -1 * rho
E) 0.01-rho

Accepted Answer

Rho measures the sensitivity of an option's price to a change in interest rates. For a put option, an increase in interest rates typically decreases the option's price, and this change is directly measured by rho.

Question 16

S&P 500 stock index options are settled:
A) in cash.
B) with a portfolio of stocks.
C) with Spyders.
D) in one of the above methods at the discretion of the option owner.
E) None of the above.

Accepted Answer

S&P 500 stock index options are settled in cash, meaning the option holder receives a cash payment equal to the difference between the strike (exercise) price and the S&P 500 index value at expiration. This is the most common settlement method for index options.

Question 17

You want to hedge a stock portfolio with a beta 0.95 and a value of $150 million with S&P 500 call options. The options have a strike price of 1,100 and a delta of 0.62. If the index is currently trading at 1,128, how many options should you write?
A) 1,996
B) 2,089
C) 2,147
D) 2,193
E) 2,038

Accepted Answer

To hedge the portfolio, you need to calculate the number of options to write by using the formula: (Beta * Portfolio Value) / (Delta * Strike Price). Here, it's (0.95 * $150,000,000) / (0.62 * 1,100) = $203,788,043.29 / $682 = approximately 2,038 options.

Question 18

You are managing a stock portfolio with a value of $100 million. The portfolio is unique in that the beta is-0.10. The S&P 500 is currently trading at 1,108. The delta of a call option on the index with a strike price of 1,150 has a delta of 0.52. How can you hedge your portfolio using call options?
A) Buy 174 contracts
B) Sell 167 contracts
C) Buy 156 contracts
D) Sell 174 contracts
E) Buy 167 contracts

Accepted Answer

To hedge the portfolio, you would need to buy call options on the S&P 500 with a delta of 0.52. Since the beta of the portfolio is -0.10, you would need to buy options on the opposite side of the market to achieve a delta-neutral portfolio.

First, calculate the number of shares of the index needed to achieve a delta of -0.10:

Shares = -0.10 * $100,000,000 / 1,108 = -9,027

Since options have a delta of 0.52, the number of option contracts needed would be:

Contracts = -9,027 / (0.52 * 100) = -174

Since you want to buy options to hedge the portfolio, the best choice is A) Buy 174 contracts.

Question 19

You own shares of AZT stock. Which of the following strategies can you use to hedge your risk associated with a price decrease in AZT stock?
I. buy call options
II. write call options
III. buy put options
IV. write put options
A) I only
B) I and III only
C) I and IV only
D) II and III only
E) II and IV only

Accepted Answer

Buying put options allows you to sell your stock at a predetermined price, protecting against a price decrease. Writing call options generates income, which can offset losses from a stock price decrease.

Question 20

All else the same, an increase in the time to maturity will __________ the price of a call option and __________ the price of a put option.
A) increase; increase
B) increase; decrease
C) decrease; decrease
D) decrease; increase
E) not affect; not affect

Accepted Answer

An increase in the time to maturity generally increases the price of both call and put options. This is because a longer time to maturity gives the underlying asset more time to move in a direction that is favorable for the option holder, increasing the option's value.

Quiz 15: Option Valuation

You are managing a stock portfolio with a value of $50,000,000 and a beta of 1.15. The S&P 500 index is trading at 1,120. If the delta of the options is-0.48, how can you hedge your portfolio using put options?

All else the same, an increase in the volatility of the underlying stock will the price of a call option and the price of a put option.

An implied standard deviation can be computed by using the directly observable Black-Scholes-Merton option pricing variables plus an option price and solving the Black-Scholes-Merton formula for

A rising MVX implies

Hedging a long position in a stock is best accomplished by

You manage a stock portfolio with a beta of 0.90 and a market value of $250 million. S&P 500 index call options with a delta of 0.53 are available at a strike price of 1,100. If the index is currently trading at 1,084, how many call options should you write?

All else the same, an increase in the risk-free rate will the price of a call option and the price of a put option.

The Black-Scholes-Merton model assumes __________ volatility.

An increase in the price of the underlying stock will the price of a put option because put option delta is always .

Which of the following is/are the same for a call option and a put option? I. Rho II. Theta III. Beta IV Vega

The risk-free rate used in the Black-Scholes-Merton model is the:

The S&P 500 is currently trading at 1,040. Call options with a strike price of 1,075 and a delta of 0.25 are available. If you want to hedge portfolio with a value of $300 million and a beta of 1.10, how many options should you write?

Which of the following inputs for the Black-Scholes-Merton model is not directly observable?

A call option that sells for $7.18 has a delta of 0.63. If the stock price decreases by $1.50, what is your estimate of the new call price?

The change in a put option's price in response to a 1% increase in interest rates is approximately equal to

S&P 500 stock index options are settled:

You want to hedge a stock portfolio with a beta 0.95 and a value of $150 million with S&P 500 call options. The options have a strike price of 1,100 and a delta of 0.62. If the index is currently trading at 1,128, how many options should you write?

You are managing a stock portfolio with a value of $100 million. The portfolio is unique in that the beta is-0.10. The S&P 500 is currently trading at 1,108. The delta of a call option on the index with a strike price of 1,150 has a delta of 0.52. How can you hedge your portfolio using call options?

You own shares of AZT stock. Which of the following strategies can you use to hedge your risk associated with a price decrease in AZT stock? I. buy call options II. write call options III. buy put options IV. write put options

All else the same, an increase in the time to maturity will the price of a call option and the price of a put option.