1. You are conducting hypothesis testing on 8 different tests using two types of statistical software. The output of the first software uses the p-value against the significance level and the output of the second software uses the test statistic against the critical value.

For a one-tailed test at the significance levels indicated in the software output, you must decide whether or not to reject the null hypothesis H0. How many times will you reject H0 given the results of the following 8 different tests?

A. 3 times

B. 4 times

C. 5 times

D. 6 times

2. An analyst has computed the following statistics on companies X and Y for his merger arbitrage model:

Expected value of stock price of X is 3

Expected value of stock price of Y is 2

Expected value of stock price of X times the stock price of Y is 20

Variance on stock price of X is 2

Variance on stock price of Y is 5

Upon a closer examination, the analyst finds the data odd. The analyst turns to you for advice. Which of the following statements would you use to confirm that there is a mistake in the numbers presented to you?

A. The variance of the stock price of X should not be higher than its expected value.

B. The covariance is less than 10, which is impossible given the calculated statistics.

C. The covariance is more than 10, which is impossible given the calculated statistics.

D. The covariance should be zero given the independence of companies X and Y.

3. Which of the following factors will not necessarily increase the price of a European call option on a dividend paying stock as this factor increases in value?

A. The risk free rate.

B. The stock price.

C. The time to expiration.

D. The volatility of the stock price.

4. An analyst observes that the market price of a call option is USD 5 higher than the theoretical price dictated by an option pricing model. Assuming the same strike price and time to expiration, what should be the relationship between the market price of a put option and its theoretical price dictated by the option pricing model?

A. The market price will be higher than the theoretical price by USD 5.

B. The market price will be higher than the theoretical price by an amount lower than USD 5.

C. The market price will be lower than the theoretical price by USD 5.

D. The market price will be lower than the theoretical price by an amount lower than USD 5.

5. Which type of option produces discontinuous payoff profiles, meaning that the payoff does not increase or decrease continuously with the underlying asset value?

A. Chooser options.

B. Barrier options.

C. Binary options.

D. Lookback options.

1. You are conducting hypothesis testing on 8 different tests using two types of statistical software. The output of the first software uses the p-value against the significance level and the output of the second software uses the test statistic against the critical value.

For a one-tailed test at the significance levels indicated in the software output, you must decide whether or not to reject the null hypothesis H0. How many times will you reject H0 given the results of the following 8 different tests?

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A. 3 times

B. 4 times

C. 5 times

D. 6 times

Correct answer is D

A is incorrect. Using the rules: reject H0 if p-value < α and reject H0 if test statistic > critical value, we conclude that 6 and not 3 tests will be rejected.

B is incorrect. Using the rules: reject H0 if p-value < α and reject H0 if test statistic > critical value, we conclude that 6 and not 4 tests will be rejected.

C is incorrect. Using the rules: reject H0 if p-value < α and reject H0 if test statistic > critical value, we conclude that 6 and not 5 tests will be rejected.

D is correct. Using the rules: reject H0 if p-value < α and reject H0 if test statistic > critical value, we conclude that 6 tests will be rejected.

2. An analyst has computed the following statistics on companies X and Y for his merger arbitrage model:

Expected value of stock price of X is 3

Expected value of stock price of Y is 2

Expected value of stock price of X times the stock price of Y is 20

Variance on stock price of X is 2

Variance on stock price of Y is 5

Upon a closer examination, the analyst finds the data odd. The analyst turns to you for advice. Which of the following statements would you use to confirm that there is a mistake in the numbers presented to you?

A. The variance of the stock price of X should not be higher than its expected value.

B. The covariance is less than 10, which is impossible given the calculated statistics.

C. The covariance is more than 10, which is impossible given the calculated statistics.

D. The covariance should be zero given the independence of companies X and Y.

Correct answer is C

A is incorrect.  Nothing stated would prohibit the variance of the price of X from being greater than its expected value. 

B is incorrect. The covariance is greater than 10. Cov(X,Y) = E(XY) ? E(X)E(Y) = 14.

C is correct. Cov(X,Y) = E(XY) ? E(X)E(Y) = 14, but the sqrt(Var(X)) * sqrt(Var(Y)) less than 14 which violates the condition that Cov(X,Y) < sqrt(Var(X)) * sqrt(Var(Y)).

D is incorrect.  Nothing stated implies that the prices are independent.

3. Which of the following factors will not necessarily increase the price of a European call option on a dividend paying stock as this factor increases in value?

A. The risk free rate.

B. The stock price.

C. The time to expiration.

D. The volatility of the stock price.

Correct answer is C

A is incorrect. An increase in the risk free rate will decrease PV(X) and necessarily increase the price of the European call.

B is incorrect. An increase in the stock price will necessarily increase the price of the European call.

C is correct. Because dividends paid before the expiration of the option might decrease the value of the stock price, it is possible that the value of the call option will decrease as the time to expiration is increased passed scheduled dividend payout dates.

D is incorrect. An increase in the underlying stock price will necessarily increase the price of the European call.

Assigned ffice:smarttags" />Reading:

John Hull, Options, Futures, and Other Derivatives, 6th ed. (New York: Prentice Hall, 2002), Chapter 9.

4. An analyst observes that the market price of a call option is USD 5 higher than the theoretical price dictated by an option pricing model. Assuming the same strike price and time to expiration, what should be the relationship between the market price of a put option and its theoretical price dictated by the option pricing model?

A. The market price will be higher than the theoretical price by USD 5.

B. The market price will be higher than the theoretical price by an amount lower than USD 5.

C. The market price will be lower than the theoretical price by USD 5.

D. The market price will be lower than the theoretical price by an amount lower than USD 5.

Correct answer is A

A is correct. Given the same strike price and time to expiration, option market prices that deviate from those dictated by the Black-Scholes model are going to deviate in the same amount whether they are for calls or puts.

B is incorrect. The deviation will be for the same amount, not a lower amount. Given the same strike price and time to expiration, option market prices that deviate from those dictated by the Black-Scholes model are going to deviate in the same amount whether they are for calls or puts.

C is incorrect. The market price will be higher, not lower than the theoretical price. Given the same strike price and time to expiration, option market prices that deviate from those dictated by the Black-Scholes model are going to deviate in the same amount whether they are for calls or puts.

D is incorrect. The market price will be higher, not lower than the theoretical price. Given the same strike price and time to expiration, option market prices that deviate from those dictated by the Black-Scholes model are going to deviate in the same amount whether they are for calls or puts.      

Assigned Reading:

John Hull, Options, Futures, and Other Derivatives, 6th ed. (New York: Prentice Hall, 2002), Chapter 16

5. Which type of option produces discontinuous payoff profiles, meaning that the payoff does not increase or decrease continuously with the underlying asset value?

A. Chooser options.

B. Barrier options.

C. Binary options.

D. Lookback options.

Correct answer is C

A is incorrect. The payoff profile of a chooser option is continuous.

B is incorrect. The payoff profile of a barrier option is continuous.

C is correct. The binary option is the only one that produces discontinuous payoff profiles because it pays one price at the expiration if the asset value is above the strike price and nothing if the asset price is below the strike price.

D is incorrect. The payoff profile of a lookback option is continuous.

Assigned Reading:

John Hull, Options, Futures, and Other Derivatives, 6th ed. (New York: Prentice Hall, 2002), Chapter 22.

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