1. The Markov property of stock prices is consistent with which form of market efficiency?

A. Constant

B. Semi-strong

C. Strong

D. Weak

2. When can you use the Normal distribution to approximate the Poisson distribution, assuming you have "n" independent trials each with a probability of success of "p"?

A. When the mean of the Poisson distribution is very small.

B. When the variance of the Poisson distribution is very small. 

C. When the number of observations is very large and the success rate is close to 1.

D. When the number of observations is very large and the success rate is close to 0.

3. There are several approaches to forecasting operational risk losses. Which of the following alternatives cannot be used to forecast a typical operational loss?

A. GARCH models

B. Factor-based models

C. Loss scenario models

D. Statistical/Actuarial models

4. Let Z be a standard normal random variable. An event X is defined to happen if either z takes a value between ?1 and 1 or z takes any value greater than 1.5. What is the probability of event X happening if N(1) = 0.8413, N(0.5) = 0.6915 and N(-1.5) = 0.0668, where N() is the cumulative distribution function of a standard normal variable?

A. 0.083

B. 0.2166

C. 0.6826

D. 0.7494

5. Exporters are affected in different ways due to movement in foreign currency value with the base of domestic currency. Which of the following situations provides the maximum benefit to an Exporter?

A. Exporter of goods with elastic demand as the value of foreign currency rises.

B. Exporter of goods with inelastic demand as the value of foreign currency falls. 

C. Exporter of goods with inelastic demand as the value of foreign currency rises. 

D. Exporter of goods with elastic demand as the value of foreign currency falls. 

1. The Markov property of stock prices is consistent with which form of market efficiency?

A. Constant

B. Semi-strong

C. Strong

D. Weak

Correct answer is Dfficeffice" />

D is correct. The Markov process assumes that only the present value of a variable is relevant for predicting the future.  The present value of the stock incorporates all past history.  The probability distribution of the price at any future time is not dependent on the path followed by the stock price in the past.  Competition ensures that this holds true.

Reference: John Hull, Options, Futures, and Other Derivatives, 6th ed. Chapter 12.

INCORRECT: A

There is no constant form of market efficiency.

INCORRECT: B

The semi-strong form of market efficiency implies today's price of a stock reflects all public information about that stock, which is stronger than the Markov property which states that only the present value of a variable is relevant for predicting the future.

INCORRECT: C

The strong form of market efficiency implies today's price of a stock reflects all information about that stock, which is stronger than the Markov property which states that only the present value of a variable is relevant for predicting the future.

2. When can you use the Normal distribution to approximate the Poisson distribution, assuming you have "n" independent trials each with a probability of success of "p"?

A. When the mean of the Poisson distribution is very small.

B. When the variance of the Poisson distribution is very small. 

C. When the number of observations is very large and the success rate is close to 1.

D. When the number of observations is very large and the success rate is close to 0.

Correct answer is C

The Normal distribution can approximate the distribution of a Poisson random variable with a large lambda parameter (λ).  This will be the case when both the number observations (n) is very large and the success rate (p) is close to 1 since Λ = n*p. 

INCORRECT: A

The mean of a Poisson distribution must be large to allow approximation with a Normal distribution.

INCORRECT: B

The variance of a Poisson distribution must be large to allow approximation with a Normal distribution.

INCORRECT: D

The Normal distribution can approximate the distribution of a Poisson random variable with a large lambda parameter (λ).  But since λ = n*p, where n is the number observations and p is the success rate λ will not be large if p is close to 0.

3. There are several approaches to forecasting operational risk losses. Which of the following alternatives cannot be used to forecast a typical operational loss?

A. GARCH models

B. Factor-based models

C. Loss scenario models

D. Statistical/Actuarial models

Correct answer is A

A is correct. GARCH models forecast volatility where the variance rate follows a mean-reverting process.

B is incorrect. Loss scenario models are used to forecast operational losses.

C is incorrect. Statistical/actuarial models are used to forecast operational losses.

D is incorrect. Factor-based models are used to forecast operational losses.

4. Let Z be a standard normal random variable. An event X is defined to happen if either z takes a value between ?1 and 1 or z takes any value greater than 1.5. What is the probability of event X happening if N(1) = 0.8413, N(0.5) = 0.6915 and N(-1.5) = 0.0668, where N() is the cumulative distribution function of a standard normal variable?

A. 0.083

B. 0.2166

C. 0.6826

D. 0.7494

Correct answer is D

et A be the event that z takes a value between 1 and ?1 and B be the event that z takes a value greater than 11/2 . The probability of z being between 1 and ?1 is the area under the standard normal curve between 1 and   -1. From the properties of a standard normal distribution, we know that:

N(-1) = 1.0 - N(1) = 1.0 ? 0.8413 = 0.1587

Therefore, the probability of z being between 1 and ?1 = P(A) =  N(1) - N(-1) = 0.6826

The probability of z being greater than 11/2  = P(B) = 1 - N(11/2) = N(-11/2) = 0.0668

Event X = A U B and P(X) = P(A) + P(B) since A and B are mutually exclusive.

Hence, P(X) = 0.7494

5. Exporters are affected in different ways due to movement in foreign currency value with the base of domestic currency. Which of the following situations provides the maximum benefit to an Exporter?

A. Exporter of goods with elastic demand as the value of foreign currency rises.

B. Exporter of goods with inelastic demand as the value of foreign currency falls. 

C. Exporter of goods with inelastic demand as the value of foreign currency rises. 

D. Exporter of goods with elastic demand as the value of foreign currency falls. 

Correct answer is C

A is incorrect.  Exporters will gain on payment for existing foreign currency dues in terms of domestic currency.  However, as demand of the goods is elastic, Importers in foreign country may find another buyer or a substitute of it domestically.  Hence, in quantity terms, the sales may decline over the period or else price may need to be reduced to maintain quantity sale.  Hence, maximization of gain may not be achieved.

B is incorrect.  With foreign currency value falling, Exporter will be in a loss as they will be able to realize less in terms of domestic currency.

C is correct. Maximum gain can be achieved when there is favorable situation on both the sides -  Price Realization and Quantity.  Rising foreign currency value will make the export realization more profitable in terms of domestic currency.  An in-elastic demand is favorable to the exporter / seller in terms of quantity sale, as Price need not be reduced significantly. 

D is incorrect.  Falling currency value will reduce the Price Realization to Exporter.

Reference: ffice:smarttags" />Para 8.1, Chapter 8 of Risk Management and Derivatives by Stulz, Rene.