Describe different ways of choosing probability distributions in creating simulation models. Describe the relationship between the accuracy of a simulation model and the number of scenarios run in the simulation. Understand and interpret the results generated by Monte Carlo simulation.
Questions:
400.1. Barbara the Analyst has been tasked to chose a univariate probability distribution in order to create a simulation model of future market returns. One of her key steps utilizes the chi-square distribution. Among the following four methods reviewed by Pachamanova and Fabozzi, which approach is she most likely using?
a. Bootstrapping
b. Assume a distribution, then use historical data to estimate parameters
c. Use historical data to find a distribution
d. Ignore the past and look forward with a subjective choice of distribution
400.2. Peter the Analyst has generated 800 independent scenarios of future single-period portfolio values. He observes the mean (average) of his simulated output distribution and determines a 95.0% confidence interval with a length of approximately $300.00; i.e., length is the difference between the upper and lower bound of the confidence interval. Peter's manager wants him to increase the accuracy of his estimate of the population's mean by reducing the length of the confidence interval to about $60.00. How many scenarios should Peter run?
a. 800; no change in trials but increase the confidence level
b. 4,000
c. 7,200
d. 20,000
400.3. According to Pachamanova and Fabozzi each of the following is true about understanding and interpreting the results generated by Monte Carlo simulation, except which is false?
a. A simulation model applies an input probability distribution(s) to a deterministic model in order to generate many scenarios (a.k.a., trials) which produce output variables and the corresponding output probability distribution
b. Despite several advantages, the key weakness (drawback) of simulations is an inability to generate statistical measures of central tendency and volatility for the output probability distribution
c. Simulation is similar to statistical sampling in that we try to represent uncertainty by generating scenarios, that is, “sampling” values for the output parameter of interest from an underlying probability distribution
d. The simulated output's minimum and the maximum are highly sensitive to the number of simulated values and whether the simulated values in the tails of the distribution provide good representation for the tails of the distribution
Answers here:
Questions:
400.1. Barbara the Analyst has been tasked to chose a univariate probability distribution in order to create a simulation model of future market returns. One of her key steps utilizes the chi-square distribution. Among the following four methods reviewed by Pachamanova and Fabozzi, which approach is she most likely using?
a. Bootstrapping
b. Assume a distribution, then use historical data to estimate parameters
c. Use historical data to find a distribution
d. Ignore the past and look forward with a subjective choice of distribution
400.2. Peter the Analyst has generated 800 independent scenarios of future single-period portfolio values. He observes the mean (average) of his simulated output distribution and determines a 95.0% confidence interval with a length of approximately $300.00; i.e., length is the difference between the upper and lower bound of the confidence interval. Peter's manager wants him to increase the accuracy of his estimate of the population's mean by reducing the length of the confidence interval to about $60.00. How many scenarios should Peter run?
a. 800; no change in trials but increase the confidence level
b. 4,000
c. 7,200
d. 20,000
400.3. According to Pachamanova and Fabozzi each of the following is true about understanding and interpreting the results generated by Monte Carlo simulation, except which is false?
a. A simulation model applies an input probability distribution(s) to a deterministic model in order to generate many scenarios (a.k.a., trials) which produce output variables and the corresponding output probability distribution
b. Despite several advantages, the key weakness (drawback) of simulations is an inability to generate statistical measures of central tendency and volatility for the output probability distribution
c. Simulation is similar to statistical sampling in that we try to represent uncertainty by generating scenarios, that is, “sampling” values for the output parameter of interest from an underlying probability distribution
d. The simulated output's minimum and the maximum are highly sensitive to the number of simulated values and whether the simulated values in the tails of the distribution provide good representation for the tails of the distribution
Answers here: