cyber21

Monte Carlo simulation is necessary to:

A) reduce sampling error.

B) compute continuously compounded returns.

C) approximate solutions to complex problems.

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This is the purpose of this type of simulation. The point is to construct distributions using complex combinations of hypothesized parameters.

cyber21

In which of the following cases would Monte Carlo simulation least likely be needed? Payoff of a:

A) GNME.

B) roulette wheel.

C) European option.

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The probability distribution of a roulette wheel would be easy to estimate using empirical or a priori methodology.

cyber21

A multivariate distribution:

A) specifies the probabilities associated with groups of random variables.

B) applies only to binomial distributions.

C) gives multiple probabilities for the same outcome.

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This is the definition of a multivariate distribution.

cyber21

In addition to the usual parameters that describe a normal distribution, to completely describe 10 random variables, a multivariate normal distribution requires knowing the:

A) overall correlation.

B) 10 correlations.

C) 45 correlations.

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The number of correlations in a multivariate normal distribution of n variables is computed by the formula ((n) × (n-1)) / 2, in this case (10 × 9) / 2 = 45.

cyber21

A multivariate distribution is best defined as describing the behavior of:

A) two or more independent random variables.

B) a random variable with more than two possible outcomes.

C) two or more dependent random variables.

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A multivariate distribution describes the relationships between two or more random variables, when the behavior of each random variable is dependent on the others in some way.

cyber21

In a multivariate normal distribution, a correlation tells the:

A) relationship between the means and variances of the variables.

B) overall relationship between all the variables.

C) strength of the linear relationship between two of the variables.

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This is true by definition. The correlation only applies to two variables at a time.

cyber21

A multivariate normal distribution that includes three random variables can be completely described by the means and variances of each of the random variables and the:

A) correlation coefficient of the three random variables.

B) conditional probabilities among the three random variables.

C) correlations between each pair of random variables.

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A multivariate normal distribution that includes three random variables can be completely described by the means and variances of each of the random variables and the correlations between each pair of random variables. Correlation measures the strength of the linear relationship between two random variables (thus, "the correlation coefficient of the three random variables" is inaccurate).

cyber21

Which of the following would least likely be categorized as a multivariate distribution?

A) The return of a stock and the return of the DJIA.

B) The days a stock traded and the days it did not trade.

C) The returns of the stocks in the DJIA.

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The number of days a stock traded and did not trade describes only one random variable. Both of the other cases involve two or more random variables.

cyber21

Joan Biggs, CFA, acquires a large database of past returns on a variety of assets. Biggs then draws random samples of sets of returns from the database and analyzes the resulting distributions. Biggs is engaging in:

A) Monte Carlo simulation.

B) historical simulation.

C) discrete analysis.

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This is a typical example of historical simulation.

cyber21

Many analysts prefer to use Monte Carlo simulation rather than historical simulation because:

A) computers can manipulate theoretical data much more quickly than historical data.

B) past distributions cannot address changes in correlations or events that have not happened before.

C) it is much easier to generate the required variables.

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While the past is often a good predictor of the future, simulations based on past distributions are limited to reflecting changes and events that actually occurred. Monte Carlo simulation can be used to model based on parameters that are not limited to past experience.