问题如下：
Alicia Maxwell, an analyst for a REIT, is evaluating the potential purchase of a hotel property. She plans to use simulation analysis to estimate the distribution of the property’s annual operating cash flow for the next five years.
Revenue Construction
Maxwell recognizes that annual gross revenue for the property depends on the nightly room rate and the occupancy rate. She believes that the primary driver for the nightly room rate is the Employment Cost Index (ECI) and that the primary driver for the occupancy rate is the Consumer Sentiment Index (CSI). In the process of simulating revenues, she examines the ECI and the CSI quarterly over the past 20 years and their relation to the nightly room rate and occupancy rates of the REIT’s existing properties, respectively. She estimates the following:
Nightly room rate = $23 + 0.9(ECIt–1)
Occupancy rate = 0.25 + 0.7(CSIt–1)
Occupancy rates are assumed to be non-negative and cannot exceed 100%.
Maxwell generates 10,000 trials of the ECI and CSI based on the historical mean level of the indexes and their monthly standard deviations. Although the distribution of historical CSI is not symmetric, she assumes that both ECI and CSI are normally distributed. Maxwell is aware that if the inputs are correlated, this may present a problem. She also observes that the CSI and the ECI are correlated with one another and that the relation between the CSI and the occupancy rate is stronger than that between the ECI and nightly room rates. Maxwell estimates the corresponding nightly room rate and the occupancy rate based on these historical relations, multiplies these by the number of hotel nights in a year, and generates 10,000 estimates of annual gross revenue.
Expense Assumptions
Maxwell examines current expenses for the REIT’s other hotel properties and selects the distributions for the simulation of operating expenses and management fees. Maxwell estimates operating expenses to be uniformly distributed between 68% and 70% of revenues and that the property management fee for the hotel is uniformly distributed between 5.9% and 6.1% of total annual revenue.
Simulation Results and Analysis
Maxwell has three concerns regarding the results from the simulation trials:
Concern 1: Although the distribution of historical CSI is slightly skewed, Maxwell uses the normal distribution to simulate the monthly CSI.
Concern 2: Property management firms may demand higher property management fees (that is, a higher percentage of revenue) when the CSI is lower
Concern 3: When comparing the distribution of CSI over the past 20 years with those of the past 30 years, she notices a substantial difference in the mean and standard deviation of the CSI distribution.
Which of Maxwell’s three concerns can be best described as being attributable to non-stationary distributions?
选项：
A. Concern 1
B. Concern 2
C. Concern 3
解释：
C is correct. A substantial difference in the mean and standard deviation of CSI over the past 20 years relative to those of the past 30 years suggests a change in (i.e., non-stationary) distribution. Even when the data fits a statistical distribution or when historical data distributions are available, shifts in the market structure may lead to shifts in the distributions as well, as evidenced by the shift between the 20- and 30-year distributions of CSI. In some cases, such shifts can change the form of the distribution and in other cases, they can change the parameters of the distribution.
A is incorrect because Concern 1 is a description of real data not fitting distributions. The problem with the real world is that the data seldom fits the stringent requirements of statistical distributions. Using probability distributions that bear little resemblance to the true distribution underlying an input variable will yield misleading results.
B is incorrect because Concern 2 is an issue of correlation that is not incorporated into the simulation. Correlation across input variables can be modeled into simulations. This works only if the correlations remain stable and predictable, however. To the extent that correlations between input variables change over time, as is expressed in Concern 2, it becomes far more difficult to model them.
