Question 1

A correlation matrix must always be symmetric, so that the correlations above the diagonal are a mirror image of those below it.

Accepted Answer

A correlation matrix is always symmetric because the correlation between variable A and variable B is the same as the correlation between variable B and variable A. Therefore, the values above the diagonal must match the values below it.

Question 2

RISKSIMTABLE is a function in @RISK for running several simulations simultaneously, one for each setting of an input or decision variable.

Accepted Answer

The statement is true. RISKSIMTABLE allows for running several simulations simultaneously, one for each setting of an input or decision variable.

Question 3

Oregon State University has reached the final four in the 2016 NCAA Women's Basketball Tournament, and as a result, a sweatshirt supplier in Corvallis is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Oregon State, University of Washington, Syracuse, and University of Connecticut) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.
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Demand distribution at regular price Demand distribution at reduced price
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-Use @RISK simulation add-in to analyze the sweatshirt sales. Do this for the discrete distributions given in the problem.

Accepted Answer

The answer of Oregon State University has reached the final...

Question 4

Suppose that Ms. Smart invests 25% of her portfolio in four different stocks. The mean and standard deviation of the annual return on each stock are shown in the first table below. The correlations between the annual returns on the four stocks are shown in the second table below.
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-(A) Use @RISK with 100 replications, provide a summary statistics of portfolio return; namely, minimum, maximum, mean, and standard deviation.
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(B) Use your answers to (A) to estimate the probability that Mrs. Smart's portfolio's annual return will exceed 20%.
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(C) Use your answers to (A) to estimate the probability that Mrs. Smart's portfolio will lose money during the course of a year.
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(D) Suppose that the current price of each stock is as follows: stock 1: $16; stock 2: $18; stock 3: $20; and stock 4: $22. Ms. Smart has just bought an option involving these four stocks. If the price of stock 1, six months from now are is $18 or more, the option enables Ms. Smart to buy, if she desires, one share of each stock for $20 six months from now. Otherwise the option is worthless. For example, if the stock prices six months from now are: stock 1: $18; stock 2: $20; stock 3: $21; and stock 4: $24, then Ms. Smart would exercise her option to buy stocks 3 and 4 and receive (21- 20) + (24-20) = $5 in each cash flow. How much is this option worth if the risk-free rate is 8%?

Accepted Answer

The answer of Suppose that Ms. Smart invests 25% of...

Question 5

Oregon State University has reached the final four in the 2016 NCAA Women's Basketball Tournament, and as a result, a sweatshirt supplier in Corvallis is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Oregon State, University of Washington, Syracuse, and University of Connecticut) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.
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Demand distribution at regular price Demand distribution at reduced price
​ 
-Use simulation to analyze the supplier's problem. Determine how many sweatshirts he should produce to maximize the expected profit.

Accepted Answer

The answer of Oregon State University has reached the final...

Question 6

It is usually not too difficult to predict the shape of the output distribution from the shape(s) of the input distribution(s).

Accepted Answer

The shape of the output distribution can be significantly different from the input distribution(s) due to the non-linear transformations and interactions within the model or process being applied, making it challenging to predict without specific analysis.

Question 7

Oregon State University has reached the final four in the 2016 NCAA Women's Basketball Tournament, and as a result, a sweatshirt supplier in Corvallis is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Oregon State, University of Washington, Syracuse, and University of Connecticut) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.
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Demand distribution at regular price Demand distribution at reduced price
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-(A) Assume that the weight of each can in a six-pack has a 0.8 correlation with the weight of the other cans in the six-pack. What mean fill quantity (within 0.05 ounce) maximizes expected profit per six-pack?
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(B) If the weights of the cans in the six-pack are probabilistically independent, what mean fill quantity (within 0.05 ounce) will maximize expected profit per six-pack?
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(C) How can you explain the difference in the answers for (A) and (B)?

Accepted Answer

The answer of Oregon State University has reached the final...

Question 8

Which of the following statements are true?
A) The @RISK contains a number of functions such as RISKNORMAL and RISKDISCRETE that make it easy to generate observations from the most important probability distributions.
B) You can specify any cell or range of cells in your simulation model as output cells.
When you run the simulation, @RISK automatically keeps summary measures (averages, standard deviation, percentiles, and others) from the values generated in these output cells across the replications.
C) @RISK has a special function, RISKSIMTABLE, which allows you to run the same simulation several times, using a different value of some key input variable each time.
D) All of these statements are true.

Accepted Answer

All of these statements are true. @RISK contains functions for generating observations from probability distributions, allows any cell or range to be specified as output for summary measures, and has a function for running multiple simulations with different input values.

Question 9

When we maximize or minimize the value of a decision variable by running several simulations simultaneously, we have found an optimal solution to the problem and attitude toward risk becomes irrelevant.

Accepted Answer

Attitude toward risk can still be relevant even when maximizing or minimizing a decision variable through simulations. The decision maker may have to weigh the potential gains and losses of different options and decide on a course of action based on their tolerance for risk.

Question 10

Oregon State University has reached the final four in the 2016 NCAA Women's Basketball Tournament, and as a result, a sweatshirt supplier in Corvallis is trying to decide how many sweatshirts to print for the upcoming championships. The final four teams (Oregon State, University of Washington, Syracuse, and University of Connecticut) have emerged from the quarterfinal round, and there is a week left until the semifinals, which are then followed in a couple of days by the finals. Each sweatshirt costs $12 to produce and sells for $24. However, in three weeks, any leftover sweatshirts will be put on sale for half price, $12. The supplier assumes that the demand (in thousands) for his sweatshirts during the next three weeks, when interest is at its highest, follows the probability distribution shown in the table below. The residual demand, after the sweatshirts have been put on sale, also has the probability distribution shown in the table below. The supplier realizes that every sweatshirt sold, even at the sale price, yields a profit. However, he also realizes that any sweatshirts produced but not sold must be thrown away, resulting in a $12 loss per sweatshirt.
​
Demand distribution at regular price Demand distribution at reduced price
​ 
-Use @RISK simulation add-in to analyze the sweatshirt sales. Do this for normal distributions, where we assume that the regular demand is normally distributed with mean 10,000 and standard deviation 1500, and that the demand at the reduced price is normally distributed with mean 5,000 and standard deviation 1500.

Accepted Answer

The answer of Oregon State University has reached the final...

Question 11

Analysts often plan a simulation so that the confidence interval for the mean of some important output will be sufficiently narrow. The reasoning is that narrow confidence intervals imply more precision about the estimated mean of the output variable.

Accepted Answer

This statement is true. Analysts aim to have narrow confidence intervals as it signifies a more precise estimate of the mean of the output variable.

Question 12

Data tables in spreadsheet simulations are useful for taking a "prototype" simulation and replicating its key results a desired number of times.

Accepted Answer

Data tables can be used to run simulations multiple times with different inputs or scenarios and quickly see the resulting outcomes. This is useful for creating projections, analyzing risks, and testing different strategies.

Question 13

Many companies have used simulation to determine which of several possible investment projects they should choose. This is often referred to as
A) risk analysis
B) @RISK investment
C) unbounded risk
D) risk management

Accepted Answer

The use of simulation to evaluate potential investment projects is a common form of risk analysis. By simulating various scenarios and outcomes, companies can better assess the potential risks and rewards of each investment option. This can help inform their decision-making process and ultimately lead to more successful investments. While @RISK is a specific software program used for simulation and risk analysis, it is not the best choice for this question as it is only one tool among many that can be used for these purposes. Unbounded risk and risk management are related concepts but are not specific to the use of simulation in investment decision making.

Question 14

Different random numbers generated by the computer are probabilistically dependent. This implies that when we generate a random number in a particular cell, it has some effect on the values of any other random numbers generated in the spreadsheet.

Accepted Answer

Different random numbers generated by the computer are probabilistically independent, meaning that the generation of one random number does not affect the generation of another.

Question 15

A correlation matrix must always have 1's along its diagonal (because a variable is always perfectly correlated with itself) and the correlations between variables elsewhere.

Accepted Answer

This statement is true. The diagonal of a correlation matrix always contains 1's because every variable's correlation with itself is perfect (i.e., r=1).

Question 16

Correlation between two random input variables might not change the mean of an output, but it can definitely affect the variability and shape of an output distribution.

Accepted Answer

Correlation between input variables can impact the spread and shape of output distribution through covariance and variances, which in turn can affect the mean or expected value. Therefore, the statement is true.

Question 17

(A) What are the appropriate probability distributions to model the number of faculty members showing up in each lot?
(B) Given the current situation, estimate the probability that on a peak day, at least one faculty member with a sticker will be unable to find a parking space. Assume that the number who shows up at each lot is independent of the number who shows up at the other two lots.
(C) Suppose that faculty members are allowed to park in any lot. Does this help solve the problem? Why or why not?
(D) Suppose that the numbers of faculty who show up at the three lots are correlated, with each correlation equal to 0.80. Does your answer to (C) change? Why or why not?

Accepted Answer

The answer of (A) What are the appropriate probability distributions...

Question 18

Suppose you run a simulation model several times with different order quantities. What can we infer about the the quantity that maximizes the output, the company's profit?
A) This quantity is the optimal order quantity.
B) This quantity might be the optimal order quantity, but we also need to consider the company's attitude toward risk.
C) This is not necessarily the optimal order quantity, because it may have produced the largest profit by luck.
D) We cannot infer anything about the quantity.

Accepted Answer

The simulation model can provide insight into the order quantities that could potentially maximize profit. However, other factors such as the company's risk attitude need to be considered before determining the optimal order quantity. It is important to not solely rely on luck or simulation results without considering other important factors.

Question 19

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds one standard error on either side of the average to obtain an approximate 95% confidence interval.

Accepted Answer

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds 1.96 standard errors on either side of the average to obtain an approximate 95% confidence interval.

Question 20

Suppose you are going to invest equal amounts in three stocks. The annual return from each stock is normally distributed with a mean of 0.01 (1%) and a standard deviation of 0.06. The annual return on your portfolio, the output variable of interest, is the average of the three stock returns. Run @RISK, using 1000 iterations, on each of the scenarios described in the questions below, and report few results from the summary report sheets.
-(A) The three stock returns are highly correlated. The correlation between each pair is 0.9
(B) The three stock returns are practically independent. The correlation between each pair is 0.1
(C) The first two stocks are moderately correlated. The correlation between their returns is 0.4. The third stock's return is negatively correlated with the other two. The correlation between its return and each of the first two is -0.8.
(D) Compare the portfolio distributions from @RISK for the three scenarios in (A), (B) and (C). What do you conclude?
(E) You might think of a fourth scenario, where the correlation between each pair of returns is a large negative number such as -0.80. But explain intuitively why this makes no sense. Try running a simulation with these negative correlations to see what happens.

Accepted Answer

The answer of Suppose you are going to invest equal...

Quiz 15: Introduction to Simulation Modeling

A correlation matrix must always be symmetric, so that the correlations above the diagonal are a mirror image of those below it.

RISKSIMTABLE is a function in @RISK for running several simulations simultaneously, one for each setting of an input or decision variable.

It is usually not too difficult to predict the shape of the output distribution from the shape(s) of the input distribution(s).

Which of the following statements are true?

When we maximize or minimize the value of a decision variable by running several simulations simultaneously, we have found an optimal solution to the problem and attitude toward risk becomes irrelevant.

Analysts often plan a simulation so that the confidence interval for the mean of some important output will be sufficiently narrow. The reasoning is that narrow confidence intervals imply more precision about the estimated mean of the output variable.

Data tables in spreadsheet simulations are useful for taking a "prototype" simulation and replicating its key results a desired number of times.

Many companies have used simulation to determine which of several possible investment projects they should choose. This is often referred to as

Different random numbers generated by the computer are probabilistically dependent. This implies that when we generate a random number in a particular cell, it has some effect on the values of any other random numbers generated in the spreadsheet.

A correlation matrix must always have 1's along its diagonal (because a variable is always perfectly correlated with itself) and the correlations between variables elsewhere.

Correlation between two random input variables might not change the mean of an output, but it can definitely affect the variability and shape of an output distribution.

Suppose you run a simulation model several times with different order quantities. What can we infer about the the quantity that maximizes the output, the company's profit?

A common guideline in constructing confidence intervals for the mean is to place upper and lower bounds one standard error on either side of the average to obtain an approximate 95% confidence interval.