# Monte Carlo Analysis Excel

## Monte Carlo Analysis Excel Benötigen Sie weitere Hilfe?

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In the science and engineering communities, MC simulation is often used for uncertainty analysis , optimization , and reliability-based design.

In manufacturing, MC methods are used to help allocate tolerances in order to reduce cost. There are certainly other fields that employ MC methods, and there are also times when MC is not practical for extremely large problems, computer speed is still an issue.

However, MC continues to gain popularity, and is often used as a benchmark for evaluating other statistical methods. This article will guide you through the process of performing a Monte Carlo simulation using Microsoft Excel.

Although Excel will not always be the best place to run a scientific simulation, the basics are easily explained with just a few simple examples.

If you frequently use Excel for modeling, whether for engineering design or financial analysis, I highly suggest one of the Excel add-ins listed below.

The popularity of Monte Carlo methods have led to a number of superb commercial tools. The programs listed below work directly with Excel as add-ins.

Crystal Ball and Risk are the two most popular and are very high quality which you would expect from the price. Risk Solver is an amazing new add-in created by the makers of the famous Excel Solver add-in.

Risk Solver runs at lightning speed and certainly rivals Crystal Ball and Risk. Meredith, Scott M. Anderson, Dennis J. Sweeney, Thomas A.

Powell, Dartmouth College, and Kenneth R. For each return cell in the spreadsheet column D , we use the random function NormalValue :.

In figure B, the return in each period has been changed from a fixed 5. The returns in each period are randomly generated.

If you recalculate the model at this step, you will see each return change. The total return F11 can also differ significantly from the original value The key to using Monte Carlo simulation is to take many random values, recalculating the model each time, and then analyze the results.

A Monte Carlo simulation calculates the same model many many times, and tries to generate useful information from the results.

This is because the simulation hasn't collected data for the cell yet. Once you run a simulation, this error will go away. In this example, cell H11 calculates the average value of cell F11 over all the trials, or iterations, of the Monte Carlo simulation.

When you run a Monte Carlo simulation, at each iteration new random values are placed in column D and the spreadsheet is recalculated.

This results in a different value in cell F Once the simulation is complete, the average value can be calculated from this set of stored values.

As noted above, the average return given by the Monte Carlo simulation is close to the original, fixed model. However, we can get much more useful information from the Monte Carlo simulation by looking at ranges and percentiles.

To begin with, we can look at the minimum and maximum values identified during the simulation using the SimulationMin and SimulationMax functions:.

In Figure D, cell I11 contains the minimum value of cell F11 seen during the simulation. This is significantly worse then the average, and represents the risk contained in the portfolio model.

Looking at the absolute minimum and maximum values tends to overstate the outliers, or tails, of the possible outcomes of the portfolio model.

We can also look at percentile probabilities, using the SimulationPercentile function:. To understand what the percentiles mean, imagine that we take every result seen in cell F11 over the Monte Carlo simulation, and place them in order lowest to highest.

The first value would be the minimum, as seen above; no values in the results are lower than the minimum value.

Therefore the maximum value is the th Percentile. By changing the percentile values, we can determine the expected return of the portfolio with different probabilities.

This kind of analysis can be useful in determining the real levels of risk associated with an investment portfolio.

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## Monte Carlo Analysis Excel Video

In this example, cell H11 calculates the average value of cell F11 over all the trials, or iterations, of the Monte Carlo simulation.

When you run a Monte Carlo simulation, at each iteration new random values are placed in column D and the spreadsheet is recalculated.

This results in a different value in cell F Once the simulation is complete, the average value can be calculated from this set of stored values.

As noted above, the average return given by the Monte Carlo simulation is close to the original, fixed model. However, we can get much more useful information from the Monte Carlo simulation by looking at ranges and percentiles.

To begin with, we can look at the minimum and maximum values identified during the simulation using the SimulationMin and SimulationMax functions:.

In Figure D, cell I11 contains the minimum value of cell F11 seen during the simulation. This is significantly worse then the average, and represents the risk contained in the portfolio model.

Looking at the absolute minimum and maximum values tends to overstate the outliers, or tails, of the possible outcomes of the portfolio model.

We can also look at percentile probabilities, using the SimulationPercentile function:. To understand what the percentiles mean, imagine that we take every result seen in cell F11 over the Monte Carlo simulation, and place them in order lowest to highest.

The first value would be the minimum, as seen above; no values in the results are lower than the minimum value. Therefore the maximum value is the th Percentile.

By changing the percentile values, we can determine the expected return of the portfolio with different probabilities. This kind of analysis can be useful in determining the real levels of risk associated with an investment portfolio.

Instead of finding the expected return at different percentiles, we can turn the analysis around and find the probability of reaching a particular target return with the SimulationInterval function:.

This kind of analysis can be useful in determining confidence levels. For example, in evaluating alternative investments, we can compare the probabilities of reaching certain minimum returns.

The above discussion describes converting a simple fixed portfolio model into a Monte Carlo simulation, and the kinds of analysis that can be done with a Monte Carlo simulation.

This is a very simple example; many different analysis functions are available, and there are many different ways to generate random data in a model.

Of course any analysis is only as good as the model and the data that are entered. This model is very simple in that it ignores investment costs and inflation.

The model is also very sensitive to the mean and standard deviation of our expected return. By using a Monte Carlo simulation, and with some basic analysis of the results, we have a lot more detailed information about the possible outcomes of this portfolio.

This will allow you to concentrate on how to adapt the Monte Carlo method to your own company. Again, the problem with this approach is that we know the forecast will be incorrect, because most forecasts are incorrect, and we have no way to express how far wrong the profit forecast might reasonably be.

This table translates our four key assumptions into five results that we can use for each iteration of our forecast. To calculate a random number from a normal curve of potential sales, we need to know the mean and standard deviation of our sales curve.

If you can calculate those values directly, you could enter them into cells E5 and F5 directly. However, the yellow cells illustrate a less rigorous way to find these numbers, a way that works pretty well.

Therefore, if we estimate the highest-feasible amount of sales, we could say that the number represents the second standard deviation above the mean, and enter it in cell C5 in the Stats Table, repeated below.

And we could say that our estimate of the lowest-feasible amount of sales represents the second standard deviation below the mean, and enter that number in cell D5 in the table.

And the standard deviation is merely one-fourth the range between the max and min values, as calculated by this formula:.

And now, we need Excel to return a random number from the normal distribution that's defined by the mean value in cell E5 and the standard deviation in cell F5.

To do so, we use this formula:. Now copy the range E5:H5 downward, as shown in the table. Then enter the labels shown in column I.

To assign these labels as names for the adjacent cells in column H, first select the range H5:I8. For convenience, these four names begin with "c.

Because Excel sorts names alphabetically in most lists, this will group those four names together in those lists, so you can find them easily.

Also, when we use these names in formulas, we'll have no doubt that they came from the Current Results section of the Stats Table.

This figure illustrates the model we'll use. To create this figure, add a new worksheet to your Monte Carlo workbook, and name the worksheet Model.

Finally, to finish the figure, use the Create Names dialog to assign the labels in columns E to the cells on their left, and then do the same for column H.

Notice that each time you recalculate your workbook, the model generates different results. We now need to capture those results automatically for many recalculations.

We're now going to set up a Data Table. This table will automatically recalculate Excel, return the values for the items named in row 2 of this figure, record those values in row 4, recalculate, record the current items in row 5, and so on Then enter the labels, which are shown in bold in the preceding figure.

It's now time to set up the Data Table. After you do so, Excel will calculate the workbook times, because the Data Table will contain rows.

Each row of the completed table will contain the values returned to row 3 of the figure after each calculation. Before you start your Data Table, however, set your calculation option to manual.

By taking this step, make sure that your Data Table will calculate only when you press the F9 key or save your workbook. Now, to set up the table so that it displays results that start in cell C4 of the figure below Strictly speaking, Data Tables are intended to enter a value into either one or two cells that your model uses for each calculation.

But in this case, your model ignores the values entered in the empty cell. Instead, it merely recalculates the model each time a new value is written.

The model's values change each time because of the random numbers that the model contains. And then the Data Table captures the results we've specified using the formulas in row 3.

Here's the top of the completed Data Table. So that we can reference the columns of this table easily, we need to name them.

To name the columns, we can't use the Create Names dialog because we need to exclude row 3 from the defined names.

Now repeat this process for the other columns shown in the figure above, from Sales through the TaxRate. To begin, enter the labels shown in this figure.

Then use the Create Names dialog to assign the labels in the range I1:I3 to the cells on their right. Then do the same with the labels in the range M1:M2.

The Seq Sequence columns, beginning in cells I7 and M7, count the number of bins into which we want to summarize our data.

Use the Series dialog Home, Editing, Fill, Series to set up a series from 1 through 21 for both sets of sequences.

The two Frequency sections at the bottom of the figure above generate the data we'll use for the histograms in our report. The ProfBins column contains data that defines the beginning and ending values for the profit bins.

Here are the first two formulas in this column:. Copy the formula in cell J8 downward to cell J Notice that the value in cell J27 approximately equals the MaxProfits value.

Now select the range J6:K27 and use the Create Names dialog to assign the labels at the top of this range as the names for the two columns.

Copy the formula in cell N8 downward to cell N The value in cell N27 should approximately equal the MaxSales value. And as before, select the range N6:O27 and assign the labels at the top of the selection to the two columns below the top row in the selection.

Now hold down Ctrl and Shift and then press Enter. This key combination array-enters the formula in the selected range. And this formula returns the number of values in the Profits range that fall into each bin in the ProfBins range.

Now, with our results summarized, we must take one more step before we can create our Monte Carlo forecast. Now enter the labels shown in column L, next to the values. Why do I need to sign up with LinkedIn? Wie Funktioniert Western Union cell J11, you compute Deutsche Wettanbieter lower limit for the 95 percent confidence interval on mean profit when 40, calendars are produced with the formula D13—1. It can also be used to understand how risk works, and to comprehend the uncertainty in forecasting models. Of course any analysis is only as good as the model and the data that are entered. Running thousands of iterations or simulations of these curve may give you some insights. To find Em 2026 curves, to go the Statistical Functions within your Excel workbook and investigate.