## Documentation |

This example performs a Monte Carlo simulation of a number of stocks in a portfolio. At a given confidence level, we predict the value at risk (VaR) of the portfolio as well as the marginal value at risk (mVaR) of each of the stocks in the portfolio. We also provide confidence intervals for our estimates.

For details about the computations, view the code for pctdemo_setup_mvarview the code for pctdemo_setup_mvar.

Prerequisites:

Related examples:

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**Load the Example Settings and the Data**

We start by getting the example difficulty level. If you want to use a different example difficulty level, use `paralleldemoconfig` and then run this example again. See Customizing the Settings for the Examples in the Parallel Computing Toolbox for full details.

difficulty = pctdemo_helper_getDefaults();

We obtain the performance of the stocks, their weights in our portfolio, and other input data from `pctdemo_setup_mvar`. The number of repetitions, `numTimes`, is determined by the `difficulty` parameter. You can view the code for pctdemo_setup_mvarview the code for pctdemo_setup_mvar for full details.

```
[fig, numSims, numTimes, stock, names, weights, time, confLevel] = ...
pctdemo_setup_mvar(difficulty);
```

Let's look at the confidence level at which we are calculating the VaR and mVaR.

fprintf('Calculating VaR and mVaR at the %3.1f%% confidence level.\n', ... confLevel); startTime = clock;

Calculating VaR and mVaR at the 95.0% confidence level.

We perform `numSims` simulations `numTimes` times. This allows us to make predictions on the VaR and mVaR, as well as to compute the confidence intervals. You can view the code for pctdemo_task_mvarview the code for pctdemo_task_mvar for full details.

```
[VaR, mVaR] = pctdemo_task_mvar(numTimes, stock, weights, time, ...
numSims, confLevel);
```

The time used for the sequential computations should be compared against the time it takes to perform the same set of calculations using the Parallel Computing Toolbox in the Distributed Marginal Value-at-Risk Simulation example. The elapsed time varies with the underlying hardware.

```
elapsedTime = etime(clock, startTime);
fprintf('Elapsed time is %2.1f seconds\n', elapsedTime);
```

Elapsed time is 11.2 seconds

We use `pctdemo_plot_mvar` to create a graph of the value at risk of our portfolio at the given confidence level. The graph also shows the marginal value at risk of the individual stocks in our portfolio at that same confidence level. You can view the code for pctdemo_plot_mvarview the code for pctdemo_plot_mvar for full details.

pctdemo_plot_mvar(fig, VaR, mVaR, time, names);

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