# TURBULENTRISK

## Description

Using the Mahalanobis distance, this risk model characterizes the degree of unusualness in a cross section of asset returns and partitions the historical data into periods of financial turbulence and quiecense. These periods are usually marked by large asset movements (volatility) and/or unusual changes in correlations (e.g. when non-correlated assets become correlated) and considered statistical outliers.

The risk model is useful for stress testing and constructing resilient portfolios.

{% hint style="info" %}
This risk model is also available in the Windham Portfolio Advisor. For a deeper dive into the model, please see <https://wpahelp.windhamlabs.com/expected-risk/quiet-and-turbulent-risk>
{% endhint %}

## Syntax

The following describes the function signature for use in Microsoft Excel's formula bar.

```excel-formula
=TURBULENTRISK(type, assetReturns, threshold, dataPeriodicity)
```

### Input(s)

| Argument            | Description                                                                                                                                                                                                                                                                                                                                                                                                       |
| ------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **type**            | <p>Required. Enumeration string to specify calculation type:<br>   "risk", "sigma", or "stdev"<br>   "correlation", "corr", or "rho", <br>   "covariance", "covar", or "cov"</p>                                                                                                                                                                                                                                  |
| **assetReturns**    | Required. Time series or matrix of asset returns.                                                                                                                                                                                                                                                                                                                                                                 |
| **threshold**       | Required. Probability threshold of turbulent periods (0.00 - 1.00). This threshold is the converted into the equivalent chi-squared,$$\chi\_{N}^2$$, score. Under a multivariate normal assumption, the cutoff can be interpreted as an approximation of the percentage of the sub-sample of outliers (turbulent). This approximation may vary depending on the underlying characteristics of the empirical data. |
| **dataPeriodicity** | <p>Optional. Periodicity of the data, used for annualization. If you do not enter the argument, it defaults to 1. <br><em>e.g. Daily = 255, Monthly = 12,  Yearly = 1, Quarterly = 4.</em></p>                                                                                                                                                                                                                    |

### Output(s)

Depending on the specified output *type*, the function will return the respective vector of risk estimates (annualized standard deviations), correlation matrix, or a covariance matrix.

## Example

![](https://258561627-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MK66-MGuoULhqCDXLwy%2F-ML9dRbWbwW2SVWdnYpe%2F-ML9nbPdbg6SDVajlh8J%2Fimage.png?alt=media\&token=9c7c896d-11ee-42ac-b238-ffce8f8fa2bb)

{% file src="<https://258561627-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MK66-MGuoULhqCDXLwy%2F-MQVC6qUEDTtxolmHdXn%2F-ML9nw7N3O1nehODTWjB%2FTURBULENTRISK.xlsx?alt=media&token=ee8f4b23-d3e1-4a02-bf2c-ef6218f18037>" %}
Example Workbook: TURBULENTRISK
{% endfile %}

The following video describes the conceptual application of this methodology.

{% embed url="<https://windhamcapital.wistia.com/medias/ti6fqxaqxf>" %}
Windham's Risk Model
{% endembed %}