# QUIETRISK

A robust statistical risk model using the Mahalanobis distance.

## 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 quiescence. Turbulent 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. Conversely, quiescent periods are market by subdued asset movements (lower volatility) and/or lower correlation surprises and are considered statistical inliers.

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

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

## Syntax

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

### Input(s)

Argument | Description |
---|---|

| Required. Enumeration string to specify calculation type: "risk", "sigma", or "stdev" "correlation", "corr", or "rho" "covariance", "covar", or "cov" |

| Required. Time series or matrix of asset returns. |

| Required. Probability threshold of quiet 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 inliers (quiet). This approximation may vary depending on the underlying characteristics of the empirical data. |

| Optional. Periodicity of the data, used for annualization. If you do not enter the argument, it defaults to 1. e.g. Daily = 255, Monthly = 12, Yearly = 1, Quarterly = 4. |

### 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

The following video describes the conceptual application of the methodology.

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