# Quiet and Turbulent Risk

A risk model for statistically partitioning returns into regimes.

These risk regime methodologies draw on user defined parameters and Windham’s proprietary turbulence methodology to partition historical returns into distinct samples that are characteristic of turbulent and quiet periods.

Turbulent periods are identified by statistically unusual asset movements within a specified date range. These periods are usually marked by large asset movements (volatility) and/or unusual changes in correlations (e.g. when non-correlated assets become correlated).

The Windham Portfolio Advisor uses a multivariate vector distance to isolate periods in which returns are unusual either in their magnitude or in their interaction with each other. For example, a period may qualify as unusual because two assets whose returns are typically positively correlated generate returns that move in the opposite direction.

These periods with unusual returns represent statistical outliers, and they are typically associated with turbulent markets. We create a sub-sample of these outliers and estimate volatilities and correlations from these turbulent sub-samples. We also estimate volatilities and correlations from the remaining returns, which we associate with quiet markets.

To identify outliers, one must also identify a tolerance boundary that divides inliers from outliers, or the turbulence threshold. In the software, the turbulence threshold is a user defined metric. For more information, see “Setting the Turbulence Threshold.”

Clients can then choose to work with either the turbulent or quiet subsample exclusively, or with a blend of the two. For more information on setting parameters for the quiet-turbulent blend model, see “Setting the Turbulent Blend Probability.”

Risk regime analysis has several uses. By evaluating exposure to loss during turbulent conditions, investors can stress test portfolios and construct portfolios that are more resilient to turbulent markets. These methodologies also allow investors to shift the risk profiles of their portfolios depending on their views regarding the likelihood of turbulent or quiet market conditions.

### Turbulent Threshold

The turbulent threshold specifies the percentage of periods that will be classified as outliers, under a multivariate Gaussian assumption. We convert this threshold using the chi-squared inverse function.

For example, if a user selects a threshold of 20% and is working with a multivariate normal sample, the 20% most statistically unusual periods will be classified as turbulent. The remaining 80% of the periods will be classified as quiet. This parameter applies to quiet, turbulent, and quiet-turbulent blend methodologies.

### Blend Probability

The turbulent blend probability allows clients to select the weight that will be given to the turbulent subsample. This is useful if a client believes that turbulent periods will be more prevalent in the future or wants to construct a portfolio more resilient to market turbulence.

For example, if a client selects 40% for the blend probability, then the turbulent subsample will be weighted at 40%, relative to a 60% weighting for the quiet subsample. If the turbulent threshold for this analysis is set at 20%, then a subsample consisting of the top 20% of unusual returns will be given a 40% weighting.

## FAQ

### Identifying Turbulent Periods

How can I identify periods that are marked as turbulent after exporting the turbulence index data (time series) from the Windham Software into Excel?

First, determine the turbulent threshold value by calculating the chi-squared score using the following equation in Excel:

The probability parameter is the same value as specified as the Turbulent Threshold in the risk estimation screen of the Windham Software. The number of assets is equivalent to the number of instruments selected in the Windham Software case file.

The turbulence index values that are strictly greater than the calculated chi-squared score are marked as turbulent periods. Once these turbulent periods are identified, the partitioned subsample is used for estimating standard deviation and correlation.

### Missing Data

I am running an analysis using eight asset classes dating back to January 1999 with monthly data. One of the asset classes dates back to January 2006. I am using Maximum Likelihood Estimation (MLE) option on the estimation screens. When I look at “Quiet-Turbulent Regime” tab, the chart only shows data from 2006 to the present.

How can I make sure the software takes into account the whole period from January 1999 to the present when considering the quiet/turbulent regime?

The turbulence index can only be calculated for overlapping data series. MLE only provides a statistical approximation of the cumulative historical return, risk, and correlations. It will NOT create or populate missing data points (which would be required to identify turbulent periods).

To calculate the turbulent index for the full intended period, it is recommended to remove the asset class with the short history (i.e. 2006 - present asset class). For more robust results, you can also replace the most recent asset with a similar proxy that has a longer history.

## Endmatter

### Research paper

The following published research article in the Financial Analyst Journal describes portfolio construction using risk regime in detail.

### Video

This video introduces a method to partition historical returns into those that are associated with quiet periods and those that reflect market turbulence.

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