# ANNUALIZERISK

## Description

If we assume that assets' time series instantaneous rates of returns are normally distributed, then its discrete returns are lognormally distributed. To account for this, we annualize measures of risk by converting the discrete means and standard deviations into its continuous counterparts prior to annualization.

{% hint style="info" %}
To read more about the mathematics behind this, please see <https://wpahelp.windhamlabs.com/expected-risk/annualizing-volatility-and-return>
{% endhint %}

## Syntax

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

```excel-formula
=ANNUALIZERISK(mu, sigma, dataPeriodicity)
```

### Input(s)

| Argument            | Description                                                                                                                                                                                    |
| ------------------- | ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
| **mu**              | Required. Vector or time series matrix of discrete asset returns.                                                                                                                              |
| **sigma**           | Required. Vector of risk estimates to be annualized.                                                                                                                                           |
| **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)

Vector of annualized risk estimates.

## Example

![](https://258561627-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MK66-MGuoULhqCDXLwy%2F-ML9GsEK2JXm2MqRSh7k%2F-ML9Zx6YLLYyevd_8MfG%2Fimage.png?alt=media\&token=e1eb8a54-4c8f-476a-9ad3-e85532f9b063)

{% file src="<https://258561627-files.gitbook.io/~/files/v0/b/gitbook-legacy-files/o/assets%2F-MK66-MGuoULhqCDXLwy%2F-MQV8ZNqGqhwdgFRnCZ0%2F-ML9_1hApx1QMCOd7sQQ%2FANNUALIZERISK.xlsx?alt=media&token=e1e7f088-fb49-4eeb-859c-6027c86d8a66>" %}
Example Workbook: ANNUALIZERISK
{% endfile %}