## What is Realized Volatility?

Realized volatility is the assessment of variation in returns for an investment product by analyzing its historical returns within a defined time period. Assessment of degree of uncertainty and/or potential financial loss/gain from investing in a firm may be measured using variability/ volatility in stock prices of the entity. In statistics, the most common measure to determine variability is by measuring the standard deviation, i.e., the variability of returns from the mean. It is an indicator of the actual price risk.

The realized volatility or actual volatility in the market is caused by two components- a continuous volatility component and a jump component, which influence the stock prices. Continuous volatility in a stock market is affected by the intra-day trading volumes. For example, a single high volume trade transaction can introduce a significant variation in the price of an instrument.

Analysts make use of high-frequency intraday data to determine measures of volatility at hourly/daily/weekly or monthly frequency. The data may then be utilized to forecast the volatility in returns.

### Realized Volatility Formula

It is measured by calculating the standard deviation from the average price of an asset in a given time period. Since volatility is non-linear, realized variance is first calculated by converting returns from a stock/asset to logarithmic values and measuring the standard deviation of log normal returns.

The formula of Realized volatility is the square root of realized variance.

Variance in daily returns of the underlying is calculated as follows:

**r**

_{t}= log(P_{t})- log (P_{t-1})- P= stock price
- t= time period

This approach assumes the mean to be set to zero, considering the upside and downside trend in the movement of stock prices.

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Realized variance is calculated by computing the aggregate of returns over the time period defined

where N= number of observations (monthly/ weekly/ daily returns). Typically, 20, 50, and 100-day returns are calculated.

**Realized Volatility (RV) Formula = √ Realized Variance**

The results are then annualized. Realized volatility is annualized by multiplying daily realized variance with a number of trading days/weeks/ months in a year. The square root of the annualized realized variance is the realized volatility.

### Examples of Realized Volatility

#### Example #1

For example, supposed realized volatility for two stocks with similar closing prices is calculated for 20, 50, and 100 days for stock and is annualized with values as follows:

Stock 1 |
Stock 2 |

RV_{100} = 25% |
RV_{100} = 20% |

RV_{50} = 35% |
RV_{50} = 17% |

RV_{20} = 50% |
RV_{20} = 15% |

Looking at the pattern of increasing volatility in the given time frame, it can be inferred that stock-1 has been trading with high variation in prices in recent times (i.e., 20 days), whereas stock-2 has been trading without any wild swings.

#### Example #2

Let us calculate the realized volatility of the dow index for 20 days. Details of the daily stock prices can be extracted in excel format from online sites such as yahoo finance.

The fluctuation in stock prices is depicted in the chart below.

As may be observed, the stock price is on the decline with the maximum price deviation of USD 6.

Deviation in daily returns are calculated as follows:

Variance in daily returns is the square of daily deviations.

The calculation of realized variance for 20 days is the aggregate return for 20 days. And the formula of realized volatility is the square root of realized variance.

In order to make the result compared to other stocks, the value is then annualized.

### Advantages

- It measures the actual performance of an asset in the past and helps to understand the stability of the asset based on its past performance.
- It is an indicator of how an asset’s price has changed in the past and the time period in which it has undergone the change.
- Higher the volatility, the higher the price risk associated with the stock, and therefore higher the premium attached to the stock.
- The realized volatility of the asset may be used to forecast future volatility, i.e., implied volatility of the asset. While entering into transactions with complex financial products such as derivatives, options, etc., the premiums are determined based on the volatility of the underlying and influences the prices of these products.
- It is the starting point for option pricing.
- Realized volatility is measured based on statistical methods and is, therefore, a reliable indicator of the volatility in asset value.

### Disadvantages

It is a measure of historical volatility and is therefore not forward-looking. It does not factor in any major “shocks” in the market that may arise in the future, which may affect the value of the underlying.

### Limitation

- The volume of data used influences the end results during the calculation of realized volatility. At least 20 observations are statistically required to calculate a valid value of realized volatility. Therefore, realized volatility is better used to measure longer-term price risk in the market (~ 1 month or more).
- Realized volatility calculations are directionless. i.e., it factors in upward and downward trends in price movements.
- It is assumed that asset prices reflect all available information while measuring volatility.

### Important Points

- In order to calculate the downside risk associated with a stock, the measurement of realized volatility may be restricted to downside price movements.
- An increase in realized volatility of a stock over a time period would imply a significant change in the inherent value of the stock owning to external/internal factors.
- An increase in volatility implies a higher premium on option prices. The value of a stock can be inferred by comparing the realized volatility and estimated future volatility (implied volatility) of the options.
- Comparing the volatility of a stock with the benchmark index helps determine the stability of stock: the lower the volatility, the more predictable the price of the asset.
- A decrease in the realized volatility of a stock over a time period would indicate the stabilization of the stock.

Realized volatility measures help to quantify the inherent price risk arising out of volume fluctuations and external factors of a stock based on its historical performance. Combined with implied volatility, it also helps determine option prices based on the volatility in the underlying stock.

### Recommended Articles

This has been a guide to what is Realized Volatility and its definition. Here we discuss the formula to calculate realized volatility along with examples and explanations. You can learn more from the following articles –

- Formula of Population Variance
- Formula of Variance Analysis
- Correlation vs Covariance
- Variance vs Standard Deviation

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