# RV (Realized Volatility)

## Basic Points

- RV (realized volatility) shows the actual trading range of how much a stock is moving.
- It is calculated based on historical movements, and measures the standard deviation, which means about how far it can be expected to move with a 68.3% chance.
- Another way to look at it is that 68.3% of historical moves would have fallen under what is measured as a standard deviation.
- Realized volatility can be applied to any length of time period, and can also be used as a forecast of future [realized] volatility.

## Expert: Understanding Realized Volatility

Realized Volatility is also known as historical volatility (HV). This metric serves to quantify and express how much an asset is moving, whether past, present, or modeled for the future. Since it would be odd to project “historical volatility” for the future, realized volatility is used as an interchangeable term so that it can be forecasted as future RV.

Although the mathematical translations are the same, a popular convention is that, unless otherwise specified, HV refers to daily data. Meanwhile, RV is often expressed on a variety of intervals including ultra-short-term analysis, such as on the minute level.

The meaning of RV mathematically is that it is the square root of variance, which is also the general relation of “volatility” to variance, whether realized or implied. Variance is then calculated by squaring all deviations from the mean, and then averaging them.

The idea of using mathematical models such as GARCH to forecast RV is to estimate the price that implied volatility (IV) will end up at. Likewise, the options market is continually trying to price in how far IV will move.

The main idea here in the connection between implied and realized volatility is that the options market is moving IV through imbalances in buying and selling options, and through this auction process, IV is attempting to end up projecting the same range that would match the RV calculation. “In theory, it is the future realized volatility over the life of the option that we need to input into the theoretical pricing model” (Natenberg, 2015, p. 86). But strategically, if IV appears to be overshooting RV, then this creates a tactical premium-selling opportunity. “By selling options at prices lower than theoretical value, a trader creates a positive theoretical edge” (p. 90). And therefore, if IV is undershooting RV on the target timeframe being traded, then, all else equal, there is edge to buy option premium. This way, there can be profit from sharper moves than the options market is pricing in. However, this is only edge and not certainty, and so, like always, risk management and proper sizing is needed to stay safe and avoid unnecessarily heavy losses.