# Realised Volatility (RV)

Volatility measures the variability of returns of an underlying asset and in some sense provides a measure of the risk of holding that underlying.

The following are some of the commonly observed properties of (equity market) volatility:

• Volatility tends to be anti-correlated with the underlying over short time periods

• Volatility can increase suddenly in ‘spikes’

• Volatility can be observed to experience different regimes

• Volatility tends to be mean reverting (within regimes)

This list suggests some of the reasons why investors may wish to trade volatility:

- as a partial hedge against the underlying – especially for a volatility spike caused by a sudden market sell-off

- as a diversifying asset class

- to take a macro view e.g. for a potential change in volatility regime

Measuring realised volatility and variance

Realised (or historical) volatility can be measured in a variety of ways.

• Annualised standard deviation of daily (log) returns calculcated from a data set over some fixed period of time

Avantages: easy to calculate and understand

Disadvantages: as it uses a fixed time period, it can suddenly drop as a large return falls out of the window of observation.

To alleviate this problem --> more sophisticated measures of RV: exponentially weighted measures / GARCH models

Volatility can also be calculated using returns of various frequencies: intra-day, daily, weekly, ...

If returns independent --> over long enough time-frame, RV should be independent of the frequency of returns used to calculate it.

In practice --> daily close-to-close returns are usually used.

Volatility is usually quoted as an annualised volatility and expressed as a percentage.

The annualised volatility represents the expected annual std dev in distribution of the underlying, assuming returns are independent.

To move from the std dev of daily log returns to annualised volatility --> * A volatility of 16% equates to a standard deviation of daily moves of around 1%.

• Root-mean-squared measure: like a standard deviation but assuming a zero mean

It is this RMS volatility measure which is used to define the payouf of the variance swap contract.

Volatility conveys information about the usual size of moves in the underlying in relation to its absolute price.

Volatility is a more intuitive concept than variance --> it is measured in the same units as the underlying

But variance is in some sense more fundamental:

- variance is additive, whereas volatility is not.

- delta hedging of options seeks to capture realised variance, although exposure complicated by path dependency issues.

Variance swaps pay-out is purely based on realised variance. 