# Calculating front month VIX future returns

I'm currently reading a paper* which deals with seperating the volatility of volatility index (VVIX) into a physical measure of volatility of volatility (RVVIX) and a risk premium of v.o.v (VVRP). To do so, one has to:

"RVVIX is obtained by computing the realized variance of the five-minute front-month VIX future returns over the past one month."

1. Does anyone know if this RRVIX data can be obtained somewhere or from a certain database (I couldn't find it)
2. Can anyone give me an explanation how to actually do those calculations, I'm really struggling to understand the process. E.g. "front month VIX future returns" means those are futures with the nearest expirations dates, but what futures exactly need to be considered (just because there are different prices and therefore different returns).

I know this question is probably very basic and a bit vague (I'm only an undergrad student), but I appreciate any form of help or suggestions Thanks in advance

' Volatility-of-volatility and tail risk hedging returns, Yang Ho Park, 2013

• At any time there is only one "front month" monthly VIX future. For example the Jan future expired yesterday Wednesday Jan 22, 2020, so the current "front month" VIX future is the Feb, which will expire on Wednesday February 19. At that time the front month will be the March future, and so on. There are 12 monthly expiration dates per year. Jan 24, 2020 at 13:24
• (There are now also weekly VIX futures, but those don't have much of a historical track record (they began trading in summer 2015) so they are not used in a study like this [especially since it was done in 2013! He clearly used monthly futures]). Jan 24, 2020 at 13:32
• Ok thanks a lot, this already helps me. But I'm still a bit confused, where exactly does the 5-minute intraday data come in? is this the 5 min change of the price of the future that expires at the each end of the month? Jan 24, 2020 at 15:01
• Today is 2020/01/24. The front month future is Feb 2020. We get price data for this future for 1 month (from 2019/12/24 or maybe for the last 21 trading days since on average a month has 21 trading days) until today. We break this into 5 minute trading intervals, find the return in each interval and find the variance of these numbers. That is how I would do it. HTH. Jan 24, 2020 at 15:28

but what futures exactly need to be considered (just because there are different prices and therefore different returns).

The usual way to do this is:

1. draw a schedule / list of the contracts to be considered (in this case, all the monthly expries)
2. Create a rule for determining a relative point to switch from one contract to the next (eg, the expiry minus 2 trade days) - this is called a "roll algo"
3. For each contract pair, compute the roll point in time (you might need expiry reference data to do this)
4. align the historic market data for the future contracts
5. compute an adjusted time series using geometric or arithmetic factors, starting from today, and going backwards daily in time
6. Compute a returns series using the above synthetic price series

This results in a returns series for the simulated trading strategy of owning the front month and rolling to the next expiry 2 days before the expiry etc.

Many data providers (eg, bloomberg) already compute series like these to save you the effort.