# Which Implied Volatility Ratio Is Best?

This post will be about comparing a volatility signal using three different variations of implied volatility indices to predict when to enter a short volatility position.

In volatility trading, there are three separate implied volatility indices that have a somewhat long history for trading–the VIX (everyone knows this one), the VXV (more recently changed to be called the VIX3M), which is like the VIX, except for a three-month period), and the VXMT, which is the implied six-month volatility period.

This relationship gives investigation into three separate implied volatility ratios: VIX/VIX3M (aka VXV), VIX/VXMT, and VIX3M/VXMT, as predictors for entering a short (or long) volatility position.

So, let’s get the data.

```require(downloader)
require(quantmod)
require(PerformanceAnalytics)
require(TTR)
require(data.table)

destfile="vxvData.csv")
destfile="vxmtData.csv")

VIXdates <- VIX\$Date
VIX\$Date <- NULL; VIX <- xts(VIX, order.by=as.Date(VIXdates, format = '%m/%d/%Y'))

destfile="longXIV.txt")

xivRets <- Return.calculate(Cl(xiv))
```

One quick strategy to investigate is simple–the idea that the ratio should be below 1 (I.E. contango in implied volatility term structure) and decreasing (below a moving average). So when the ratio will be below 1 (that is, with longer-term implied volatility greater than shorter-term), and the ratio will be below its 60-day moving average, the strategy will take a position in XIV.

Here’s the code to do that.

```vixVix3m <- Cl(VIX)/Cl(vxv)
vixVxmt <- Cl(VIX)/Cl(vxmt)
vix3mVxmt <- Cl(vxv)/Cl(vxmt)

stratStats <- function(rets) {
stats <- rbind(table.AnnualizedReturns(rets), maxDrawdown(rets))
stats[5,] <- stats[1,]/stats[4,]
stats[6,] <- stats[1,]/UlcerIndex(rets)
rownames(stats)[4] <- "Worst Drawdown"
rownames(stats)[5] <- "Calmar Ratio"
rownames(stats)[6] <- "Ulcer Performance Index"
return(stats)
}

maShort <- SMA(vixVix3m, 60)
maMed <- SMA(vixVxmt, 60)
maLong <- SMA(vix3mVxmt, 60)

sigShort <- vixVix3m < 1 & vixVix3m < maShort
sigMed <- vixVxmt < 1 & vixVxmt < maMed
sigLong <- vix3mVxmt < 1 & vix3mVxmt < maLong

retsShort <- lag(sigShort, 2) * xivRets
retsMed <- lag(sigMed, 2) * xivRets
retsLong <- lag(sigLong, 2) * xivRets

compare <- na.omit(cbind(retsShort, retsMed, retsLong))
colnames(compare) <- c("Short", "Medium", "Long")
charts.PerformanceSummary(compare)
stratStats(compare)

```

With the following performance:

```> stratStats(compare)
Short    Medium     Long
Annualized Return         0.5485000 0.6315000 0.638600
Annualized Std Dev        0.3874000 0.3799000 0.378900
Annualized Sharpe (Rf=0%) 1.4157000 1.6626000 1.685600
Worst Drawdown            0.5246983 0.5318472 0.335756
Calmar Ratio              1.0453627 1.1873711 1.901976
Ulcer Performance Index   3.7893478 4.6181788 5.244137
```

In other words, the VIX3M/VXMT sports the lowest drawdowns (by a large margin) with higher returns.

So, when people talk about which implied volatility ratio to use, I think this offers some strong evidence for the longer-out horizon as a predictor for which implied vol term structure to use. It’s also why it forms the basis of my subscription strategy.

NOTE: I am currently seeking a full-time position (remote or in the northeast U.S.) related to my skill set demonstrated on this blog. Please message me on LinkedIn if you know of any opportunities which may benefit from my skill set.

## 18 thoughts on “Which Implied Volatility Ratio Is Best?”

1. Thank you. For some reason, reading about this ratio approach in earlier posts just didn’t resonate, maybe because it’s a simple short vol versus cash sort of switching trade. But I think I found the results not so interesting. But for some reason, this version of it resonated with me enough to fool around with it myself, and it’s more interesting than I thought. So thanks, again.

2. Costas says:

> maShort maMed maLong <- SMA(vix3mVxmt, 60)

3. Pingback: Distilled News | Data Analytics & R

4. PK says:

Thank you for the interesting approach. Short question: By “retsShort <- lag(sigShort, 2) * xivRets" you enter a trade at the following close, but close a trade at the second next close. Is there any reason for waiting until the second next close to close a trade?
Many Thanks, Patrick

• Because if you trade futures, the CBOE doesn’t release settles until the next day at 9:45 AM EST.

Ilya, how do you get the cumulative performance chart legend to behave nicely? I’ve tried cex.legend but the box is way too big and the text way too small. Maybe only a windows issue?

• It’s just charts.PerformanceSummary, and I use windows too.

6. Peter Jacobson says:

Thank you for sharing your results. I wonder what happens if you go long VXX instead of cash when the strategy says to be out of XIV?

• Too volatile and might backlash you. You need a take-profit or stop-loss rule which is not possible if you are trading end of day… My humble opinion…

7. Thanks for sharing this, Ilya. Is there a way to plot the profits without compounding — to show the cumulative sum of daily percentage profits? Otherwise the variability increases greatly as time goes on.
Alternatively, can cumulative profits be plotted on a log scale?

• Sorry, never mind. I see that the answer to my previous question is to use geometric=FALSE in the call to charts.PerformanceSummary.

8. maas says:

Your code uses a lag of 2 for the signals. With a lag of 2, the “Long” scenario is the best one. Shouldn’t a lag of 1 give an even better result for that scenario, regardless of your reasons for taking a lag of 2? However, when the lag is changed to 1, the results deteriorate and the “Long” scenario is no longer the best one (the “Medium” scenario is better by far). Does that change your opinion on the best ratio to use?

• No, absolutely not. Lag of 1 means “observe close, buy the close”, which means scaling is impossible.