A quick look at FX realized vol

Much has been said about the decline in volatility. At the moment I am very active in FX spot trading and as a generalization do better the more vol there is.

 I wanted to see how things stood on the crosses I am most active in, namely EUR/USD, GBP/USD and USD/JPY.

 I took hourly data from FxPro (not my broker, nor an endorsement), calculated volatility as the high minus the low, and summed the total for each day. You can think of it as how many pips were on offer if one could correctly call the high and low of each hour of each day.

 All up there is about 90 days of data, so it covers roughly the last four months. I also took the average of the last five days which are the red X’s on the box plots. We are here.

As you can see, vol is below average. It was quiet week overall, bank holidays in the US and parts of Europe, and only a moderate amount of data coming out. Next week should be a bit busier I think.

Since I had all the data I also took at look at the average hourly RV per day.

I don’t want to read too much into this chart but things have been quiet. I read somewhere else fx vol is approaching levels of 2007 which was a very quiet time indeed.

Some R code is up here, data is here.

What can we use the VIX for?

In part 1, we took a look at VIX and the relationship it had between historical volatility and realized volatility.

Continuing on, I thought I would take a look at next day returns and the VIX. There is a relationship between SPX and VIX in that when SPX drops, VIX typically rises. This leads the question: does a high VIX serve as a useful indicator of what might happen to SPX the next day?

A problem in answering this is quantifying what we mean by a "high" VIX. A VIX of 25 might be high if it has been under 20 for the last 3 months, but might be considered low if it has been around 30.

To deal with this I use a proportional measure based on its previous trading range. If it is at the top of its range, it gets a 1, and at the bottom it gets a 0. Anywhere in between it gets a number between 0 and 1.

I used data from 2000-2013 and a 252 period lookback, which is roughly 1 year, recording the next day return of SPX. I split this data into 5 groups, the first with relative VIX readings up to 0.2, the second between 0.2 and 0.4, and so on up to 1.0. Then I plotted the next day returns as a boxplot, giving the distribution of returns for a VIX reading in its relative quintile.

The box on the far left corresponds to the lowest relative VIX levels, while the box on the far right corresponds to the highest.

One thing that jumps out to me is that the mean of all these returns is more or less zero. Using this relative measure of VIX has no value as a predictor of next day returns, as whatever measure we use, a mean return of zero will see us end up flat (or in practice, probably down a bit). If there was a real edge, we would expect the mean return to be somewhere other than zero.

The second thing that I notice is the distribution of returns is a lot wider for the right most two boxes, which corresponds to relative VIX measure above 0.60, i.e. relatively higher volatility. Now this makes sense, as we would reasonably expect periods of higher volatility to have higher volatility.

It seems that high readings of VIX can serve as a useful predictor of higher periods of next day volatility, and for someone trying to implement a volatility filter, that could be quite useful.

Conclusion

To recap, we have seen that:

1) VIX is not very good at forecasting 30 day realized volatility.
2) Historical volatility can be a reasonable proxy for IV/VIX.
3) Higher periods of volatility do portend continued higher volatility, at least for the short term (1 day).

Note that 3 does contradict the mean reversion of volatility, because it is looking at the next day returns only. Over a longer period we would certainly expect it mean revert, otherwise we'd be experiencing some very, very bumpy rides ...

Also, I did similar analysis using RUT & RVX and NDX & VXN, both of which had very similar results. We will take a look at them in the next post where we use the findings from this post and the previous to implement a volatility filter.

Code for this post and the previous is up: here

Density Plot with ggplot

This is a follow on from the post Using apply sapply and lappy in R.

The dataset we are using was created like so:

m <- matrix(data=cbind(rnorm(30, 0), rnorm(30, 2), rnorm(30, 5)), nrow=30, ncol=3)

Three columns of 30 observations, normally distributed with means of 0, 2 and 5. We want a density plot to compare the distributions of the three columns using ggplot.

First let's give our matrix some column names:

colnames(m) <- c('method1', 'method2', 'method3')

head(m)

#         method1    method2  method3

#[1,]  0.06288358  2.7413567 4.420209

#[2,] -0.11240501  3.4126550 4.827725

#[3,]  0.02467713  1.0868087 4.044101

ggplot has a nice function to display just what we were after geom_density and it's counterpart stat_density which has more examples. 

ggplot likes to work on data frames and we have a matrix, so let's fix that first

df <- as.data.frame(m)

df

#       method1    method2  method3

#1   0.06288358  2.7413567 4.420209

#2  -0.11240501  3.4126550 4.827725

#3   0.02467713  1.0868087 4.044101

#4  -0.73854932 -0.4618973 3.668004

Enter stack

What we would really like is to have our data in 2 columns, where the first column contains the data values, and the second column contains the method name. 

Enter the base function stack, which is a great little function giving just what we need:

dfs <- stack(df)

dfs

#        values     ind

#1   0.06288358 method1

#2  -0.11240501 method1

#…

#88  5.55704736 method3

#89  6.40128267 method3

#90  3.18269138 method3

We can see the values are in one column named values, and the method names (the previous column names) are in the second column named ind. We can confirm they have been turned into a factor as well:

is.factor(dfs[,2])

#[1] TRUE

stack has a partner in crime, unstack, which does the opposite:

unstack(dfs)

#       method1    method2  method3

#1   0.06288358  2.7413567 4.420209

#2  -0.11240501  3.4126550 4.827725

#3   0.02467713  1.0868087 4.044101

#4  -0.73854932 -0.4618973 3.668004

Back to ggplot

So, lets try plot our densities with ggplot:

ggplot(dfs, aes(x=values)) + geom_density()

The first argument is our stacked data frame, and the second is a call to the aes function which tells ggplot the 'values' column should be used on the x-axis.

However, our plot is not quite looking how we wish:

Hmm. 

We want to group the values by each method used. To do this we will use the 'ind' column, and we tell ggplot about this by using aes in the geom_density call:

ggplot(dfs, aes(x=values)) + geom_density(aes(group=ind))

This is getting closer, but it's not easy to tell each one apart. Let's try colour the different methods, based on the ind column in our data frame.

ggplot(dfs, aes(x=values)) + geom_density(aes(group=ind, colour=ind))

Looking better. I'd like to have the density regions stand out some more, so will use fill and an alpha value of 0.3 to make them transparent.

ggplot(dfs, aes(x=values)) + geom_density(aes(group=ind, colour=ind, fill=ind), alpha=0.3)

That is much more in line with what I wanted to see. Note that the alpha argument is passed to geom_density() rather than aes().

That's all for now.