Does Implied Volatility Predict Future Realized Volatility?
Contributed by Zach Escalante. He is currently in the NYC Data Science Academy 12 week full time Data Science Bootcamp program taking place between April 11th to July 1st, 2016. This post is based on his first class project - R Visualization (due on the 2th week of the program).
Introduction:
The question of whether implied volatility (IV) is a precursor to future realized volatility (RV) of assets has been the subject of much academic research (1). My goal in doing this analysis was to see if we could visually ascertain whether data in exchange rate between the Brazilian Real (BRL) and United States Dollar (USD) lends itself to supporting our hypothesis that IV is a forerunner to RV.
The reason I have decided to use BRL/USD as the asset on which we will conduct our analysis is that since the time of the 2008 financial crisis, much of the movement in currencies has been the result of central bank (CB) policies and decisions. This has created a binary atmosphere in currency markets
where FX rates of large, highly credit-worthy countries (think Japan, Germany, the US or Britain) are ultimately predicated upon whether that country's CB decides to pursue a tighter/looser monetary policy. A contrast to this is Brazil, where notable geo-political events (including the potential impeachment of their current president, Dilma Rousseff) outside the scope of local central bank policy have been significant factors in the movements in BRL, and have introduced an additional source of volatility.
Exploratory Data Analysis:
The data set that I used to conduct my analysis was the three month historical IV (3MIV) and three month historical RV (3MRV). This was obtained from Bloomberg L.P. and can only be accessed with a paid subscription to Bloomberg. The first charts I produced were the last years' BRL/USD FX rate, and the last years' 3MIV vs 3MRV:
We see from the graph of BRLUSD over the past year that the BRL bottomed in value against the USD around October of 2015 and then fell back that level again in January of 2016 after having briefly strengthened in between. Since January it has risen from just over 4:1 against the USD to just under 3.6:1. This is still well below the 3:1 level it touched last Spring.
Over this same time period, we see that volatility was spiking in October of 2015 and January of 2016, concurrent with the BRL touching its lowest levels. We also see that the 3MIV seems to precede 3MRV directionally on at least three occasions (circled in red).
At this point, it became clear that more historical observations would be necessary in order to see if this relationship persisted, or was a recent phenomenon specifically related to the impeachment proceedings of Dilma Rousseff. To analyze this, I obtained the past five years data of 3MIV and 3MHV and created this bar chart:
We see here that on at least seven occasion a rise in 3MRV is precede by a spike in 3MIV over the past five years. I find this to be a very interesting phenomenon which should be explored further.
Conclusion:
My conclusion is that there does exist a relationship between implied volatility and historical volatility for the Brazilian Real should be investigated further. This can clearly be seen from the data collected and graphed in the preceding examples, and should make for some very interesting research questions in the future.
Research Questions for the Future:
These are several questions that are a natural extension of the analysis I have already conducted and would like to explore in the future:
- Does the volatility skew corresponding with spikes in 3MIV tell us anything about which direction the FX rates moves when 3MRV rises?
- Can we make any implications regarding the direction of the currency in relation to the ratio of puts to calls?
- What did movements in Brazilian Equity Indices look like over this time period?
- Do Brazilian Equity Indices experience similar volatility patterns?
Coding This Project:
To write the code for this project, I first imported a CSV file with all of my data as columns:
ImpVol <- read.csv("IV.csv") HistVol <- read.csv("realVol.csv") Rates <- read.csv("1yr_swaps.csv") FX <- read.csv("brlFx.csv")
Then used the 'merge' function to match each of these columns against their corresponding dates:
vol <- merge(iVol, hVol) #this merged hist imp vol and hist realized vol
One of the more interesting aspects of creating these graphs had to do with plotting time series in the R package ggplot2, which I finally solved in the following manner with the help of the "melt" function in R:
sub <- last_year[, c(1, 4, 8)] #temporary data frame which received subin <- melt(sub, id = "Date") #which was passed 3MIV & 3MRV data Vol1516 <- ggplot(subin, aes(x=Date, y=value, colour=variable)) +geom_line() + scale_colour_manual(values=c("blue","green")) + ggtitle("BRL Imp Vol vs Hist Vol 2015-2016") + ylab(" ") Vol1516
Thank you for taking the time to read this blog post! If you have questions, comments or suggestions, please feel free to reach out and provide your feedback.
The complete code is included below:
install
getwd() setwd("/Users/zacharyescalante/R_Projects/Project_1") ImpVol <- read.csv("IV.csv") HistVol <- read.csv("realVol.csv") Rates <- read.csv("1yr_swaps.csv") FX <- read.csv("brlFx.csv") #Remove the first 6 rows of FX data frame FX <- FX[-c(1:6),] colnames(FX) <- c("Date", "BRL") #Change the column names
#Remove the first 5 rows of Rates data frame Rates <- Rates[-c(1:6),-c(3:4)] #Delete rows 1-6 and columns 3-4 colnames(Rates) <- c("Date", "iRate")
#Remove first columns 1, 5, 8 of ImpVol iVol <- ImpVol[,-c(1, 5, 8)]
#Remove x bland of HistVol hVol <- HistVol[, -c(1, 5, 8)]
vol <- merge(iVol, hVol) vol <- vol[-1,]
#At this point each of the csv files has been loaded as a dataframe #and we now have to combine the data. We have already combined the #implied volatility data since those two data frames were identical #and this will cut down on data manipulation. Next we need to cut the #Date columns so that they match and we can use join/merge functions #in order to create one large data frame with all of our data
#Delete the leading zero for dates in the 'Date' column of 'vol' dataframe
#Convert the 'Date' column from factor -> character vol[,1] <- as.character(vol$Date) head(vol) class(vol$Date)
#Convert the 'Date' column for Rates from factor -> character Rates[,1] <- as.character(Rates$Date) Rates[,2] <- as.numeric(as.character(Rates$iRate)) head(Rates) class(Rates$Date) class(Rates$iRate)
##Convert the 'Date' column for FX from factor -> character FX[,1] <- as.character(FX$Date) FX[,2] <- as.numeric(as.character(FX$BRL)) head(FX) class(FX$Date) class(FX$BRL)
#Run a for loop to concatenate the strings with leading zeros #and remove leading zeros for the day value nrow(vol)
for(i in 1:nrow(vol)) { if(substring(vol$Date[i], 1,1) == '0') { vol$Date[i] = substr(vol$Date[i], 2, nchar(vol$Date[i])) } else{vol$Date[i] = vol$Date[i]} vol$Date[i] = sub("/0", "/", vol$Date[i]) }
brl_data <- merge(vol, Rates) #Finish mergin the data brl_data <- merge(brl_data, FX) brl_data$Date <- as.Date(brl_data$Date, "%m/%d/%Y") #conver the 'Date' column to 'date' format class(brl_data$Date) #show that the new class is 'date'
clean<-arrange(brl_data, desc(Date)) head(clean) class(clean$BRL) class(clean$iRate)
last_year <- clean[1:252,] last_year2 <- clean[253:500,] head(last_year) class(last_year$BRL) class(last_year$iRate)
#Create graphs
#2014/2015 Implied Vol vs Hist Vol. sub <- last_year2[, c(1, 4, 8)] subin <- melt(sub, id = "Date") Vol1415 <- ggplot(subin) + geom_line(aes(x=Date, y=value, colour=variable)) + scale_colour_manual(values=c("blue","green")) + ggtitle("BRL Imp Vol vs Hist Vol 2014-2015") + ylab(" ") Vol1415
#FX Graph for 2014/2015 FX1415 <- ggplot(last_year2, aes(x=Date, y=BRL)) + geom_line(color = "dark green") + ggtitle("BRLUSD 2014-2015") FX1415
#2015/2016 Implied Vol vs Hist Vol. sub <- last_year[, c(1, 4, 8)] subin <- melt(sub, id = "Date") Vol1516 <- ggplot(subin, aes(x=Date, y=value, colour=variable)) + geom_line() + scale_colour_manual(values=c("blue","green")) + ggtitle("BRL Imp Vol vs Hist Vol 2015-2016") + ylab(" ") Vol1516
#FX Graph for 2015/2016 FX1516 <- ggplot(last_year, aes(x=Date, y=BRL)) + geom_line(color = "dark green") + ggtitle("BRLUSD 2015-2016") FX1516
#2015/2016 Volatitily Bar Chart sub <- last_year[, c(1, 4, 8)] subin <- melt(sub, id = "Date") ggplot(subin, aes(x=Date, y = value, fill = variable)) + geom_bar(stat = "identity", position = "dodge") + scale_fill_discrete(name = "Volatility") + ggtitle("Hist vs Implied Volatility") + scale_fill_manual(values = c("blue", "green"))
#Historic Volatitily Bar Chart sub <- clean[, c(1, 4, 8)] subin <- melt(sub, id = "Date") HistVol <- ggplot(subin, aes(x=Date, y = value, fill = variable)) + geom_bar(stat = "identity", position = "dodge") + scale_fill_discrete(name = "Volatility") + ggtitle("Hist vs Implied Volatility") + scale_fill_manual(values = c("blue", "green")) HistVol
#Historic Vol comparison - Line Chart tmp <- clean[,c(1, 4, 8)] tmp2 <-melt(tmp, id = "Date") volHist <- ggplot(tmp2) + geom_line(aes(x=Date, y=value, colour=variable)) + scale_colour_manual(values=c("blue","green")) + scale_fill_discrete(name = "Volatility") + ggtitle("Hist Volatility Comparison") + ylab(" ") volHist
#Historic FX Chart
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Zachary Escalante
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