example of R's optimize function: weighting us 2x10 curve to have zero correlation to usdjpy

optimize.r

library(fredr)
require(xts)

# note you'll need an API key
fredr_set_key("123YourFREDAPIKey321")

# helper function to convert tib to xts
xtsT <- function(TIB) xts(TIB$value, TIB$date)

# helper function to remove rows that have NA values
rmNA <- function(X) X[complete.cases(X), ]

# get data
us2yr <- xtsT(fredr("DGS2", observation_start=as.Date('2016-01-01')))
us10yr <- xtsT(fredr("DGS10", observation_start=as.Date('2016-01-01')))
usdjpy <- xtsT(fredr("DEXJPUS", observation_start=as.Date('2016-01-01')))

# create portfolio: % returns for USDJPY and bps changes for 2x10 curve
portfolio <- rmNA(cbind(usdjpy, us2yr,  us10yr))
portfolio_diff <- rmNA(100 * cbind(diff(portfolio[, 1], log=T),
			diff(portfolio[, 2:3])))

# embed problem in a function
corFun <- function(b, targetCor = 0) {
	spread <- portfolio_diff[, 'us10yr'] - b * portfolio_diff[, 'us2yr']
	abs(cor(spread, portfolio_diff[, 'usdjpy']) - targetCor)
}

# optimise the function
optWeight <- optimize(corFun, lower = 0, upper = 2)

# plot the range of results
plot(sapply(seq(0, 2, 0.01), corFun), x = seq(0, 2, 0.01),
     main = "Correlation of weighted US 2x10 curve trade with USDJPY",
     xlab = "weighting on 2yr",
     ylab = "Correlation with USDJPY")
abline(v = 1, col=8, lty=2, lwd=1)
abline(h = 0, col=2, lty=2, lwd=1)
points(optWeight$minimum, 0, pch=17, col=2, type='p')