Concordance Discordance

> start.date <- "2003-01-01"
> end.date <- "2009-08-28"
> library(corpcor)
> library(mnormt)
> library(fields)
> library(fPortfolio)
> library(fPortfolioBacktest)
> library(PerformanceAnalytics)
> library(xts)
> annualized.returns <- function(x) {
+     n <- length(x)
+     (x[n] - x[1])/x[1]
+ }
> nifty.data <- read.csv("C:/Cauldron/Benchmark/PMS/Product/MF/nifty_mar_12.csv",
+     stringsAsFactors = FALSE, header = T)
> nifty.data$trade.date <- as.Date(nifty.data$Date, format = "%d-%m-%Y")
> gold.data <- read.csv("C:/Cauldron/Benchmark/PMS/Product/MF/gold_mar_10.csv",
+     stringsAsFactors = FALSE, header = T)
> gold.data$trade.date <- as.Date(gold.data$Date, format = "%d-%m-%Y")
> liquid.data <- read.csv("C:/Cauldron/Benchmark/PMS/Product/MF/liquid_april_22.csv",
+     stringsAsFactors = FALSE, header = T)
> liquid.data$trade.date <- as.Date(liquid.data$Date, format = "%d-%m-%Y")
> nifty.data$nifty.100 <- as.numeric(nifty.data$nifty.100)
> gold.data$gold <- as.numeric(gold.data$gold)
> liquid.data$liquid <- as.numeric(liquid.data$liquid)
> nifty.ts <- as.timeSeries(nifty.data$nifty.100, timeDate(nifty.data$trade.date))
> rownames(nifty.ts) <- nifty.data$trade.date
> colnames(nifty.ts) <- "nifty.100"
> gold.ts <- as.timeSeries(gold.data$gold, timeDate(gold.data$trade.date))
> rownames(gold.ts) <- gold.data$trade.date
> colnames(gold.ts) <- "gold"
> liquid.ts <- as.timeSeries(liquid.data$liquid, timeDate(liquid.data$trade.date))
> rownames(liquid.ts) <- liquid.data$trade.date
> colnames(liquid.ts) <- "liquid"
> rawdata <- merge(nifty.ts, gold.ts)
> rawdata <- na.locf(rawdata)
> workdata <- window(rawdata, start = start.date, end = end.date)
> dates <- as.Date(rownames(workdata))
> workdata.xts <- xts(workdata[, 1:2], dates)
> workdata.ret.roll.y <- cbind(rollapply(workdata.xts[, 1], width = 252, annualized.returns,
+     align = "right"), rollapply(workdata.xts[, 2], width = 252, annualized.returns,
+     align = "right"))
> colnames(workdata.ret.roll.y) <- c("Nifty100Ret", "GoldRet")
> workdata.ret.master <- workdata.ret.roll.y
> workdata.ret.master <- as.timeSeries(coredata(workdata.ret.master), timeDate(as.Date(index(workdata.ret.master))))
> dates.liquid <- as.Date(rownames(liquid.ts))
> liquiddata.xts <- xts(liquid.ts[, 1], dates.liquid)
> liquiddata.ret.roll.y <- rollapply(liquiddata.xts[, 1], width = 300, annualized.returns,
+     align = "right")
> colnames(liquiddata.ret.roll.y) <- c("Liquid")
> liqworkdata.ret.master <- liquiddata.ret.roll.y
> liqworkdata.ret.master <- as.timeSeries(coredata(liqworkdata.ret.master), timeDate(as.Date(index(liqworkdata.ret.master))))
> all.master <- merge(workdata.ret.master, liqworkdata.ret.master)
> all.master <- window(all.master, start = start.date, end = end.date)
> all.master <- all.master[(!is.na(all.master[, 1])), ]
> all.master <- all.master[(!is.na(all.master[, 2])), ]
> all.master <- all.master[(!is.na(all.master[, 3])), ]
> plot(all.master[, 1], ylim = c(-0.6, 1.2), col = "blue", ylab = "Return", lwd = 1.5)
> par(new = T)
> plot(all.master[, 2], ylim = c(-0.6, 1.2), col = "sienna", ylab = "", lwd = 1.5)
> par(new = T)
> plot(all.master[, 3], ylim = c(-0.6, 1.2), col = "green", ylab = "", lwd = 1.5)
> legend("topright", legend = c("NIFTY 100", "Gold", "Liquid"), fill = c("blue",
+     "sienna", "green"))

> cor(all.master)
            Nifty100Ret GoldRet  Liquid
Nifty100Ret      1.0000 -0.1321 -0.4214
GoldRet         -0.1321  1.0000  0.2406
Liquid          -0.4214  0.2406  1.0000

> n <- dim(all.master)[1]
> sqrt(9 * n/4) * abs(cor(coredata(all.master), method = "kendall"))
            Nifty100Ret GoldRet Liquid
Nifty100Ret       57.00   5.980 11.287
GoldRet            5.98  57.000  6.955
Liquid            11.29   6.955 57.000

> n <- dim(all.master)[1]
> sqrt(n) * abs(cor(coredata(all.master), method = "spearman"))
            Nifty100Ret GoldRet Liquid
Nifty100Ret      38.000   6.213 10.741
GoldRet           6.213  38.000  8.687
Liquid           10.741   8.687 38.000