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Using Correlations to determine the market regime switching

blog shows a market timing strategy which determines the market switching point. The market is represented by S&P 500. The strategy calculates the correlation matrix changes of the 500 stocks within S&P. The performance of this strategy looks quite promising.

However, to download the historical data of all the 500 stocks and calculate the correlation matrix are not a trivial tasks, not mentioning the changes of the 500 stocks included in SPX index in the past. Therefore, an easy substitute of the 500 stocks will be the sector ETFs which represents the 9 different sectors of the US market.

We are using SPDR sector ETFs (XLE, XLF and etc) and SPY (the SPDR ETF of the S&P 500 index).

Data D

We use quantmod to download the time series of SPY and the other 9 sector ETFs.

library(xts)

## Warning: package 'xts' was built under R version 3.0.2

## Loading required package: zoo
## 
## Attaching package: 'zoo'
## 
## The following object is masked from 'package:base':
## 
##     as.Date, as.Date.numeric

library(zoo)
library(Quandl)

## Warning: package 'Quandl' was built under R version 3.0.2

library(quantmod)

## Loading required package: Defaults
## Loading required package: TTR
## Version 0.4-0 included new data defaults. See ?getSymbols.

load(file = "etf.RData")

Correlations

Now first calculate the returns of SPY and ETFs, and then calculate the rolling correlation matrix

returns = log(lag(data_etf, 1)/data_etf)
returns = returns[2:nrow(returns)]

# Calculate the average correlations
vcorr <- function(x) {
    corr = cor(x)
    n = ncol(x)
    nr = n * (n - 1)
    vc = (sum(corr) - n)/2
    return(vc)
}


rsize = 60
for (i in 1:nrow(returns)) {
    if (i < rsize) 
        data_all$vcorr[i] = 0 else data_all$vcorr[i] = vcorr(returns[(i - rsize + 1):i])
}

vcorr_ma <- rollmean(data_all$vcorr, 100)


par(mfrow = c(2, 1), oma = c(0, 0, 0, 0))
plot(data_all$SPY)
par(new = TRUE)
plot(vcorr_ma)
# lines(data_all$vcorr, col='green')

Prediction Power of Correlation

signal <- (data_all$vcorr < (0.9 * vcorr_ma))
signal1 <- (data_all$vcorr > (1.1 * vcorr_ma))

plot(data_all$SPY)
points(data_all$SPY[signal], col = "green", pch = 20)
points(data_all$SPY[signal1], col = "red", pch = 1)