Country Seasonality

#*****************************************************************
# Read historical data from AQR library
# [Betting Against Beta: Equity Factors, Monthly](https://www.aqr.com/library/data-sets/betting-against-beta-equity-factors-monthly)
#******************************************************************
library(readxl)
library(SIT)
library(quantmod)

data = env()
data.set = 'betting-against-beta-equity-factors'

# monthly market returns in excess of t-bills
data$market.excess = load.aqr.data(data.set, 'monthly', 'MKT')

#monthly U.S. Treasury bill rates.
data$risk.free = load.aqr.data(data.set, 'monthly', 'RF', last.col2extract = 2)

# total market return
aqr.market = data$market.excess + as.vector(data$risk.free)

# compute equity 
equity = bt.apply.matrix(1+ifna(aqr.market,0),cumprod)
	equity[is.na(aqr.market)] = NA
	
year.ends = date.ends(equity, 'year')	

# create back-test environment with annual prices 
data = env()
for(n in names(aqr.market))
	data[[n]] = make.stock.xts(equity[year.ends,n])
bt.prep(data, align='keep.all', fill.gaps = F, dates='1986::')

plota.matplot( scale.one(data$prices), main='Asset Performance')

#*****************************************************************
# Stats
#*****************************************************************
prices = data$prices
	n = ncol(prices)

ret = prices / mlag(prices) - 1
signal = ret < 0

signals = list(down1yr = signal, down2yr = signal & mlag(signal), down3yr=signal & mlag(signal) & mlag(signal,2))

# compute stats
make.stats(signals, ret)

#*****************************************************************
# Strategy
#*****************************************************************
models = run.models(signals, data)

#*****************************************************************
# Stats
#*****************************************************************
make.stats = function(signals, ret) {
	# compute stats
	stats = list()
	for(signal in names(signals)) {
		temp = signals[[signal]]
		stats[[paste(signal,'hold1yr')]] = coredata(ret)[ifna(mlag(temp),F)]
		stats[[paste(signal,'hold2yr')]] = 1/2 * coredata(ret + mlag(ret,-1))[ifna(mlag(temp),F)]
		stats[[paste(signal,'hold3yr')]] = 1/3 * coredata(ret + mlag(ret,-1) + + mlag(ret,-3))[ifna(mlag(temp),F)]
	}
	stats = lapply(stats,na.omit)
	# sapply(stats,mean) # mean

	# make a barplot
	par(mar = c(8, 4, 2, 1))
	boxplot(stats,las=2)
		abline(h=0,col='gray')
}

#*****************************************************************
# Strategy
#*****************************************************************
run.models = function(signals, data) {
	models = list()

	data$weight[] = NA
		data$weight[] = ntop(prices, n)
	models$equal.weight = bt.run(data, trade.summary=T, silent=T)

	for(signal in names(signals)) {
		temp = signals[[signal]]
		data$weight[] = NA
			data$weight[] = ntop(temp, n)
		models[[paste(signal,'hold1yr')]] = bt.run(data, trade.summary=T, silent=T)
		
		temp = signals[[signal]]
			temp = temp | mlag(temp)
		data$weight[] = NA
			data$weight[] = ntop(temp, n)
		models[[paste(signal,'hold2yr')]] = bt.run(data, trade.summary=T, silent=T)
		
		temp = signals[[signal]]
			temp = temp | mlag(temp) | mlag(temp,2)
		data$weight[] = NA
			data$weight[] = ntop(temp, n)
		models[[paste(signal,'hold3yr')]] = bt.run(data, trade.summary=T, silent=T)
	}

	# create report
	plotbt(models, plotX = T, log = 'y', LeftMargin = 3, main = NULL)	    	
		mtext('Cumulative Performance', side = 2, line = 1)
	
	print(plotbt.strategy.sidebyside(models, make.plot=F, return.table=T,perfromance.fn = engineering.returns.kpi))
	
	models
}