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XIV Seasonality

02 Dec 2014

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A New (Better?) Measure of Risk and Uncertainty: The Volatility of Acceleration Volatility of Acceleration Part Two

Load historical data for SPY.

	#*****************************************************************
	# Load historical data
	#*****************************************************************
	library(SIT)
	load.packages('quantmod')
	
	tickers = spl('SPY')
	
	data <- new.env()
	getSymbols(tickers, src = 'yahoo', from = '1970-01-01', env = data, auto.assign = T)
		for(i in ls(data)) data[[i]] = adjustOHLC(data[[i]], use.Adjusted=T)	
	bt.prep(data, align='remove.na')

Next let’s compute statistics and trading signal.

	price = data$prices$SPY
	ret = price / mlag(price) - 1	
	ret = diff(log(price))
	
	vol = runSD(ret, 10)
	vol1 = SMA(abs(ret), 20)

	# VOA = volatility of acceleration
	# VOA= average of: | ln(pt/pt-1)- ln(pt-1/pt-2) |... | ln(pt-n/pt-n-1)|
	# VOA is the average of the absolute value of the first difference of daily log returns
	voa = SMA(abs(diff(ret)), 10)
	voa1 = runSD(diff(ret), 10)
	
# this look like MAD	
	
	# Forecast VOA (F-VOA)= VOA(t)+ k*(VOA(t)- VOA(t-1))
	fvoa = voa + (voa - mlag(voa))
	
	
	plota(voa['2008:01::2008:10'], type='l', col='orange', lwd=2)	
	plota.lines(vol['2008:01::2008:10'], col='blue', lwd=2)	
	plota.lines(fvoa['2008:01::2008:10'], col='green', lwd=2)	
	plota.legend(spl('Volatlity,Volatlity of Acceleration'), spl('orange,blue'))

plot of chunk plot-3

Note, check ?filter

Now we ready to back-test our strategy:

	#*****************************************************************
	# Code Strategies
	#*****************************************************************
	models = list()

	data$weight[] = NA
		data$weight[] = 1
	models$strategy = bt.run.share(data, clean.signal=F, silent=T)
	
	#*****************************************************************
	# standard volatility position sizing. 
	# In this case we use the same 10-day measure for both and a 1% daily target risk 
	#(1.5% for volatility of acceleration to reflect difference in scale)
	#*****************************************************************
	weight = 0.01/(vol *sqrt(1) )
		
	data$weight[] = NA
		data$weight[] = weight
	models$VOL = bt.run.share(data, clean.signal=F, silent=T)
	
	weight = 0.015/(voa *sqrt(1) )
		
	data$weight[] = NA
		data$weight[] = weight
	models$VOA = bt.run.share(data, clean.signal=F, silent=T)
	
	weight = 0.015/(fvoa *sqrt(1) )
		
	data$weight[] = NA
		data$weight[] = weight
	models$FVOA = bt.run.share(data, clean.signal=F, silent=T)

and create reports

Create Report:

	#*****************************************************************
	# Create Report
	#*****************************************************************
	plotbt(models, plotX = T, log = 'y', LeftMargin = 3, main = NULL)
		mtext('Cumulative Performance', side = 2, line = 1)

plot of chunk plot-5

	print(plotbt.strategy.sidebyside(models, make.plot=F, return.table=T))
  strategy VOL VOA FVOA
Period Jan1993 - Dec2014 Jan1993 - Dec2014 Jan1993 - Dec2014 Jan1993 - Dec2014
Cagr 9.43 13.34 18.72 21.41
Sharpe 0.57 0.78 0.83 0.87
DVR 0.42 0.56 0.56 0.55
Volatility 19.05 18.33 24.32 26.45
MaxDD -55.19 -49.21 -57.73 -56.34
AvgDD -2.06 -3.2 -4.15 -4.6
VaR -1.89 -1.84 -2.42 -2.46
CVaR -2.83 -2.69 -3.54 -3.76
Exposure 99.98 99.8 99.78 99.76

(this report was produced on: 2014-12-07)

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