# Normalizing SPY ETF time series data with its sector ETFs?

I am looking to compare the returns of a sector rotation strategy between the various SPDR sector ETFs

• XLY,

• XLP,

• XLE,

• XLF,

• XLV,

• XLI,

• XLB,

• XLK,

• XLU

vs. the returns of just investing in the SPY overall S&P 500 ETF.

I am using the price data of the 9 ETFs vs. the price data of the SPY ETFs and would like to normalize based on a fixed notional. The sector ETF prices are between 24.75-81.11. The SPY ETF sits at around 200.

How do I best compare their returns?

Ways I've heard of are:

a'(i) := [ a(i) - mean( a ) ] / std_dev( a )
a'(i) := [ a(i) - min( a ) ] / [ max ( a ) - min ( a ) ]


I also see a number of suggestions at: How to normalize stock data but am not sure which one would be most appropriate for this purpose.

I suppose moving averages can also be used. I'm working with 5 years of daily close price data.

• Beware that these "Sectors" introduce some additional factors. The methodology used by the Select Sector indexes is quite different from the S&P 500 methodology. The "select" part introduces additional capping criteria which changes the weighting of stocks. In addition, some of the "Sectors" are actually industry groups, multiple sectors combined, others with items excluded too. us.spindices.com/documents/methodologies/… Jan 7 '16 at 3:20