# 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/… – Norgate Data Jan 7 '16 at 3:20

## 2 Answers

Why not just use Geometric Mean Returns? Each time you buy/sell an ETF calculate the holding period return as a percentage and plug into the formula. The answer is a percentage that you can use to calculate the approximate money appreciation (or loss) against your "fixed notional"

Perhaps I don't understand what you mean by "normalizing time series data".

To compare the two strategies, I would simply compute the Sharpe ratio of the two: holding the SPY vs the rotation strategy. This is a "normalized" comparison in that it takes into account both the mean return and the standard deviation of return.

• I am taking the Sharpe ratio already but I'd like to look at the tick-by-tick returns from both strategies as well. This would require tick by tick (day by day) return data to be normalized based on mean and sd. – Jerry Zhang Dec 7 '15 at 16:49