Comparing Sector Rotation with SPY Using Returns and Risk-Adjusted Metrics
Summary
The document asks how to compare a sector rotation strategy using SPDR sector ETFs with a buy-and-hold investment in SPY when their share prices differ. It considers standardizing or scaling price series, but the replies redirect attention from nominal price levels to investment returns.
One response recommends calculating each ETF trade’s percentage holding-period return and compounding those returns geometrically to estimate appreciation or loss on a fixed notional. Another suggests comparing the rotation strategy and SPY with Sharpe ratios, which account for both average returns and return variability. The exchange gives no worked calculations, assumptions about transaction costs, or evidence from the proposed five years of daily data. The choice of metric depends on the comparison goal: compounded wealth captures growth, while Sharpe summarizes return per unit of volatility; neither alone describes every aspect of strategy performance.
Key ideas
- ETF share prices need not be equal to compare investment performance.
- Calculate percentage holding-period returns and compound them geometrically to express performance on a fixed notional.
- A Sharpe ratio comparison incorporates both average return and return variability.
- The exchange provides suggestions but no empirical results or treatment of trading costs.
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# Normalizing SPY ETF time series data with its sector ETFs? # 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. ## Answer by Valtinho (score 3, accepted) https://quant.stackexchange.com/a/24760 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" ## Answer by nbbo2 (score 0) https://quant.stackexchange.com/a/22163 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.
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