# ETFs have lower tracking error than Futures?

I used the daily returns of SPX Index, SPY US Equity, and SPA Index. I then calculate their standard deviation as hedging instruments with respect to SPX Index, i.e., (spx_ret - spy_ret) or (spx_ret - spa_ret). However, the results I obtained were strange:

SD (spx_ret - spy_ret) = 0.0012959
SD (spx_ret - spa_ret) = 0.0006794


How can an ETF have a larger tracking error? I thought Futures are almost like a "perfect hedge" and ETFs have huge tracking error due to management and rebalancing fees. Am I missing something in the calculation?

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1) isn't the ETF error larger (0.0012959 > 0.0006794)? 2) I would expect the ETF tracking error to be lower. It holds the actual index components and has fewer transactions than the futures index. The futures contracts must be rolled periodically, while the ETF only needs to transact for index constituent changes. –  Joshua Ulrich Jul 16 '14 at 11:52
yes typo. etf error is larger –  Mariska Jul 16 '14 at 23:40

You can't really adjust, those are traded instruments so whatever price they finish at is the "right" price. If you want to formalize it a little (assuming no dividends ie you're looking at an excess-return index), the value of your future is $\exp(-r(T-t))S_t$ with $T$ the expiry of the future (it's an arbitrage argument, you borrow money, buy the stocks etc.). If you want to be really precise, you also need to take into account the margining of the future (you post cash to the exchange which in turns gives you interest). –  Matt B. Jul 17 '14 at 10:49