Replicating Relative-Performance Indexes with Long-Short Positions and Options

# Answer by Tal Fishman (score 1, accepted)


# Buying one company or index against another, is this readily possible with options, with an accurate return (also Alpha Indexes)












There's a relatively new product in the market / on the Nasdaq called Alpha Indexes. It lets one own a company -- e.g. Apple, GE, Google, etc -- as the difference between how that company does (the "target"), and a benchmark (e.g. SPY). That seems like a "stock analyst's dream", being able to say they believe company XYZ will grow their earnings and do better than the market by X%, rather than assigning a future price to something that could be greatly affected by other factors (e.g. Euro debt crisis or whatever next crisis), which frankly, seems highly incestuous: having to pick the price of a particular instrument, that is affected greatly by other instruments in ways it should not be (vs. investing on relative performance).

The question I have is, how closely can this return be done today with options. What are the parallels, and how close/far off are they? Perhaps beyond company XYZ vs SPY, what if someone just wants to own gold against copper, or Apple against Microsoft, etc. That seems like just substituting another benchmark in.

## Answer by Tal Fishman (score 1, accepted)

https://quant.stackexchange.com/a/2495

My understanding is that this is a completely new product which is not perfectly statically replicable given current instruments. The product, which your explanation does not make clear, is an option on an index, where the index value is close to (but not exactly, due to dividends) the total return from a long-short position in the two underlyings. It is not replicable with existing options because, for example, the deltas of options on the underlyings would change if the two underlyings moved in the same direction in lock-step, but the delta of this new option would not (the index value would remain at 100).

To use your example, simulating AVSPY (AAPL vs. SPY) is very easy using equal dollar positions long AAPL and short SPY. However, that is not the point. AVSPY is just an index underlying for a new options chain. One could, of course, replicate this option dynamically by trading the AAPL-SPY long-short pair, but that is subject to all the usual caveats of dynamic replication.

## Answer by chrisaycock (score 2)

https://quant.stackexchange.com/a/2494

These Alpha Indexes are a bet on the excess returns of the target instrument. Options are, ultimately, a bet on the volatility of the underlying. The two are not related. If you wanted to replicate an Alpha Index of gold against copper, just buy gold and short copper (usually through the futures market). Again, this has nothing to do with options.