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It has been long observed (Lo and MacKinlay 1988) that, for a mean-reverting process, the high frequency volatility is bigger than the low frequency volatility, hence an arbitrage opportunity. For instance, the daily volatility > monthly volatility > yearly volatility. Conceivably, we may make a profit by buying the bigger volatility and selling the smaller volatility. In fact, we can mathematically compute the expected P&L for any price process.

The success of the VolArb strategy depends on

- finding or constructing a piece-wise mean-reverting or slowly-moving-mean asset,
- trading the “right” volatility difference(s).

Each of the two topics is an important subject in its own right.

We have extensively evaluated the performance of VolArb on trading currency pairs in many settings, taking into account bid-ask. For low frequency trading, the P&L is above 6% of the *maximal* exposure with a max draw down of 2 – 3%. The Sharpe ratio ranges from 2 to 3. For higher frequency trading, e.g., intra-day, the P&L ranges from 20% – 40% of the *maximal* exposure with a max draw down of 2 – 8%. The Sharpe ratio is above 2.

# References

- VolArb P&L
- Poterba and Summers
- Lo, A. W. and C. MacKinlay (1988) “The Size and Power of the Variance Ratio Tests in Finite Samples: A Monte Carlo Investigation” Journal of Econometrics 40, 203-38.
- On H-volatility in financial mathematics

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