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Suppose I'm running automated classic price arbitrage on 3 currencies (let's ignore the unfeasibility of this in our day and age). We have currency pairs Gold/Silver, Silver/Bronze, and Gold/Bronze.

I have two questions:

(1) In general, is it better (in terms of being able to successfully execute a complete set of arbitrage trades over some period of time) for these pairs to demonstrate high or low volatility within that period of time?

(2) Assume that Gold/Silver demonstrates

(a) low volatility (b) high volatility.

In each of these cases, is which is better (in terms of being able to successfully execute a complete set of arbitrage trades over some period of time): having the other pairs demonstrate high volatility or low volatility within that period of time? Why?

Forgive me if this is an exceedingly elementary question.

Follow up question: considering that it's best to execute a set of arb trades as soon as possible (lest someone else do it before you and move the prices against you), you'd probably want to measure volatility over second-long periods. Would volatility calculations over such [small] timeframes lose their significance?

Edit: This link, "A Dozen Things I’ve Learned from Jim Simons" quotes Simons as saying:

Once in a while the phenomena we exploit are particularly present. We like a reasonable amount of volatility. In our business we want some action [...] Tumult is usually good for us.

This makes me think that higher volatility is better for arbitrage, but why? Also, this tumult may be amenable to several of Renaissance's strategies, but we don't know that arbitrage is one of said strategies, so I can't really draw any conclusions.

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  • $\begingroup$ This is too subjective and anecdotal to be a formal answer, but in my experience arbitrage opportunities are more common in times of higher than normal volatility. I saw this up close during the Financial Crisis of 2007-2008. In essence an arbitrage opp is a sign the markets are not working well. To take advantage of such opps however, you have to have enough risk capital, which is hard to come by during a financial crisis. In more normal times the arb opportunites largely disappear. $\endgroup$ – Alex C Aug 12 '17 at 19:31

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