Let's say I have one asset and two different return distributions. One is more volatile. The other is less volatile. Let's also assume I can buy and sell options for this asset at the same implied volatility. If I go long straddles on the volatile distribution and short straddles on the less volatile distribution (buying/selling equal amounts of IV) - would that not be an arbitrage profit?
What's the scenario here exactly? One asset with different instruments, and different distributions in each? I.e., gold ETF versus gold futures... or something similar? You'd certainly be right about arbitrage if you knew the realized volatility of one instrument class was substantially different from the realized volatility of another, but both had identical implied volatility. The devil is in the details of course, and how/why this might be possible... (different trading hours? margins?)... arbitrage due to simple mispricing is possible, but extremely rare.
That's the right idea. Assuming for a minute this is possible (I fully appreciate your point that mispricings are very rare), am I correct to say the next concern would be to have enough capital to withstand any drawdawns? Granted, in the long run, the realized volty would work to your advantage, but I'm assuming there would be some periods in between where it may cause a drawdown.
I mean, how would we know? It really depends on the nature of the two distributions and why it exists. I'd suggest that, rather than just buying/selling (and holding)... you should turn this into a delta-hedging exercise. Hedge your long/short positions in each instrument at the implied volatility that you believe is "correct" for each on a regular (EOD?) basis. Theoretically speaking, you wouldn't even have any possibility of loss... ever. (Except the exact PNL depends on the value of gamma on the path you take... but anyways, close enough.)