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Why buying a call at 20 vol and selling a put at 40 vol is not an arb

Why buying a call at 20 vol and selling a put at 40 vol is not an arb

The above scenario is posed by an imaginary character in the book as “the greatest trade in the world”.
 
Why is it not?
 
[Kris: In short — the path dependence of volatility…The author disambiguates the noise that comes from non-continuous hedging around a fixed vol and the idea that true volatility is not constant and depends on the level of spot]
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