Hello friends.
I think the clearest way to understand the correlation exposure of a best-of is to look at it through the lens of a worst-of. The worst-0f is replicated by vanilla call 1 + vanilla call 2 - best-of 1 and 2 calls. Go through a couple at-expiry scenarios to convince yourself that that is in fact the case. Neither of the vanillas on their own have any correlation exposure, so the worst-of and best-of have exactly opposite correlation exposure, which I think is pretty intuitive anyway. The worst-of is long correlation. This is true because if the correlation were very negative, that would mean one call would go in the money just as the other call would go out of the money, which in turn would mean the worst-of would pay off zero. You need to the correlation to be as high as possible so that both calls can go as far in the money as possible at the same time. Because buying the worst-of makes you long correlation, if you were to instead buy a best-of you would then be short correlation (and want correlation to be -1). If you were to sell a best-of, you would actually want the correlation to be as high as possible, i.e. as close to +1 as possible, so that you would have the opportunity for both calls to go out of the money and for the best-of to therefore be worth zero.