Hi @

[email protected] In my example (ie, flipping two coins such that head pays $1.00 and tails pays zero), if you perfect negative correlation, then your outcome must be {heads, tails} or {tails, heads}. Under an option on the worse of two with payoff = min(S1,S2), you are ensured a zero payoff because you are ensured a tail. Either the first flip is a tail, or if it is a heads, then the second flip must be a tail.

Or maybe we can think of it this way. Two assets, S1 and S2, each with outcome "high value" or "low value" such that the four outcomes are:

- S1 = low value, S2 = low value --> "better of two" payoff is low, "worse of two" payoff is low
- S1 = low value, S2 = high value --> "better of two" payoff is high, "worse of two" payoff is low
- S1 = high value, S2 = low value --> "better of two" payoff is high, "worse of two" payoff is low
- S1 = high value, S2 = high value --> "better of two" payoff is high, "worse of two" payoff is high

What about correlation?

- Zero correlation implies each of the four outcomes is equally likely, in which case (under zero correlation), the "better of two" has a 75% probability of high payoff but the worse of two has only a 25% probability of high payoff.
- Perfect
*positive *correlation implies only outcomes (1) or (4); i.e., they are both low or high together. The "better of two" probability of high payoff *decreases *to 50%; the worse of two probability of high payoff *increases *to 50%.
- Perfect
*negative* correlation implies only outcomes (2) or (3); i.e., they are opposite high/low. The "better of two" probability of high payoff *increases *to 100%; the worse of two probability of high payoff *decreases *to zero(!).

I hope that's a useful perspective, thanks!

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