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@paulgp @nikir1 Quite nice. @choffstein also sets things up nicely to explain why vol drag (yes, just the generic difference between arithmetic and geometric means) is especially bad with leverage: The correlation between the “two portfolios”—benchmark and active bets (1/) @choffstein/1790820725621739544On twitter.com
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@paulgp @nikir1 @choffstein In the example, the benchmark (Russel 1000) is positively correlated with the active bets (Russel Growth – Benchmark), with rho ≈ 0.24 But that’s just another way of saying that the Russel Growth is levered relative to the benchmark. And that leverage makes the “vol drag” worse @choffstein/1790820726829662322Permalink On twitter.com
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@paulgp @nikir1 @choffstein If we regressed (RG-B) returns on B returns, we’d get a regression coefficient equal to—as always—the correlation scaled by the relative volatilities. Corey gave us all those numbers! (RG-B) = a + bB + e b = correlation * (volRGmB / volB) ≈ 0.24 * (0.34%/1.12%) ≈ 0.07Permalink On twitter.com
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@paulgp @nikir1 @choffstein So the active bets (i.e., the Long–Short) has a beta of 0.07 That means the portfolio (i.e., 100% benchmark + 100% LS) has a beta of 1.07. Leverage!Permalink On twitter.com
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@paulgp @nikir1 @choffstein All in all g ≈ a - v/2 = (aB - vB/2) + (aLS - vLS/2) - (σB σLS 𝜌) • The first term includes the benchmark’s vol drag • The second term includes the active bets’ vol drag • The third term is the *extra* drag from the active bets’ leverage Fun. (N/N) @choffstein/1790820725621739544Permalink On twitter.com
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