====================================================================== PORTFOLIO SORTS & ECONOMIC SIGNIFICANCE ====================================================================== ATM IV (30d) → 1-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 3.17 7.98 12.97 0.615 2.382 3777 Q2 3.69 9.29 15.75 0.590 2.284 3777 Q3 4.50 11.34 18.10 0.627 2.426 3777 Q4 6.02 15.16 21.28 0.713 2.759 3777 Q5 8.67 21.85 29.73 0.735 2.846 3777 L/S(5-1) 5.51 13.88 25.55 0.543 2.103 3777 ATM IV (30d) → 5-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 29.29 15.23 11.82 1.288 10.979 3777 Q2 27.47 14.28 15.05 0.949 8.090 3777 Q3 21.90 11.39 17.42 0.654 5.571 3777 Q4 17.87 9.29 20.85 0.446 3.799 3777 Q5 25.90 13.47 29.53 0.456 3.887 3777 L/S(5-1) -3.39 -1.76 26.13 -0.067 -0.575 3777 Volatility Skew (25d) → 1-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 4.91 12.37 18.36 0.674 2.609 3778 Q2 4.35 10.97 17.22 0.637 2.467 3778 Q3 5.73 14.44 18.78 0.769 2.978 3778 Q4 5.89 14.84 20.42 0.727 2.813 3778 Q5 6.13 15.46 24.22 0.638 2.471 3778 L/S(5-1) 1.22 3.08 19.70 0.157 0.606 3778 Volatility Skew (25d) → 5-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 62.40 32.45 17.74 1.829 15.593 3778 Q2 33.24 17.28 16.37 1.056 9.001 3778 Q3 22.98 11.95 18.06 0.662 5.640 3778 Q4 14.25 7.41 19.62 0.378 3.218 3778 Q5 -9.78 -5.08 23.98 -0.212 -1.807 3778 L/S(5-1) -72.18 -37.53 20.10 -1.868 -15.918 3778 Implied Skewness → 1-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 7.67 19.33 24.36 0.794 3.072 3777 Q2 4.56 11.48 20.21 0.568 2.199 3777 Q3 4.92 12.41 18.49 0.671 2.598 3777 Q4 4.99 12.57 17.75 0.708 2.742 3777 Q5 4.37 11.00 16.84 0.653 2.530 3777 L/S(5-1) -3.31 -8.33 17.91 -0.465 -1.800 3777 Implied Skewness → 5-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 42.45 22.08 24.22 0.912 7.769 3777 Q2 15.43 8.03 19.58 0.410 3.493 3777 Q3 18.44 9.59 17.64 0.544 4.634 3777 Q4 18.93 9.84 16.98 0.580 4.940 3777 Q5 23.39 12.16 15.88 0.766 6.527 3777 L/S(5-1) -19.06 -9.91 18.81 -0.527 -4.493 3777 Implied Kurtosis → 1-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 7.90 19.91 24.26 0.821 3.177 3777 Q2 4.79 12.08 20.67 0.584 2.261 3777 Q3 4.16 10.49 18.77 0.559 2.164 3777 Q4 4.23 10.65 17.34 0.614 2.377 3777 Q5 4.79 12.06 15.65 0.771 2.984 3777 L/S(5-1) -3.11 -7.85 18.30 -0.429 -1.660 3777 Implied Kurtosis → 5-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 -24.35 -12.66 23.88 -0.530 -4.519 3777 Q2 10.82 5.63 20.22 0.278 2.372 3777 Q3 30.12 15.66 17.93 0.874 7.444 3777 Q4 47.43 24.66 16.32 1.511 12.880 3777 Q5 60.33 31.37 15.15 2.071 17.651 3777 L/S(5-1) 84.68 44.04 18.91 2.328 19.843 3777 Put-Call Volume Ratio → 1-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 2.99 7.53 18.09 0.416 1.662 4024 Q2 6.05 15.24 19.52 0.780 3.119 4024 Q3 6.22 15.68 19.74 0.794 3.174 4024 Q4 6.28 15.83 19.30 0.820 3.278 4024 Q5 5.46 13.76 18.53 0.743 2.968 4024 L/S(5-1) 2.47 6.24 12.04 0.518 2.070 4024 Put-Call Volume Ratio → 5-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 58.19 30.26 17.47 1.732 15.234 4024 Q2 37.30 19.39 18.71 1.036 9.118 4024 Q3 26.60 13.83 19.32 0.716 6.300 4024 Q4 12.21 6.35 18.66 0.340 2.994 4024 Q5 -0.05 -0.03 17.68 -0.002 -0.014 4024 L/S(5-1) -58.25 -30.29 12.22 -2.478 -21.796 4024 Put-Call OI Ratio → 1-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 4.72 11.88 18.65 0.637 2.546 4024 Q2 4.20 10.59 17.87 0.592 2.368 4024 Q3 4.53 11.43 19.01 0.601 2.402 4024 Q4 6.72 16.93 19.64 0.862 3.445 4024 Q5 6.75 17.01 20.12 0.846 3.379 4024 L/S(5-1) 2.04 5.13 13.28 0.386 1.544 4024 Put-Call OI Ratio → 5-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 24.26 12.61 18.30 0.689 6.062 4024 Q2 18.55 9.64 17.37 0.555 4.884 4024 Q3 25.65 13.34 17.53 0.761 6.693 4024 Q4 31.82 16.55 19.01 0.870 7.655 4024 Q5 34.38 17.88 19.44 0.919 8.089 4024 L/S(5-1) 10.13 5.27 13.27 0.397 3.492 4024 IV Term Structure Slope → 1-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 7.72 19.46 25.81 0.754 2.457 2676 Q2 1.85 4.67 19.88 0.235 0.765 2676 Q3 2.47 6.23 18.81 0.331 1.079 2676 Q4 4.16 10.48 18.14 0.578 1.883 2676 Q5 5.81 14.63 20.14 0.726 2.367 2676 L/S(5-1) -1.92 -4.83 20.46 -0.236 -0.769 2676 IV Term Structure Slope → 5-Day Returns: Q Mean(bps) Ann.Ret% Ann.Vol% Sharpe t-stat N Q1 20.45 10.63 25.99 0.409 2.935 2676 Q2 9.71 5.05 20.02 0.252 1.810 2676 Q3 24.57 12.78 18.55 0.689 4.941 2676 Q4 34.51 17.94 17.72 1.013 7.265 2676 Q5 42.23 21.96 19.52 1.125 8.070 2676 L/S(5-1) 21.79 11.33 20.30 0.558 4.004 2676 ====================================================================== LONG-SHORT PORTFOLIO SUMMARY (Q5 - Q1) ====================================================================== sort_variable return_horizon mean_daily_bps annualized_return_pct sharpe_ratio t_statistic ATM IV (30d) 1-Day 5.507 13.878 0.543 2.103 ATM IV (30d) 5-Day -3.391 -1.763 -0.067 -0.575 Volatility Skew (25d) 1-Day 1.223 3.083 0.157 0.606 Volatility Skew (25d) 5-Day -72.178 -37.533 -1.868 -15.918 Implied Skewness 1-Day -3.305 -8.329 -0.465 -1.800 Implied Skewness 5-Day -19.064 -9.913 -0.527 -4.493 Implied Kurtosis 1-Day -3.114 -7.847 -0.429 -1.660 Implied Kurtosis 5-Day 84.684 44.036 2.328 19.843 Put-Call Volume Ratio 1-Day 2.474 6.236 0.518 2.070 Put-Call Volume Ratio 5-Day -58.247 -30.289 -2.478 -21.796 Put-Call OI Ratio 1-Day 2.036 5.131 0.386 1.544 Put-Call OI Ratio 5-Day 10.126 5.266 0.397 3.492 IV Term Structure Slope 1-Day -1.915 -4.826 -0.236 -0.769 IV Term Structure Slope 5-Day 21.786 11.329 0.558 4.004 ====================================================================== DOUBLE SORT: IV_ATM x IMPLIED_SKEWNESS → 5-Day Returns ====================================================================== Low Skew Med Skew High Skew Low IV 8.15 24.12 35.90 Med IV 22.11 23.80 15.62 High IV 41.76 2.72 -47.82 t-statistics: Low Skew Med Skew High Skew Low IV 2.037 11.080 24.972 Med IV 6.477 10.148 5.830 High IV 13.121 0.649 -6.171 ====================================================================== TRANSACTION COST SENSITIVITY (Long-Short on Implied Skewness, 5D) ====================================================================== TC (bps) Net Ret(bps) Ann.Ret% Sharpe 0 -19.06 -9.91 -0.527 5 -21.06 -10.95 -0.582 10 -23.06 -11.99 -0.638 15 -25.06 -13.03 -0.693 20 -27.06 -14.07 -0.748 30 -31.06 -16.15 -0.859 50 -39.06 -20.31 -1.080 PORTFOLIO SORTS COMPLETE.