Advanced Statistics: S&P Swing
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
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| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.043 | ||||
| SD | 0.263 | ||||
| Sharpe ratio (Glass type estimate) | 0.165 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.163 | ||||
| df | 82.000 | ||||
| t | 0.433 | ||||
| p | 0.333 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.581 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.910 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.582 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.909 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.262 | ||||
| Upside Potential Ratio | 1.766 | ||||
| Upside part of mean | 0.292 | ||||
| Downside part of mean | -0.249 | ||||
| Upside SD | 0.203 | ||||
| Downside SD | 0.165 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.231 | ||||
| Mean of criterion | 0.043 | ||||
| SD of predictor | 0.241 | ||||
| SD of criterion | 0.263 | ||||
| Covariance | -0.001 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.017 | ||||
| a (intercept, estimate of alpha) | 0.047 | ||||
| Mean Square Error | 0.070 | ||||
| DF error | 81.000 | ||||
| t(b) | -0.140 | ||||
| p(b) | 0.555 | ||||
| t(a) | 0.452 | ||||
| p(a) | 0.326 | ||||
| Lowerbound of 95% confidence interval for beta | -0.259 | ||||
| Upperbound of 95% confidence interval for beta | 0.225 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.161 | ||||
| Upperbound of 95% confidence interval for alpha | 0.255 | ||||
| Treynor index (mean / b) | -2.551 | ||||
| Jensen alpha (a) | 0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.010 | ||||
| SD | 0.260 | ||||
| Sharpe ratio (Glass type estimate) | 0.037 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.037 | ||||
| df | 82.000 | ||||
| t | 0.098 | ||||
| p | 0.461 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.708 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.783 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.708 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.782 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.054 | ||||
| Upside Potential Ratio | 1.525 | ||||
| Upside part of mean | 0.273 | ||||
| Downside part of mean | -0.263 | ||||
| Upside SD | 0.186 | ||||
| Downside SD | 0.179 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.204 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.214 | ||||
| SD of criterion | 0.260 | ||||
| Covariance | -0.002 | ||||
| r | -0.041 | ||||
| b (slope, estimate of beta) | -0.050 | ||||
| a (intercept, estimate of alpha) | 0.020 | ||||
| Mean Square Error | 0.068 | ||||
| DF error | 81.000 | ||||
| t(b) | -0.371 | ||||
| p(b) | 0.644 | ||||
| t(a) | 0.193 | ||||
| p(a) | 0.424 | ||||
| Lowerbound of 95% confidence interval for beta | -0.318 | ||||
| Upperbound of 95% confidence interval for beta | 0.218 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | 0.225 | ||||
| Treynor index (mean / b) | -0.194 | ||||
| Jensen alpha (a) | 0.020 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.115 | ||||
| Expected Shortfall on VaR | 0.142 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.058 | ||||
| Expected Shortfall on VaR | 0.114 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 83.000 | ||||
| Minimum | 0.786 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.022 | ||||
| Maximum | 1.259 | ||||
| Mean of quarter 1 | 0.929 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.098 | ||||
| Inter Quartile Range | 0.027 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.157 | ||||
| Mean of outliers low | 0.896 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.145 | ||||
| Mean of outliers high | 1.143 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.383 | ||||
| VaR(95%) (moments method) | 0.034 | ||||
| Expected Shortfall (moments method) | 0.072 | ||||
| Extreme Value Index (regression method) | 0.011 | ||||
| VaR(95%) (regression method) | 0.088 | ||||
| Expected Shortfall (regression method) | 0.140 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.150 | ||||
| Median | 0.291 | ||||
| Quartile 3 | 0.433 | ||||
| Maximum | 0.574 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.574 | ||||
| Inter Quartile Range | 0.283 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.065 | ||||
| Compounded annual return (geometric extrapolation) | 0.055 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.096 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.096 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.388 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.034 | ||||
| SD | 0.221 | ||||
| Sharpe ratio (Glass type estimate) | 0.153 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.153 | ||||
| df | 1831.000 | ||||
| t | 0.405 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.588 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.894 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.588 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.894 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.218 | ||||
| Upside Potential Ratio | 4.775 | ||||
| Upside part of mean | 0.742 | ||||
| Downside part of mean | -0.708 | ||||
| Upside SD | 0.158 | ||||
| Downside SD | 0.155 | ||||
| N nonnegative terms | 640.000 | ||||
| N negative terms | 1192.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1832.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | 0.034 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.221 | ||||
| Covariance | -0.006 | ||||
| r | -0.115 | ||||
| b (slope, estimate of beta) | -0.109 | ||||
| a (intercept, estimate of alpha) | 0.060 | ||||
| Mean Square Error | 0.048 | ||||
| DF error | 1830.000 | ||||
| t(b) | -4.939 | ||||
| p(b) | 0.557 | ||||
| t(a) | 0.715 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.153 | ||||
| Upperbound of 95% confidence interval for beta | -0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.104 | ||||
| Upperbound of 95% confidence interval for alpha | 0.223 | ||||
| Treynor index (mean / b) | -0.310 | ||||
| Jensen alpha (a) | 0.060 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.009 | ||||
| SD | 0.226 | ||||
| Sharpe ratio (Glass type estimate) | 0.039 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.039 | ||||
| df | 1831.000 | ||||
| t | 0.104 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.702 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.780 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.702 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.780 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.053 | ||||
| Upside Potential Ratio | 4.406 | ||||
| Upside part of mean | 0.730 | ||||
| Downside part of mean | -0.721 | ||||
| Upside SD | 0.153 | ||||
| Downside SD | 0.166 | ||||
| N nonnegative terms | 640.000 | ||||
| N negative terms | 1192.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1832.000 | ||||
| Mean of predictor | 0.207 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.226 | ||||
| Covariance | -0.006 | ||||
| r | -0.118 | ||||
| b (slope, estimate of beta) | -0.114 | ||||
| a (intercept, estimate of alpha) | 0.032 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 1830.000 | ||||
| t(b) | -5.089 | ||||
| p(b) | 0.559 | ||||
| t(a) | 0.382 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.158 | ||||
| Upperbound of 95% confidence interval for beta | -0.070 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.134 | ||||
| Upperbound of 95% confidence interval for alpha | 0.199 | ||||
| Treynor index (mean / b) | -0.078 | ||||
| Jensen alpha (a) | 0.032 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1832.000 | ||||
| Minimum | 0.761 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.112 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 293.000 | ||||
| Percentage of outliers low | 0.160 | ||||
| Mean of outliers low | 0.985 | ||||
| Number of outliers high | 288.000 | ||||
| Percentage of outliers high | 0.157 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.748 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.030 | ||||
| Extreme Value Index (regression method) | 0.346 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.017 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.046 | ||||
| Maximum | 0.620 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | 0.039 | ||||
| Mean of quarter 4 | 0.245 | ||||
| Inter Quartile Range | 0.038 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.091 | ||||
| Mean of outliers high | 0.620 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.073 | ||||
| VaR(95%) (moments method) | 0.240 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 3.644 | ||||
| VaR(95%) (regression method) | 1.016 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.064 | ||||
| Compounded annual return (geometric extrapolation) | 0.054 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.088 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.222 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.918 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.005 | ||||
| Sharpe ratio (Glass type estimate) | -10.786 | ||||
| Sharpe ratio (Hedges UMVUE) | -10.724 | ||||
| df | 130.000 | ||||
| t | -7.627 | ||||
| p | 0.778 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -13.835 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -7.703 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13.787 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7.661 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -9.507 | ||||
| Upside Potential Ratio | 1.588 | ||||
| Upside part of mean | 0.010 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.002 | ||||
| Downside SD | 0.006 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 109.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.124 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.148 | ||||
| SD of criterion | 0.005 | ||||
| Covariance | 0.000 | ||||
| r | 0.161 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.848 | ||||
| p(b) | 0.398 | ||||
| t(a) | -7.783 | ||||
| p(a) | 0.840 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -9.950 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.005 | ||||
| Sharpe ratio (Glass type estimate) | -10.786 | ||||
| Sharpe ratio (Hedges UMVUE) | -10.724 | ||||
| df | 130.000 | ||||
| t | -7.627 | ||||
| p | 0.778 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -13.835 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -7.704 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13.787 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7.661 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -9.507 | ||||
| Upside Potential Ratio | 1.587 | ||||
| Upside part of mean | 0.010 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.002 | ||||
| Downside SD | 0.006 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 109.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.113 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.148 | ||||
| SD of criterion | 0.005 | ||||
| Covariance | 0.000 | ||||
| r | 0.162 | ||||
| b (slope, estimate of beta) | 0.006 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.867 | ||||
| p(b) | 0.397 | ||||
| t(a) | -7.780 | ||||
| p(a) | 0.840 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.012 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -9.834 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.999 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.001 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.999 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.001 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -7.663 | ||||
| VaR(95%) (moments method) | -0.140 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.797 | ||||
| VaR(95%) (regression method) | -0.004 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.005 | ||||
| Maximum | 0.009 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.009 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | 0.000 | ||||
| Mean of outliers high | NA | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | NA | ||||
| VaR(95%) (moments method) | NA | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.515 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.515 | ||||
| Compounded annual return / Expected Shortfall lognormal | -15.149 | ||||