Advanced Statistics: Swing it
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.030 | ||||
| SD | 0.056 | ||||
| Sharpe ratio (Glass type estimate) | -0.532 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.526 | ||||
| df | 62.000 | ||||
| t | -1.219 | ||||
| p | 0.886 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.390 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.331 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.386 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.335 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.784 | ||||
| Upside Potential Ratio | 1.167 | ||||
| Upside part of mean | 0.044 | ||||
| Downside part of mean | -0.074 | ||||
| Upside SD | 0.041 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.274 | ||||
| Mean of criterion | -0.030 | ||||
| SD of predictor | 0.309 | ||||
| SD of criterion | 0.056 | ||||
| Covariance | -0.002 | ||||
| r | -0.098 | ||||
| b (slope, estimate of beta) | -0.018 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 61.000 | ||||
| t(b) | -0.770 | ||||
| p(b) | 0.778 | ||||
| t(a) | -0.984 | ||||
| p(a) | 0.835 | ||||
| Lowerbound of 95% confidence interval for beta | -0.063 | ||||
| Upperbound of 95% confidence interval for beta | 0.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.075 | ||||
| Upperbound of 95% confidence interval for alpha | 0.026 | ||||
| Treynor index (mean / b) | 1.677 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.055 | ||||
| Sharpe ratio (Glass type estimate) | -0.563 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.556 | ||||
| df | 62.000 | ||||
| t | -1.290 | ||||
| p | 0.899 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.422 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.300 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.417 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.305 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.810 | ||||
| Upside Potential Ratio | 1.125 | ||||
| Upside part of mean | 0.043 | ||||
| Downside part of mean | -0.074 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.038 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 63.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.055 | ||||
| Covariance | -0.001 | ||||
| r | -0.077 | ||||
| b (slope, estimate of beta) | -0.014 | ||||
| a (intercept, estimate of alpha) | -0.028 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 61.000 | ||||
| t(b) | -0.600 | ||||
| p(b) | 0.725 | ||||
| t(a) | -1.123 | ||||
| p(a) | 0.867 | ||||
| Lowerbound of 95% confidence interval for beta | -0.061 | ||||
| Upperbound of 95% confidence interval for beta | 0.033 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.077 | ||||
| Upperbound of 95% confidence interval for alpha | 0.022 | ||||
| Treynor index (mean / b) | 2.186 | ||||
| Jensen alpha (a) | -0.028 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.956 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.068 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.190 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.190 | ||||
| Mean of outliers high | 1.022 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -35.557 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.109 | ||||
| VaR(95%) (regression method) | 0.013 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.038 | ||||
| Quartile 1 | 0.041 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.073 | ||||
| Maximum | 0.101 | ||||
| Mean of quarter 1 | 0.038 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.101 | ||||
| Inter Quartile Range | 0.032 | ||||
| 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) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.129 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.129 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.376 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.018 | ||||
| SD | 0.164 | ||||
| Sharpe ratio (Glass type estimate) | -0.108 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.108 | ||||
| df | 1394.000 | ||||
| t | -0.249 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.957 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.742 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.957 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.742 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.158 | ||||
| Upside Potential Ratio | 2.884 | ||||
| Upside part of mean | 0.325 | ||||
| Downside part of mean | -0.342 | ||||
| Upside SD | 0.120 | ||||
| Downside SD | 0.113 | ||||
| N nonnegative terms | 136.000 | ||||
| N negative terms | 1259.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1395.000 | ||||
| Mean of predictor | 0.416 | ||||
| Mean of criterion | -0.018 | ||||
| SD of predictor | 0.544 | ||||
| SD of criterion | 0.164 | ||||
| Covariance | -0.034 | ||||
| r | -0.385 | ||||
| b (slope, estimate of beta) | -0.116 | ||||
| a (intercept, estimate of alpha) | 0.031 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1393.000 | ||||
| t(b) | -15.552 | ||||
| p(b) | 0.739 | ||||
| t(a) | 0.466 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.131 | ||||
| Upperbound of 95% confidence interval for beta | -0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.099 | ||||
| Upperbound of 95% confidence interval for alpha | 0.160 | ||||
| Treynor index (mean / b) | 0.152 | ||||
| Jensen alpha (a) | 0.031 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.164 | ||||
| Sharpe ratio (Glass type estimate) | -0.190 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.190 | ||||
| df | 1394.000 | ||||
| t | -0.439 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.039 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.659 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.039 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.659 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.268 | ||||
| Upside Potential Ratio | 2.731 | ||||
| Upside part of mean | 0.318 | ||||
| Downside part of mean | -0.349 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.116 | ||||
| N nonnegative terms | 136.000 | ||||
| N negative terms | 1259.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1395.000 | ||||
| Mean of predictor | 0.269 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.543 | ||||
| SD of criterion | 0.164 | ||||
| Covariance | -0.034 | ||||
| r | -0.387 | ||||
| b (slope, estimate of beta) | -0.117 | ||||
| a (intercept, estimate of alpha) | 0.000 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1393.000 | ||||
| t(b) | -15.662 | ||||
| p(b) | 0.740 | ||||
| t(a) | 0.004 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | -0.132 | ||||
| Upperbound of 95% confidence interval for beta | -0.102 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.129 | ||||
| Upperbound of 95% confidence interval for alpha | 0.129 | ||||
| Treynor index (mean / b) | 0.267 | ||||
| Jensen alpha (a) | 0.000 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1395.000 | ||||
| Minimum | 0.900 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.104 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 165.000 | ||||
| Percentage of outliers low | 0.118 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 165.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.200 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | NA | ||||
| VaR(95%) (regression method) | NA | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.083 | ||||
| Maximum | 0.106 | ||||
| Mean of quarter 1 | 0.012 | ||||
| Mean of quarter 2 | 0.039 | ||||
| Mean of quarter 3 | 0.063 | ||||
| Mean of quarter 4 | 0.104 | ||||
| Inter Quartile Range | 0.056 | ||||
| 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) | -679.899 | ||||
| VaR(95%) (moments method) | 0.106 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -5.120 | ||||
| VaR(95%) (regression method) | 0.119 | ||||
| Expected Shortfall (regression method) | 0.119 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.121 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.124 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.619 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.959 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.638 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.748 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.644 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8677919395210164.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -191366177770620060885015005757440.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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 | 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 for a one-period unit investment (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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||