Advanced Statistics: Steady Profits
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 | 0.009 | ||||
| SD | 0.432 | ||||
| Sharpe ratio (Glass type estimate) | 0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.021 | ||||
| df | 51.000 | ||||
| t | 0.045 | ||||
| p | 0.482 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.920 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.963 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.920 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.963 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.035 | ||||
| Upside Potential Ratio | 1.612 | ||||
| Upside part of mean | 0.436 | ||||
| Downside part of mean | -0.427 | ||||
| Upside SD | 0.332 | ||||
| Downside SD | 0.271 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.362 | ||||
| Mean of criterion | 0.009 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.432 | ||||
| Covariance | -0.014 | ||||
| r | -0.120 | ||||
| b (slope, estimate of beta) | -0.196 | ||||
| a (intercept, estimate of alpha) | 0.080 | ||||
| Mean Square Error | 0.188 | ||||
| DF error | 50.000 | ||||
| t(b) | -0.855 | ||||
| p(b) | 0.802 | ||||
| t(a) | 0.359 | ||||
| p(a) | 0.361 | ||||
| Lowerbound of 95% confidence interval for beta | -0.657 | ||||
| Upperbound of 95% confidence interval for beta | 0.265 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.370 | ||||
| Upperbound of 95% confidence interval for alpha | 0.531 | ||||
| Treynor index (mean / b) | -0.048 | ||||
| Jensen alpha (a) | 0.080 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.080 | ||||
| SD | 0.427 | ||||
| Sharpe ratio (Glass type estimate) | -0.187 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.184 | ||||
| df | 51.000 | ||||
| t | -0.389 | ||||
| p | 0.651 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.128 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.756 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.127 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.758 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.257 | ||||
| Upside Potential Ratio | 1.251 | ||||
| Upside part of mean | 0.390 | ||||
| Downside part of mean | -0.470 | ||||
| Upside SD | 0.287 | ||||
| Downside SD | 0.311 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 52.000 | ||||
| Mean of predictor | 0.325 | ||||
| Mean of criterion | -0.080 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.427 | ||||
| Covariance | -0.012 | ||||
| r | -0.114 | ||||
| b (slope, estimate of beta) | -0.199 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.184 | ||||
| DF error | 50.000 | ||||
| t(b) | -0.813 | ||||
| p(b) | 0.790 | ||||
| t(a) | -0.068 | ||||
| p(a) | 0.527 | ||||
| Lowerbound of 95% confidence interval for beta | -0.692 | ||||
| Upperbound of 95% confidence interval for beta | 0.293 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.459 | ||||
| Upperbound of 95% confidence interval for alpha | 0.428 | ||||
| Treynor index (mean / b) | 0.401 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.189 | ||||
| Expected Shortfall on VaR | 0.229 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.104 | ||||
| Expected Shortfall on VaR | 0.201 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 52.000 | ||||
| Minimum | 0.644 | ||||
| Quartile 1 | 0.971 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.409 | ||||
| Mean of quarter 1 | 0.873 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.149 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.173 | ||||
| Mean of outliers low | 0.840 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.192 | ||||
| Mean of outliers high | 1.184 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.958 | ||||
| VaR(95%) (moments method) | 0.096 | ||||
| Expected Shortfall (moments method) | 0.105 | ||||
| Extreme Value Index (regression method) | -0.021 | ||||
| VaR(95%) (regression method) | 0.142 | ||||
| Expected Shortfall (regression method) | 0.209 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.028 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.090 | ||||
| Quartile 3 | 0.170 | ||||
| Maximum | 0.717 | ||||
| Mean of quarter 1 | 0.043 | ||||
| Mean of quarter 2 | 0.090 | ||||
| Mean of quarter 3 | 0.170 | ||||
| Mean of quarter 4 | 0.717 | ||||
| Inter Quartile Range | 0.111 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.717 | ||||
| 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) | -0.033 | ||||
| Compounded annual return (geometric extrapolation) | -0.035 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.049 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.049 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.154 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.175 | ||||
| SD | 0.741 | ||||
| Sharpe ratio (Glass type estimate) | 0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.235 | ||||
| df | 1135.000 | ||||
| t | 0.490 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.706 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.177 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.706 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.177 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.410 | ||||
| Upside Potential Ratio | 3.578 | ||||
| Upside part of mean | 1.525 | ||||
| Downside part of mean | -1.350 | ||||
| Upside SD | 0.606 | ||||
| Downside SD | 0.426 | ||||
| N nonnegative terms | 248.000 | ||||
| N negative terms | 888.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1136.000 | ||||
| Mean of predictor | 0.371 | ||||
| Mean of criterion | 0.175 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.741 | ||||
| Covariance | 0.002 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.028 | ||||
| a (intercept, estimate of alpha) | 0.164 | ||||
| Mean Square Error | 0.550 | ||||
| DF error | 1134.000 | ||||
| t(b) | 0.378 | ||||
| p(b) | 0.494 | ||||
| t(a) | 0.459 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -0.119 | ||||
| Upperbound of 95% confidence interval for beta | 0.176 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.537 | ||||
| Upperbound of 95% confidence interval for alpha | 0.865 | ||||
| Treynor index (mean / b) | 6.130 | ||||
| Jensen alpha (a) | 0.164 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.080 | ||||
| SD | 0.708 | ||||
| Sharpe ratio (Glass type estimate) | -0.113 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.113 | ||||
| df | 1135.000 | ||||
| t | -0.235 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.054 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.828 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.054 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.829 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.160 | ||||
| Upside Potential Ratio | 2.766 | ||||
| Upside part of mean | 1.382 | ||||
| Downside part of mean | -1.462 | ||||
| Upside SD | 0.501 | ||||
| Downside SD | 0.500 | ||||
| N nonnegative terms | 248.000 | ||||
| N negative terms | 888.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1136.000 | ||||
| Mean of predictor | 0.327 | ||||
| Mean of criterion | -0.080 | ||||
| SD of predictor | 0.298 | ||||
| SD of criterion | 0.708 | ||||
| Covariance | 0.002 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.026 | ||||
| a (intercept, estimate of alpha) | -0.088 | ||||
| Mean Square Error | 0.502 | ||||
| DF error | 1134.000 | ||||
| t(b) | 0.373 | ||||
| p(b) | 0.494 | ||||
| t(a) | -0.260 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.112 | ||||
| Upperbound of 95% confidence interval for beta | 0.165 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.757 | ||||
| Upperbound of 95% confidence interval for alpha | 0.580 | ||||
| Treynor index (mean / b) | -3.035 | ||||
| Jensen alpha (a) | -0.088 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.070 | ||||
| Expected Shortfall on VaR | 0.086 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1136.000 | ||||
| Minimum | 0.644 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.553 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.023 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 247.000 | ||||
| Percentage of outliers low | 0.217 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 255.000 | ||||
| Percentage of outliers high | 0.224 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.823 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | 0.045 | ||||
| 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 | 15.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.109 | ||||
| Maximum | 0.721 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.069 | ||||
| Mean of quarter 4 | 0.311 | ||||
| Inter Quartile Range | 0.099 | ||||
| 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 | 0.067 | ||||
| Mean of outliers high | 0.721 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.551 | ||||
| VaR(95%) (moments method) | 0.354 | ||||
| Expected Shortfall (moments method) | 0.866 | ||||
| Extreme Value Index (regression method) | 1.929 | ||||
| VaR(95%) (regression method) | 0.537 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.033 | ||||
| Compounded annual return (geometric extrapolation) | -0.035 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.049 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.113 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.408 | ||||
| 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 | 1.149 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.468 | ||||
| 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 | 1.037 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.472 | ||||
| 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) | -8719063184750191.000 | ||||
| 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) | 326938887768318895891324778577920.000 | ||||
| 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 | ||||