Advanced Statistics: OS Long Only 2
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 | -0.075 | ||||
| SD | 0.151 | ||||
| Sharpe ratio (Glass type estimate) | -0.495 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.487 | ||||
| df | 49.000 | ||||
| t | -1.010 | ||||
| p | 0.841 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.458 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.473 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.452 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.478 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.533 | ||||
| Upside Potential Ratio | 0.466 | ||||
| Upside part of mean | 0.065 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.140 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.402 | ||||
| Mean of criterion | -0.075 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 0.151 | ||||
| Covariance | 0.012 | ||||
| r | 0.326 | ||||
| b (slope, estimate of beta) | 0.197 | ||||
| a (intercept, estimate of alpha) | -0.154 | ||||
| Mean Square Error | 0.021 | ||||
| DF error | 48.000 | ||||
| t(b) | 2.393 | ||||
| p(b) | 0.010 | ||||
| t(a) | -1.974 | ||||
| p(a) | 0.973 | ||||
| Lowerbound of 95% confidence interval for beta | 0.031 | ||||
| Upperbound of 95% confidence interval for beta | 0.363 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.311 | ||||
| Upperbound of 95% confidence interval for alpha | 0.003 | ||||
| Treynor index (mean / b) | -0.379 | ||||
| Jensen alpha (a) | -0.154 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.087 | ||||
| SD | 0.166 | ||||
| Sharpe ratio (Glass type estimate) | -0.528 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.520 | ||||
| df | 49.000 | ||||
| t | -1.077 | ||||
| p | 0.857 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.491 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.441 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.485 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.446 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.558 | ||||
| Upside Potential Ratio | 0.406 | ||||
| Upside part of mean | 0.064 | ||||
| Downside part of mean | -0.151 | ||||
| Upside SD | 0.054 | ||||
| Downside SD | 0.157 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 42.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 50.000 | ||||
| Mean of predictor | 0.365 | ||||
| Mean of criterion | -0.087 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.166 | ||||
| Covariance | 0.014 | ||||
| r | 0.351 | ||||
| b (slope, estimate of beta) | 0.237 | ||||
| a (intercept, estimate of alpha) | -0.174 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 48.000 | ||||
| t(b) | 2.597 | ||||
| p(b) | 0.006 | ||||
| t(a) | -2.077 | ||||
| p(a) | 0.978 | ||||
| Lowerbound of 95% confidence interval for beta | 0.053 | ||||
| Upperbound of 95% confidence interval for beta | 0.420 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.342 | ||||
| Upperbound of 95% confidence interval for alpha | -0.006 | ||||
| Treynor index (mean / b) | -0.369 | ||||
| Jensen alpha (a) | -0.174 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.082 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.079 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 50.000 | ||||
| Minimum | 0.770 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.079 | ||||
| Mean of quarter 1 | 0.967 | ||||
| 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 | 9.000 | ||||
| Percentage of outliers low | 0.180 | ||||
| Mean of outliers low | 0.952 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.160 | ||||
| Mean of outliers high | 1.038 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -9.919 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 1.229 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.189 | ||||
| Maximum | 0.358 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.021 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.358 | ||||
| Inter Quartile Range | 0.173 | ||||
| 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) | -0.040 | ||||
| Compounded annual return (geometric extrapolation) | -0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.119 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.119 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.423 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.078 | ||||
| SD | 0.134 | ||||
| Sharpe ratio (Glass type estimate) | -0.583 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.583 | ||||
| df | 1094.000 | ||||
| t | -1.192 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.542 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.376 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.542 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.376 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.757 | ||||
| Upside Potential Ratio | 2.585 | ||||
| Upside part of mean | 0.267 | ||||
| Downside part of mean | -0.345 | ||||
| Upside SD | 0.086 | ||||
| Downside SD | 0.103 | ||||
| N nonnegative terms | 125.000 | ||||
| N negative terms | 970.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1095.000 | ||||
| Mean of predictor | 0.438 | ||||
| Mean of criterion | -0.078 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.134 | ||||
| Covariance | 0.011 | ||||
| r | 0.266 | ||||
| b (slope, estimate of beta) | 0.112 | ||||
| a (intercept, estimate of alpha) | -0.127 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 1093.000 | ||||
| t(b) | 9.121 | ||||
| p(b) | 0.333 | ||||
| t(a) | -2.005 | ||||
| p(a) | 0.539 | ||||
| Lowerbound of 95% confidence interval for beta | 0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.136 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.252 | ||||
| Upperbound of 95% confidence interval for alpha | -0.003 | ||||
| Treynor index (mean / b) | -0.697 | ||||
| Jensen alpha (a) | -0.127 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.087 | ||||
| SD | 0.135 | ||||
| Sharpe ratio (Glass type estimate) | -0.646 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.646 | ||||
| df | 1094.000 | ||||
| t | -1.321 | ||||
| p | 0.520 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.605 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.313 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.605 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.313 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.820 | ||||
| Upside Potential Ratio | 2.476 | ||||
| Upside part of mean | 0.263 | ||||
| Downside part of mean | -0.350 | ||||
| Upside SD | 0.083 | ||||
| Downside SD | 0.106 | ||||
| N nonnegative terms | 125.000 | ||||
| N negative terms | 970.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1095.000 | ||||
| Mean of predictor | 0.387 | ||||
| Mean of criterion | -0.087 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.135 | ||||
| Covariance | 0.011 | ||||
| r | 0.265 | ||||
| b (slope, estimate of beta) | 0.113 | ||||
| a (intercept, estimate of alpha) | -0.131 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 1093.000 | ||||
| t(b) | 9.095 | ||||
| p(b) | 0.333 | ||||
| t(a) | -2.048 | ||||
| p(a) | 0.539 | ||||
| Lowerbound of 95% confidence interval for beta | 0.088 | ||||
| Upperbound of 95% confidence interval for beta | 0.137 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.256 | ||||
| Upperbound of 95% confidence interval for alpha | -0.005 | ||||
| Treynor index (mean / b) | -0.775 | ||||
| Jensen alpha (a) | -0.131 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.017 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1095.000 | ||||
| Minimum | 0.916 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.105 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 115.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 127.000 | ||||
| Percentage of outliers high | 0.116 | ||||
| Mean of outliers high | 1.009 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.391 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.006 | ||||
| Extreme Value Index (regression method) | 0.112 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.011 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 20.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.018 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.381 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.023 | ||||
| Mean of quarter 4 | 0.117 | ||||
| Inter Quartile Range | 0.020 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.150 | ||||
| Mean of outliers high | 0.172 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.825 | ||||
| VaR(95%) (moments method) | 0.116 | ||||
| Expected Shortfall (moments method) | 0.707 | ||||
| Extreme Value Index (regression method) | 1.596 | ||||
| VaR(95%) (regression method) | 0.157 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.040 | ||||
| Compounded annual return (geometric extrapolation) | -0.042 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.111 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.361 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.434 | ||||
| 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 | 1.232 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.396 | ||||
| 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 | 1.151 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.397 | ||||
| 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) | -8660712905052463.000 | ||||
| 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) | -95218421343948530045993216901120.000 | ||||
| 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 | ||||