Advanced Statistics: 29594253
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 | 10612.869 | ||||
| SD | 25815.449 | ||||
| Sharpe ratio (Glass type estimate) | 0.411 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.407 | ||||
| df | 70.000 | ||||
| t | 1.000 | ||||
| p | 0.160 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.399 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.218 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.402 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.215 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 25709.102 | ||||
| Upside Potential Ratio | 25709.615 | ||||
| Upside part of mean | 10613.080 | ||||
| Downside part of mean | -0.212 | ||||
| Upside SD | 25815.442 | ||||
| Downside SD | 0.413 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.322 | ||||
| Mean of criterion | 10612.869 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 25815.449 | ||||
| Covariance | 3032.399 | ||||
| r | 0.360 | ||||
| b (slope, estimate of beta) | 28485.171 | ||||
| a (intercept, estimate of alpha) | 1429.682 | ||||
| Mean Square Error | 588465671.563 | ||||
| DF error | 69.000 | ||||
| t(b) | 3.205 | ||||
| p(b) | 0.001 | ||||
| t(a) | 0.138 | ||||
| p(a) | 0.445 | ||||
| Lowerbound of 95% confidence interval for beta | 10757.208 | ||||
| Upperbound of 95% confidence interval for beta | 46213.134 | ||||
| Lowerbound of 95% confidence interval for alpha | -19270.354 | ||||
| Upperbound of 95% confidence interval for alpha | 22129.717 | ||||
| Treynor index (mean / b) | 0.373 | ||||
| Jensen alpha (a) | 1429.682 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 6.488 | ||||
| Sharpe ratio (Glass type estimate) | -0.007 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.007 | ||||
| df | 70.000 | ||||
| t | -0.017 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.813 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.799 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.812 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.799 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.010 | ||||
| Upside Potential Ratio | 0.411 | ||||
| Upside part of mean | 1.877 | ||||
| Downside part of mean | -1.921 | ||||
| Upside SD | 4.540 | ||||
| Downside SD | 4.570 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 69.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.268 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 6.488 | ||||
| Covariance | 0.590 | ||||
| r | 0.289 | ||||
| b (slope, estimate of beta) | 5.973 | ||||
| a (intercept, estimate of alpha) | -1.646 | ||||
| Mean Square Error | 39.125 | ||||
| DF error | 69.000 | ||||
| t(b) | 2.511 | ||||
| p(b) | 0.007 | ||||
| t(a) | -0.621 | ||||
| p(a) | 0.732 | ||||
| Lowerbound of 95% confidence interval for beta | 1.228 | ||||
| Upperbound of 95% confidence interval for beta | 10.719 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.931 | ||||
| Upperbound of 95% confidence interval for alpha | 3.640 | ||||
| Treynor index (mean / b) | -0.007 | ||||
| Jensen alpha (a) | -1.646 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.954 | ||||
| Expected Shortfall on VaR | 0.975 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.060 | ||||
| Expected Shortfall on VaR | 0.136 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 62795.000 | ||||
| Mean of quarter 1 | 0.944 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 3489.559 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.000 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.028 | ||||
| Mean of outliers high | 31398.033 | ||||
| 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 | 1.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| 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 | 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 46446.201 | ||||
| SD | 57266.225 | ||||
| Sharpe ratio (Glass type estimate) | 0.811 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.811 | ||||
| df | 1551.000 | ||||
| t | 1.974 | ||||
| p | 0.468 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.005 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.617 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.005 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.616 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 32054.029 | ||||
| Upside Potential Ratio | 32055.723 | ||||
| Upside part of mean | 46448.656 | ||||
| Downside part of mean | -2.455 | ||||
| Upside SD | 57319.641 | ||||
| Downside SD | 1.449 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 1530.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1552.000 | ||||
| Mean of predictor | 0.432 | ||||
| Mean of criterion | 46446.201 | ||||
| SD of predictor | 0.563 | ||||
| SD of criterion | 57266.225 | ||||
| Covariance | 6991.297 | ||||
| r | 0.217 | ||||
| b (slope, estimate of beta) | 22066.596 | ||||
| a (intercept, estimate of alpha) | 36912.122 | ||||
| Mean Square Error | 3127162572.718 | ||||
| DF error | 1550.000 | ||||
| t(b) | 8.747 | ||||
| p(b) | 0.392 | ||||
| t(a) | 1.605 | ||||
| p(a) | 0.480 | ||||
| Lowerbound of 95% confidence interval for beta | 17118.415 | ||||
| Upperbound of 95% confidence interval for beta | 27014.776 | ||||
| Lowerbound of 95% confidence interval for alpha | -8206.467 | ||||
| Upperbound of 95% confidence interval for alpha | 82030.711 | ||||
| Treynor index (mean / b) | 2.105 | ||||
| Jensen alpha (a) | 36912.122 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 15.238 | ||||
| Sharpe ratio (Glass type estimate) | -0.003 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.003 | ||||
| df | 1551.000 | ||||
| t | -0.007 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.808 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.802 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.808 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.802 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.004 | ||||
| Upside Potential Ratio | 1.269 | ||||
| Upside part of mean | 13.974 | ||||
| Downside part of mean | -14.018 | ||||
| Upside SD | 10.522 | ||||
| Downside SD | 11.016 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 1530.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1552.000 | ||||
| Mean of predictor | 0.275 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.559 | ||||
| SD of criterion | 15.238 | ||||
| Covariance | 2.040 | ||||
| r | 0.239 | ||||
| b (slope, estimate of beta) | 6.524 | ||||
| a (intercept, estimate of alpha) | -1.841 | ||||
| Mean Square Error | 219.039 | ||||
| DF error | 1550.000 | ||||
| t(b) | 9.707 | ||||
| p(b) | 0.380 | ||||
| t(a) | -0.303 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 5.205 | ||||
| Upperbound of 95% confidence interval for beta | 7.842 | ||||
| Lowerbound of 95% confidence interval for alpha | -13.774 | ||||
| Upperbound of 95% confidence interval for alpha | 10.093 | ||||
| Treynor index (mean / b) | -0.007 | ||||
| Jensen alpha (a) | -1.841 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.787 | ||||
| Expected Shortfall on VaR | 0.849 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1552.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 91460.000 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 710.140 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 29.000 | ||||
| Percentage of outliers low | 0.019 | ||||
| Mean of outliers low | 0.507 | ||||
| Number of outliers high | 22.000 | ||||
| Percentage of outliers high | 0.014 | ||||
| Mean of outliers high | 12507.647 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.204 | ||||
| VaR(95%) (moments method) | -0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.803 | ||||
| VaR(95%) (regression method) | -14.794 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| 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 | NA | ||||
| Mean of quarter 3 | NA | ||||
| 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 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) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.118 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.512 | ||||
| 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 | 0.984 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.519 | ||||
| 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) | -8739647454712346.000 | ||||
| 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) | -460304944858286557325533391093760.000 | ||||
| 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 | ||||