Advanced Statistics: closed
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 | 0.172 | ||||
| SD | 0.371 | ||||
| Sharpe ratio (Glass type estimate) | 0.464 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.456 | ||||
| df | 44.000 | ||||
| t | 0.898 | ||||
| p | 0.187 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.555 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.478 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.561 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.473 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.003 | ||||
| Upside Potential Ratio | 6.726 | ||||
| Upside part of mean | 0.231 | ||||
| Downside part of mean | -0.059 | ||||
| Upside SD | 0.369 | ||||
| Downside SD | 0.034 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.491 | ||||
| Mean of criterion | 0.172 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.371 | ||||
| Covariance | -0.010 | ||||
| r | -0.086 | ||||
| b (slope, estimate of beta) | -0.097 | ||||
| a (intercept, estimate of alpha) | 0.220 | ||||
| Mean Square Error | 0.140 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.563 | ||||
| p(b) | 0.712 | ||||
| t(a) | 1.042 | ||||
| p(a) | 0.152 | ||||
| Lowerbound of 95% confidence interval for beta | -0.444 | ||||
| Upperbound of 95% confidence interval for beta | 0.250 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.205 | ||||
| Upperbound of 95% confidence interval for alpha | 0.645 | ||||
| Treynor index (mean / b) | -1.775 | ||||
| Jensen alpha (a) | 0.220 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.124 | ||||
| SD | 0.284 | ||||
| Sharpe ratio (Glass type estimate) | 0.436 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.429 | ||||
| df | 44.000 | ||||
| t | 0.845 | ||||
| p | 0.201 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.582 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.450 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.587 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.445 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.519 | ||||
| Upside Potential Ratio | 5.215 | ||||
| Upside part of mean | 0.183 | ||||
| Downside part of mean | -0.060 | ||||
| Upside SD | 0.281 | ||||
| Downside SD | 0.035 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 41.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.434 | ||||
| Mean of criterion | 0.124 | ||||
| SD of predictor | 0.303 | ||||
| SD of criterion | 0.284 | ||||
| Covariance | -0.007 | ||||
| r | -0.083 | ||||
| b (slope, estimate of beta) | -0.077 | ||||
| a (intercept, estimate of alpha) | 0.157 | ||||
| Mean Square Error | 0.082 | ||||
| DF error | 43.000 | ||||
| t(b) | -0.543 | ||||
| p(b) | 0.705 | ||||
| t(a) | 0.983 | ||||
| p(a) | 0.166 | ||||
| Lowerbound of 95% confidence interval for beta | -0.365 | ||||
| Upperbound of 95% confidence interval for beta | 0.210 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.166 | ||||
| Upperbound of 95% confidence interval for alpha | 0.480 | ||||
| Treynor index (mean / b) | -1.600 | ||||
| Jensen alpha (a) | 0.157 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.117 | ||||
| Expected Shortfall on VaR | 0.146 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.943 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.707 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.080 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.976 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.089 | ||||
| Mean of outliers high | 1.221 | ||||
| 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) | 1.437 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.071 | ||||
| Quartile 1 | 0.071 | ||||
| Median | 0.071 | ||||
| Quartile 3 | 0.071 | ||||
| Maximum | 0.071 | ||||
| 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) | 0.234 | ||||
| Compounded annual return (geometric extrapolation) | 0.183 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.581 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.249 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.152 | ||||
| SD | 0.263 | ||||
| Sharpe ratio (Glass type estimate) | 0.579 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.579 | ||||
| df | 991.000 | ||||
| t | 1.127 | ||||
| p | 0.130 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.428 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.587 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.429 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.586 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.504 | ||||
| Upside Potential Ratio | 4.205 | ||||
| Upside part of mean | 0.426 | ||||
| Downside part of mean | -0.273 | ||||
| Upside SD | 0.243 | ||||
| Downside SD | 0.101 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 924.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 992.000 | ||||
| Mean of predictor | 0.489 | ||||
| Mean of criterion | 0.152 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 0.263 | ||||
| Covariance | -0.002 | ||||
| r | -0.023 | ||||
| b (slope, estimate of beta) | -0.018 | ||||
| a (intercept, estimate of alpha) | 0.161 | ||||
| Mean Square Error | 0.069 | ||||
| DF error | 990.000 | ||||
| t(b) | -0.709 | ||||
| p(b) | 0.761 | ||||
| t(a) | 1.188 | ||||
| p(a) | 0.118 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | 0.428 | ||||
| Treynor index (mean / b) | -8.333 | ||||
| Jensen alpha (a) | 0.161 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.122 | ||||
| SD | 0.238 | ||||
| Sharpe ratio (Glass type estimate) | 0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.514 | ||||
| df | 991.000 | ||||
| t | 1.000 | ||||
| p | 0.159 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.494 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.521 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.494 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.521 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.155 | ||||
| Upside Potential Ratio | 3.789 | ||||
| Upside part of mean | 0.401 | ||||
| Downside part of mean | -0.279 | ||||
| Upside SD | 0.213 | ||||
| Downside SD | 0.106 | ||||
| N nonnegative terms | 68.000 | ||||
| N negative terms | 924.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 992.000 | ||||
| Mean of predictor | 0.435 | ||||
| Mean of criterion | 0.122 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.238 | ||||
| Covariance | -0.001 | ||||
| r | -0.018 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | 0.128 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 990.000 | ||||
| t(b) | -0.569 | ||||
| p(b) | 0.715 | ||||
| t(a) | 1.043 | ||||
| p(a) | 0.149 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.113 | ||||
| Upperbound of 95% confidence interval for alpha | 0.369 | ||||
| Treynor index (mean / b) | -9.317 | ||||
| Jensen alpha (a) | 0.128 | ||||
| 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 | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 992.000 | ||||
| Minimum | 0.868 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.397 | ||||
| Mean of quarter 1 | 0.996 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 62.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 69.000 | ||||
| Percentage of outliers high | 0.070 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.371 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.302 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.010 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.033 | ||||
| Maximum | 0.182 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.026 | ||||
| Mean of quarter 4 | 0.072 | ||||
| Inter Quartile Range | 0.029 | ||||
| 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 | 0.071 | ||||
| Mean of outliers high | 0.182 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.784 | ||||
| VaR(95%) (moments method) | 0.090 | ||||
| Expected Shortfall (moments method) | 0.395 | ||||
| Extreme Value Index (regression method) | 3.059 | ||||
| VaR(95%) (regression method) | 0.121 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.231 | ||||
| Compounded annual return (geometric extrapolation) | 0.181 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.994 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.513 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.155 | ||||
| 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 | 1.047 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.447 | ||||
| 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 | 0.947 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.445 | ||||
| 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) | -8724077052906218.000 | ||||
| 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) | -106314276000084749654898063179776.000 | ||||
| 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 | ||||