Advanced Statistics: Solaris
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 | 0.158 | ||||
| SD | 0.250 | ||||
| Sharpe ratio (Glass type estimate) | 0.635 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.629 | ||||
| df | 89.000 | ||||
| t | 1.738 | ||||
| p | 0.043 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.089 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.355 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.092 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.351 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.301 | ||||
| Upside Potential Ratio | 2.607 | ||||
| Upside part of mean | 0.317 | ||||
| Downside part of mean | -0.159 | ||||
| Upside SD | 0.221 | ||||
| Downside SD | 0.122 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.198 | ||||
| Mean of criterion | 0.158 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.250 | ||||
| Covariance | 0.003 | ||||
| r | 0.047 | ||||
| b (slope, estimate of beta) | 0.047 | ||||
| a (intercept, estimate of alpha) | 0.149 | ||||
| Mean Square Error | 0.063 | ||||
| DF error | 88.000 | ||||
| t(b) | 0.443 | ||||
| p(b) | 0.329 | ||||
| t(a) | 1.588 | ||||
| p(a) | 0.058 | ||||
| Lowerbound of 95% confidence interval for beta | -0.164 | ||||
| Upperbound of 95% confidence interval for beta | 0.257 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.038 | ||||
| Upperbound of 95% confidence interval for alpha | 0.336 | ||||
| Treynor index (mean / b) | 3.374 | ||||
| Jensen alpha (a) | 0.149 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.128 | ||||
| SD | 0.237 | ||||
| Sharpe ratio (Glass type estimate) | 0.543 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.538 | ||||
| df | 89.000 | ||||
| t | 1.486 | ||||
| p | 0.070 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.179 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.261 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.182 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.258 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.987 | ||||
| Upside Potential Ratio | 2.264 | ||||
| Upside part of mean | 0.295 | ||||
| Downside part of mean | -0.166 | ||||
| Upside SD | 0.200 | ||||
| Downside SD | 0.130 | ||||
| N nonnegative terms | 32.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.166 | ||||
| Mean of criterion | 0.128 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.237 | ||||
| Covariance | 0.004 | ||||
| r | 0.069 | ||||
| b (slope, estimate of beta) | 0.066 | ||||
| a (intercept, estimate of alpha) | 0.117 | ||||
| Mean Square Error | 0.056 | ||||
| DF error | 88.000 | ||||
| t(b) | 0.647 | ||||
| p(b) | 0.260 | ||||
| t(a) | 1.329 | ||||
| p(a) | 0.094 | ||||
| Lowerbound of 95% confidence interval for beta | -0.137 | ||||
| Upperbound of 95% confidence interval for beta | 0.270 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.058 | ||||
| Upperbound of 95% confidence interval for alpha | 0.293 | ||||
| Treynor index (mean / b) | 1.934 | ||||
| Jensen alpha (a) | 0.117 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.097 | ||||
| Expected Shortfall on VaR | 0.122 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 90.000 | ||||
| Minimum | 0.822 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.034 | ||||
| Maximum | 1.347 | ||||
| Mean of quarter 1 | 0.957 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.007 | ||||
| Mean of quarter 4 | 1.102 | ||||
| Inter Quartile Range | 0.034 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.880 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.100 | ||||
| Mean of outliers high | 1.178 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -22.572 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.150 | ||||
| VaR(95%) (regression method) | 0.053 | ||||
| Expected Shortfall (regression method) | 0.088 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.058 | ||||
| Median | 0.100 | ||||
| Quartile 3 | 0.125 | ||||
| Maximum | 0.361 | ||||
| Mean of quarter 1 | 0.037 | ||||
| Mean of quarter 2 | 0.087 | ||||
| Mean of quarter 3 | 0.121 | ||||
| Mean of quarter 4 | 0.245 | ||||
| Inter Quartile Range | 0.068 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.361 | ||||
| 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) | 0.353 | ||||
| Compounded annual return (geometric extrapolation) | 0.188 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.522 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.767 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.544 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.220 | ||||
| SD | 0.434 | ||||
| Sharpe ratio (Glass type estimate) | 0.508 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.508 | ||||
| df | 1978.000 | ||||
| t | 1.396 | ||||
| p | 0.484 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.205 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.221 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.206 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.221 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.773 | ||||
| Upside Potential Ratio | 5.086 | ||||
| Upside part of mean | 1.451 | ||||
| Downside part of mean | -1.231 | ||||
| Upside SD | 0.327 | ||||
| Downside SD | 0.285 | ||||
| N nonnegative terms | 538.000 | ||||
| N negative terms | 1441.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1979.000 | ||||
| Mean of predictor | 0.301 | ||||
| Mean of criterion | 0.220 | ||||
| SD of predictor | 0.485 | ||||
| SD of criterion | 0.434 | ||||
| Covariance | 0.033 | ||||
| r | 0.156 | ||||
| b (slope, estimate of beta) | 0.140 | ||||
| a (intercept, estimate of alpha) | 0.178 | ||||
| Mean Square Error | 0.184 | ||||
| DF error | 1977.000 | ||||
| t(b) | 7.024 | ||||
| p(b) | 0.401 | ||||
| t(a) | 1.142 | ||||
| p(a) | 0.484 | ||||
| Lowerbound of 95% confidence interval for beta | 0.101 | ||||
| Upperbound of 95% confidence interval for beta | 0.179 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.128 | ||||
| Upperbound of 95% confidence interval for alpha | 0.485 | ||||
| Treynor index (mean / b) | 1.578 | ||||
| Jensen alpha (a) | 0.178 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.127 | ||||
| SD | 0.431 | ||||
| Sharpe ratio (Glass type estimate) | 0.295 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.295 | ||||
| df | 1978.000 | ||||
| t | 0.811 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.418 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.008 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.418 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.008 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.423 | ||||
| Upside Potential Ratio | 4.657 | ||||
| Upside part of mean | 1.401 | ||||
| Downside part of mean | -1.274 | ||||
| Upside SD | 0.309 | ||||
| Downside SD | 0.301 | ||||
| N nonnegative terms | 538.000 | ||||
| N negative terms | 1441.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1979.000 | ||||
| Mean of predictor | 0.183 | ||||
| Mean of criterion | 0.127 | ||||
| SD of predictor | 0.487 | ||||
| SD of criterion | 0.431 | ||||
| Covariance | 0.033 | ||||
| r | 0.156 | ||||
| b (slope, estimate of beta) | 0.139 | ||||
| a (intercept, estimate of alpha) | 0.102 | ||||
| Mean Square Error | 0.182 | ||||
| DF error | 1977.000 | ||||
| t(b) | 7.038 | ||||
| p(b) | 0.401 | ||||
| t(a) | 0.657 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | 0.100 | ||||
| Upperbound of 95% confidence interval for beta | 0.177 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.202 | ||||
| Upperbound of 95% confidence interval for alpha | 0.406 | ||||
| Treynor index (mean / b) | 0.918 | ||||
| Jensen alpha (a) | 0.102 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1979.000 | ||||
| Minimum | 0.811 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.247 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 330.000 | ||||
| Percentage of outliers low | 0.167 | ||||
| Mean of outliers low | 0.973 | ||||
| Number of outliers high | 438.000 | ||||
| Percentage of outliers high | 0.221 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.023 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.375 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.040 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 65.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.052 | ||||
| Quartile 3 | 0.095 | ||||
| Maximum | 0.387 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.073 | ||||
| Mean of quarter 4 | 0.156 | ||||
| Inter Quartile Range | 0.085 | ||||
| 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 | 0.015 | ||||
| Mean of outliers high | 0.387 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.118 | ||||
| VaR(95%) (moments method) | 0.167 | ||||
| Expected Shortfall (moments method) | 0.223 | ||||
| Extreme Value Index (regression method) | 0.006 | ||||
| VaR(95%) (regression method) | 0.158 | ||||
| Expected Shortfall (regression method) | 0.196 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.350 | ||||
| Compounded annual return (geometric extrapolation) | 0.187 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.482 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.197 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.527 | ||||
| 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 | 1.182 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.487 | ||||
| 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 | 1.060 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.493 | ||||
| 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) | -8722436070693819.000 | ||||
| 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) | 78306593184593991191051435507712.000 | ||||
| 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 | ||||