Advanced Statistics: 8d
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 | -0.002 | ||||
| SD | 0.149 | ||||
| Sharpe ratio (Glass type estimate) | -0.011 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.011 | ||||
| df | 82.000 | ||||
| t | -0.028 | ||||
| p | 0.511 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.756 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.735 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.756 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.735 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.021 | ||||
| Upside Potential Ratio | 1.273 | ||||
| Upside part of mean | 0.099 | ||||
| Downside part of mean | -0.101 | ||||
| Upside SD | 0.126 | ||||
| Downside SD | 0.078 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.238 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.195 | ||||
| SD of criterion | 0.149 | ||||
| Covariance | 0.003 | ||||
| r | 0.093 | ||||
| b (slope, estimate of beta) | 0.071 | ||||
| a (intercept, estimate of alpha) | -0.019 | ||||
| Mean Square Error | 0.022 | ||||
| DF error | 81.000 | ||||
| t(b) | 0.841 | ||||
| p(b) | 0.201 | ||||
| t(a) | -0.307 | ||||
| p(a) | 0.620 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.240 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.138 | ||||
| Upperbound of 95% confidence interval for alpha | 0.101 | ||||
| Treynor index (mean / b) | -0.022 | ||||
| Jensen alpha (a) | -0.019 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.012 | ||||
| SD | 0.143 | ||||
| Sharpe ratio (Glass type estimate) | -0.083 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.083 | ||||
| df | 82.000 | ||||
| t | -0.219 | ||||
| p | 0.587 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.829 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.662 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.828 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.663 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.146 | ||||
| Upside Potential Ratio | 1.123 | ||||
| Upside part of mean | 0.092 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.082 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.216 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.191 | ||||
| SD of criterion | 0.143 | ||||
| Covariance | 0.003 | ||||
| r | 0.116 | ||||
| b (slope, estimate of beta) | 0.086 | ||||
| a (intercept, estimate of alpha) | -0.031 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 81.000 | ||||
| t(b) | 1.052 | ||||
| p(b) | 0.148 | ||||
| t(a) | -0.537 | ||||
| p(a) | 0.704 | ||||
| Lowerbound of 95% confidence interval for beta | -0.077 | ||||
| Upperbound of 95% confidence interval for beta | 0.250 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | 0.083 | ||||
| Treynor index (mean / b) | -0.138 | ||||
| Jensen alpha (a) | -0.031 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 83.000 | ||||
| Minimum | 0.891 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.220 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.034 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.060 | ||||
| Mean of outliers low | 0.917 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.084 | ||||
| Mean of outliers high | 1.101 | ||||
| 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) | -2.590 | ||||
| VaR(95%) (regression method) | 0.085 | ||||
| Expected Shortfall (regression method) | 0.125 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.094 | ||||
| Quartile 1 | 0.141 | ||||
| Median | 0.189 | ||||
| Quartile 3 | 0.237 | ||||
| Maximum | 0.284 | ||||
| Mean of quarter 1 | 0.094 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.284 | ||||
| Inter Quartile Range | 0.095 | ||||
| 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) | 0.036 | ||||
| Compounded annual return (geometric extrapolation) | 0.033 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.115 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.115 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.397 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.013 | ||||
| SD | 0.228 | ||||
| Sharpe ratio (Glass type estimate) | 0.058 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.058 | ||||
| df | 1832.000 | ||||
| t | 0.155 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.683 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.799 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.683 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.799 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.093 | ||||
| Upside Potential Ratio | 2.912 | ||||
| Upside part of mean | 0.415 | ||||
| Downside part of mean | -0.402 | ||||
| Upside SD | 0.178 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 1768.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1833.000 | ||||
| Mean of predictor | 0.264 | ||||
| Mean of criterion | 0.013 | ||||
| SD of predictor | 0.270 | ||||
| SD of criterion | 0.228 | ||||
| Covariance | -0.007 | ||||
| r | -0.120 | ||||
| b (slope, estimate of beta) | -0.101 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.051 | ||||
| DF error | 1831.000 | ||||
| t(b) | -5.168 | ||||
| p(b) | 0.576 | ||||
| t(a) | 0.468 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -0.140 | ||||
| Upperbound of 95% confidence interval for beta | -0.063 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.128 | ||||
| Upperbound of 95% confidence interval for alpha | 0.208 | ||||
| Treynor index (mean / b) | -0.132 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.012 | ||||
| SD | 0.226 | ||||
| Sharpe ratio (Glass type estimate) | -0.054 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.054 | ||||
| df | 1832.000 | ||||
| t | -0.144 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.795 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.687 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.795 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.687 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.082 | ||||
| Upside Potential Ratio | 2.687 | ||||
| Upside part of mean | 0.400 | ||||
| Downside part of mean | -0.413 | ||||
| Upside SD | 0.169 | ||||
| Downside SD | 0.149 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 1768.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1833.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.226 | ||||
| Covariance | -0.007 | ||||
| r | -0.119 | ||||
| b (slope, estimate of beta) | -0.099 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 1831.000 | ||||
| t(b) | -5.136 | ||||
| p(b) | 0.576 | ||||
| t(a) | 0.120 | ||||
| p(a) | 0.498 | ||||
| Lowerbound of 95% confidence interval for beta | -0.137 | ||||
| Upperbound of 95% confidence interval for beta | -0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.156 | ||||
| Upperbound of 95% confidence interval for alpha | 0.177 | ||||
| Treynor index (mean / b) | 0.124 | ||||
| Jensen alpha (a) | 0.010 | ||||
| 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 | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1833.000 | ||||
| Minimum | 0.846 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.182 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 84.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 66.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.237 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.070 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.046 | ||||
| Quartile 1 | 0.072 | ||||
| Median | 0.136 | ||||
| Quartile 3 | 0.333 | ||||
| Maximum | 0.436 | ||||
| Mean of quarter 1 | 0.056 | ||||
| Mean of quarter 2 | 0.087 | ||||
| Mean of quarter 3 | 0.186 | ||||
| Mean of quarter 4 | 0.409 | ||||
| Inter Quartile Range | 0.261 | ||||
| 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) | 0.036 | ||||
| Compounded annual return (geometric extrapolation) | 0.032 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.074 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.079 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.137 | ||||
| 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 | 1.076 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.352 | ||||
| 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 | 1.011 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.356 | ||||
| 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) | -8666507078416839.000 | ||||
| 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) | 334906091326054634748597004926976.000 | ||||
| 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 | ||||