Advanced Statistics: The Winning Ticket
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 | -0.069 | ||||
| SD | 0.238 | ||||
| Sharpe ratio (Glass type estimate) | -0.290 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.286 | ||||
| df | 69.000 | ||||
| t | -0.700 | ||||
| p | 0.757 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.102 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.524 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.099 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.526 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.459 | ||||
| Upside Potential Ratio | 0.615 | ||||
| Upside part of mean | 0.092 | ||||
| Downside part of mean | -0.161 | ||||
| Upside SD | 0.183 | ||||
| Downside SD | 0.150 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.191 | ||||
| Mean of criterion | -0.069 | ||||
| SD of predictor | 0.315 | ||||
| SD of criterion | 0.238 | ||||
| Covariance | 0.007 | ||||
| r | 0.100 | ||||
| b (slope, estimate of beta) | 0.075 | ||||
| a (intercept, estimate of alpha) | -0.083 | ||||
| Mean Square Error | 0.057 | ||||
| DF error | 68.000 | ||||
| t(b) | 0.825 | ||||
| p(b) | 0.206 | ||||
| t(a) | -0.831 | ||||
| p(a) | 0.795 | ||||
| Lowerbound of 95% confidence interval for beta | -0.107 | ||||
| Upperbound of 95% confidence interval for beta | 0.257 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.283 | ||||
| Upperbound of 95% confidence interval for alpha | 0.117 | ||||
| Treynor index (mean / b) | -0.916 | ||||
| Jensen alpha (a) | -0.083 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.095 | ||||
| SD | 0.228 | ||||
| Sharpe ratio (Glass type estimate) | -0.417 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.412 | ||||
| df | 69.000 | ||||
| t | -1.006 | ||||
| p | 0.841 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.230 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.399 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.227 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.402 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.564 | ||||
| Upside Potential Ratio | 0.469 | ||||
| Upside part of mean | 0.079 | ||||
| Downside part of mean | -0.174 | ||||
| Upside SD | 0.153 | ||||
| Downside SD | 0.168 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 68.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 70.000 | ||||
| Mean of predictor | 0.141 | ||||
| Mean of criterion | -0.095 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.228 | ||||
| Covariance | 0.008 | ||||
| r | 0.117 | ||||
| b (slope, estimate of beta) | 0.085 | ||||
| a (intercept, estimate of alpha) | -0.107 | ||||
| Mean Square Error | 0.052 | ||||
| DF error | 68.000 | ||||
| t(b) | 0.972 | ||||
| p(b) | 0.167 | ||||
| t(a) | -1.123 | ||||
| p(a) | 0.867 | ||||
| Lowerbound of 95% confidence interval for beta | -0.089 | ||||
| Upperbound of 95% confidence interval for beta | 0.259 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.296 | ||||
| Upperbound of 95% confidence interval for alpha | 0.083 | ||||
| Treynor index (mean / b) | -1.119 | ||||
| Jensen alpha (a) | -0.107 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.109 | ||||
| Expected Shortfall on VaR | 0.133 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 70.000 | ||||
| Minimum | 0.739 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.432 | ||||
| Mean of quarter 1 | 0.962 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.129 | ||||
| Mean of outliers low | 0.923 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.100 | ||||
| Mean of outliers high | 1.078 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -21.832 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | -0.523 | ||||
| VaR(95%) (regression method) | 0.090 | ||||
| Expected Shortfall (regression method) | 0.188 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.032 | ||||
| Quartile 1 | 0.063 | ||||
| Median | 0.094 | ||||
| Quartile 3 | 0.282 | ||||
| Maximum | 0.469 | ||||
| Mean of quarter 1 | 0.032 | ||||
| Mean of quarter 2 | 0.094 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.469 | ||||
| Inter Quartile Range | 0.219 | ||||
| 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) | -0.044 | ||||
| Compounded annual return (geometric extrapolation) | -0.050 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.106 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.106 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.371 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 3.291 | ||||
| SD | 3.667 | ||||
| Sharpe ratio (Glass type estimate) | 0.897 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.897 | ||||
| df | 1528.000 | ||||
| t | 2.168 | ||||
| p | 0.472 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.085 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.709 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.085 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.709 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.121 | ||||
| Upside Potential Ratio | 5.085 | ||||
| Upside part of mean | 5.362 | ||||
| Downside part of mean | -2.071 | ||||
| Upside SD | 3.517 | ||||
| Downside SD | 1.054 | ||||
| N nonnegative terms | 85.000 | ||||
| N negative terms | 1444.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1529.000 | ||||
| Mean of predictor | 0.381 | ||||
| Mean of criterion | 3.291 | ||||
| SD of predictor | 0.634 | ||||
| SD of criterion | 3.667 | ||||
| Covariance | 0.429 | ||||
| r | 0.184 | ||||
| b (slope, estimate of beta) | 1.067 | ||||
| a (intercept, estimate of alpha) | 2.884 | ||||
| Mean Square Error | 12.998 | ||||
| DF error | 1527.000 | ||||
| t(b) | 7.334 | ||||
| p(b) | 0.383 | ||||
| t(a) | 1.931 | ||||
| p(a) | 0.469 | ||||
| Lowerbound of 95% confidence interval for beta | 0.781 | ||||
| Upperbound of 95% confidence interval for beta | 1.352 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.045 | ||||
| Upperbound of 95% confidence interval for alpha | 5.814 | ||||
| Treynor index (mean / b) | 3.085 | ||||
| Jensen alpha (a) | 2.884 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.095 | ||||
| SD | 2.468 | ||||
| Sharpe ratio (Glass type estimate) | -0.038 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.038 | ||||
| df | 1528.000 | ||||
| t | -0.093 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.850 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.773 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.850 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.773 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.053 | ||||
| Upside Potential Ratio | 1.720 | ||||
| Upside part of mean | 3.084 | ||||
| Downside part of mean | -3.179 | ||||
| Upside SD | 1.694 | ||||
| Downside SD | 1.794 | ||||
| N nonnegative terms | 85.000 | ||||
| N negative terms | 1444.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1529.000 | ||||
| Mean of predictor | 0.183 | ||||
| Mean of criterion | -0.095 | ||||
| SD of predictor | 0.627 | ||||
| SD of criterion | 2.468 | ||||
| Covariance | 0.351 | ||||
| r | 0.226 | ||||
| b (slope, estimate of beta) | 0.891 | ||||
| a (intercept, estimate of alpha) | -0.258 | ||||
| Mean Square Error | 5.782 | ||||
| DF error | 1527.000 | ||||
| t(b) | 9.084 | ||||
| p(b) | 0.357 | ||||
| t(a) | -0.259 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.698 | ||||
| Upperbound of 95% confidence interval for beta | 1.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.211 | ||||
| Upperbound of 95% confidence interval for alpha | 1.695 | ||||
| Treynor index (mean / b) | -0.106 | ||||
| Jensen alpha (a) | -0.258 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.222 | ||||
| Expected Shortfall on VaR | 0.269 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1529.000 | ||||
| Minimum | 0.180 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 5.494 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.082 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 95.000 | ||||
| Percentage of outliers low | 0.062 | ||||
| Mean of outliers low | 0.875 | ||||
| Number of outliers high | 106.000 | ||||
| Percentage of outliers high | 0.069 | ||||
| Mean of outliers high | 1.295 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.638 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.472 | ||||
| VaR(95%) (regression method) | -0.009 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.091 | ||||
| Median | 0.208 | ||||
| Quartile 3 | 0.416 | ||||
| Maximum | 0.840 | ||||
| Mean of quarter 1 | 0.036 | ||||
| Mean of quarter 2 | 0.150 | ||||
| Mean of quarter 3 | 0.265 | ||||
| Mean of quarter 4 | 0.653 | ||||
| Inter Quartile Range | 0.325 | ||||
| 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) | -0.044 | ||||
| Compounded annual return (geometric extrapolation) | -0.049 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.059 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.076 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.184 | ||||
| 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 | 1.817 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.789 | ||||
| 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 | 1.520 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.757 | ||||
| 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) | -8732333157184112.000 | ||||
| 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) | -2079522004912964097989916112191488.000 | ||||
| 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 | ||||