Advanced Statistics: The Trading Digest Portfolio
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 | -0.012 | ||||
| SD | 0.137 | ||||
| Sharpe ratio (Glass type estimate) | -0.084 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.083 | ||||
| df | 73.000 | ||||
| t | -0.209 | ||||
| p | 0.583 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.873 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.705 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.873 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.706 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.113 | ||||
| Upside Potential Ratio | 1.309 | ||||
| Upside part of mean | 0.134 | ||||
| Downside part of mean | -0.145 | ||||
| Upside SD | 0.090 | ||||
| Downside SD | 0.102 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 74.000 | ||||
| Mean of predictor | 0.160 | ||||
| Mean of criterion | -0.012 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.137 | ||||
| Covariance | 0.021 | ||||
| r | 0.538 | ||||
| b (slope, estimate of beta) | 0.265 | ||||
| a (intercept, estimate of alpha) | -0.054 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 72.000 | ||||
| t(b) | 5.418 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.134 | ||||
| p(a) | 0.870 | ||||
| Lowerbound of 95% confidence interval for beta | 0.168 | ||||
| Upperbound of 95% confidence interval for beta | 0.363 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.149 | ||||
| Upperbound of 95% confidence interval for alpha | 0.041 | ||||
| Treynor index (mean / b) | -0.044 | ||||
| Jensen alpha (a) | -0.054 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.140 | ||||
| Sharpe ratio (Glass type estimate) | -0.150 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.149 | ||||
| df | 73.000 | ||||
| t | -0.374 | ||||
| p | 0.645 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.940 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.640 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.939 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.641 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.194 | ||||
| Upside Potential Ratio | 1.197 | ||||
| Upside part of mean | 0.129 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.108 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 74.000 | ||||
| Mean of predictor | 0.119 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.140 | ||||
| Covariance | 0.023 | ||||
| r | 0.578 | ||||
| b (slope, estimate of beta) | 0.283 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 72.000 | ||||
| t(b) | 6.003 | ||||
| p(b) | 0.000 | ||||
| t(a) | -1.175 | ||||
| p(a) | 0.878 | ||||
| Lowerbound of 95% confidence interval for beta | 0.189 | ||||
| Upperbound of 95% confidence interval for beta | 0.377 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.147 | ||||
| Upperbound of 95% confidence interval for alpha | 0.038 | ||||
| Treynor index (mean / b) | -0.074 | ||||
| Jensen alpha (a) | -0.055 | ||||
| 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 | 0.081 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.071 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 74.000 | ||||
| Minimum | 0.839 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.097 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.047 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.162 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.243 | ||||
| Mean of outliers high | 1.049 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.048 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.136 | ||||
| VaR(95%) (regression method) | 0.039 | ||||
| Expected Shortfall (regression method) | 0.077 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.035 | ||||
| Quartile 1 | 0.087 | ||||
| Median | 0.140 | ||||
| Quartile 3 | 0.193 | ||||
| Maximum | 0.246 | ||||
| Mean of quarter 1 | 0.035 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.246 | ||||
| Inter Quartile Range | 0.106 | ||||
| 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) | 0.025 | ||||
| Compounded annual return (geometric extrapolation) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.095 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.095 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.287 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.049 | ||||
| SD | 0.376 | ||||
| Sharpe ratio (Glass type estimate) | 0.130 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.130 | ||||
| df | 1627.000 | ||||
| t | 0.325 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.656 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.917 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.656 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.917 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.193 | ||||
| Upside Potential Ratio | 4.669 | ||||
| Upside part of mean | 1.183 | ||||
| Downside part of mean | -1.134 | ||||
| Upside SD | 0.278 | ||||
| Downside SD | 0.253 | ||||
| N nonnegative terms | 374.000 | ||||
| N negative terms | 1254.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1628.000 | ||||
| Mean of predictor | 0.298 | ||||
| Mean of criterion | 0.049 | ||||
| SD of predictor | 0.605 | ||||
| SD of criterion | 0.376 | ||||
| Covariance | 0.155 | ||||
| r | 0.679 | ||||
| b (slope, estimate of beta) | 0.422 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.076 | ||||
| DF error | 1626.000 | ||||
| t(b) | 37.337 | ||||
| p(b) | 0.160 | ||||
| t(a) | -0.693 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.400 | ||||
| Upperbound of 95% confidence interval for beta | 0.444 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.294 | ||||
| Upperbound of 95% confidence interval for alpha | 0.140 | ||||
| Treynor index (mean / b) | 0.116 | ||||
| Jensen alpha (a) | -0.077 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.021 | ||||
| SD | 0.375 | ||||
| Sharpe ratio (Glass type estimate) | -0.057 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.057 | ||||
| df | 1627.000 | ||||
| t | -0.141 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.843 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.730 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.843 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.730 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.080 | ||||
| Upside Potential Ratio | 4.316 | ||||
| Upside part of mean | 1.146 | ||||
| Downside part of mean | -1.168 | ||||
| Upside SD | 0.264 | ||||
| Downside SD | 0.266 | ||||
| N nonnegative terms | 374.000 | ||||
| N negative terms | 1254.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1628.000 | ||||
| Mean of predictor | 0.117 | ||||
| Mean of criterion | -0.021 | ||||
| SD of predictor | 0.603 | ||||
| SD of criterion | 0.375 | ||||
| Covariance | 0.152 | ||||
| r | 0.673 | ||||
| b (slope, estimate of beta) | 0.418 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.077 | ||||
| DF error | 1626.000 | ||||
| t(b) | 36.677 | ||||
| p(b) | 0.164 | ||||
| t(a) | -0.630 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 0.396 | ||||
| Upperbound of 95% confidence interval for beta | 0.441 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.288 | ||||
| Upperbound of 95% confidence interval for alpha | 0.148 | ||||
| Treynor index (mean / b) | -0.051 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1628.000 | ||||
| Minimum | 0.820 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.216 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.018 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 369.000 | ||||
| Percentage of outliers low | 0.227 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 404.000 | ||||
| Percentage of outliers high | 0.248 | ||||
| Mean of outliers high | 1.018 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.818 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.045 | ||||
| Extreme Value Index (regression method) | 0.350 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.034 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.047 | ||||
| Maximum | 0.299 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.024 | ||||
| Mean of quarter 4 | 0.150 | ||||
| Inter Quartile Range | 0.043 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.299 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.156 | ||||
| VaR(95%) (moments method) | 0.140 | ||||
| Expected Shortfall (moments method) | 0.191 | ||||
| Extreme Value Index (regression method) | 1.474 | ||||
| VaR(95%) (regression method) | 0.325 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.025 | ||||
| Compounded annual return (geometric extrapolation) | 0.023 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.077 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.154 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.495 | ||||
| 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 | 1.002 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.652 | ||||
| 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 | 0.766 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.707 | ||||
| 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) | -8779980001462785.000 | ||||
| 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) | 219809317867257315399745348304896.000 | ||||
| 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 | ||||