Advanced Statistics: (64359398)
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 | 0.770 | ||||
| SD | 0.620 | ||||
| Sharpe ratio (Glass type estimate) | 1.243 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.218 | ||||
| df | 38.000 | ||||
| t | 2.240 | ||||
| p | 0.016 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.113 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.357 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.097 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.339 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.010 | ||||
| Upside Potential Ratio | 4.759 | ||||
| Upside part of mean | 1.218 | ||||
| Downside part of mean | -0.448 | ||||
| Upside SD | 0.599 | ||||
| Downside SD | 0.256 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.576 | ||||
| Mean of criterion | 0.770 | ||||
| SD of predictor | 0.354 | ||||
| SD of criterion | 0.620 | ||||
| Covariance | 0.075 | ||||
| r | 0.340 | ||||
| b (slope, estimate of beta) | 0.595 | ||||
| a (intercept, estimate of alpha) | 0.428 | ||||
| Mean Square Error | 0.349 | ||||
| DF error | 37.000 | ||||
| t(b) | 2.197 | ||||
| p(b) | 0.017 | ||||
| t(a) | 1.178 | ||||
| p(a) | 0.123 | ||||
| Lowerbound of 95% confidence interval for beta | 0.046 | ||||
| Upperbound of 95% confidence interval for beta | 1.144 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.308 | ||||
| Upperbound of 95% confidence interval for alpha | 1.163 | ||||
| Treynor index (mean / b) | 1.294 | ||||
| Jensen alpha (a) | 0.428 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.590 | ||||
| SD | 0.555 | ||||
| Sharpe ratio (Glass type estimate) | 1.063 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.042 | ||||
| df | 38.000 | ||||
| t | 1.917 | ||||
| p | 0.031 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.056 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.170 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.070 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.154 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.109 | ||||
| Upside Potential Ratio | 3.835 | ||||
| Upside part of mean | 1.073 | ||||
| Downside part of mean | -0.483 | ||||
| Upside SD | 0.501 | ||||
| Downside SD | 0.280 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 13.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.510 | ||||
| Mean of criterion | 0.590 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.555 | ||||
| Covariance | 0.069 | ||||
| r | 0.395 | ||||
| b (slope, estimate of beta) | 0.693 | ||||
| a (intercept, estimate of alpha) | 0.237 | ||||
| Mean Square Error | 0.267 | ||||
| DF error | 37.000 | ||||
| t(b) | 2.616 | ||||
| p(b) | 0.006 | ||||
| t(a) | 0.748 | ||||
| p(a) | 0.230 | ||||
| Lowerbound of 95% confidence interval for beta | 0.156 | ||||
| Upperbound of 95% confidence interval for beta | 1.230 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.405 | ||||
| Upperbound of 95% confidence interval for alpha | 0.879 | ||||
| Treynor index (mean / b) | 0.852 | ||||
| Jensen alpha (a) | 0.237 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.193 | ||||
| Expected Shortfall on VaR | 0.244 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.136 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.785 | ||||
| Quartile 1 | 0.951 | ||||
| Median | 1.044 | ||||
| Quartile 3 | 1.166 | ||||
| Maximum | 1.707 | ||||
| Mean of quarter 1 | 0.872 | ||||
| Mean of quarter 2 | 1.009 | ||||
| Mean of quarter 3 | 1.095 | ||||
| Mean of quarter 4 | 1.298 | ||||
| Inter Quartile Range | 0.216 | ||||
| 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 | 0.026 | ||||
| Mean of outliers high | 1.707 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.539 | ||||
| VaR(95%) (moments method) | 0.122 | ||||
| Expected Shortfall (moments method) | 0.142 | ||||
| Extreme Value Index (regression method) | -0.498 | ||||
| VaR(95%) (regression method) | 0.104 | ||||
| Expected Shortfall (regression method) | 0.119 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.040 | ||||
| Quartile 1 | 0.050 | ||||
| Median | 0.092 | ||||
| Quartile 3 | 0.189 | ||||
| Maximum | 0.338 | ||||
| Mean of quarter 1 | 0.047 | ||||
| Mean of quarter 2 | 0.090 | ||||
| Mean of quarter 3 | 0.186 | ||||
| Mean of quarter 4 | 0.311 | ||||
| Inter Quartile Range | 0.139 | ||||
| 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) | -15.254 | ||||
| VaR(95%) (moments method) | 0.289 | ||||
| Expected Shortfall (moments method) | 0.289 | ||||
| Extreme Value Index (regression method) | -1.823 | ||||
| VaR(95%) (regression method) | 0.399 | ||||
| Expected Shortfall (regression method) | 0.404 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.109 | ||||
| Compounded annual return (geometric extrapolation) | 0.885 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.622 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.848 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.630 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.909 | ||||
| SD | 0.839 | ||||
| Sharpe ratio (Glass type estimate) | 1.084 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.083 | ||||
| df | 864.000 | ||||
| t | 1.969 | ||||
| p | 0.025 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.004 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.163 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.003 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.163 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.903 | ||||
| Upside Potential Ratio | 8.078 | ||||
| Upside part of mean | 3.859 | ||||
| Downside part of mean | -2.950 | ||||
| Upside SD | 0.691 | ||||
| Downside SD | 0.478 | ||||
| N nonnegative terms | 454.000 | ||||
| N negative terms | 411.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 865.000 | ||||
| Mean of predictor | 0.590 | ||||
| Mean of criterion | 0.909 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.839 | ||||
| Covariance | 0.078 | ||||
| r | 0.281 | ||||
| b (slope, estimate of beta) | 0.717 | ||||
| a (intercept, estimate of alpha) | 0.487 | ||||
| Mean Square Error | 0.649 | ||||
| DF error | 863.000 | ||||
| t(b) | 8.612 | ||||
| p(b) | -0.000 | ||||
| t(a) | 1.091 | ||||
| p(a) | 0.138 | ||||
| Lowerbound of 95% confidence interval for beta | 0.553 | ||||
| Upperbound of 95% confidence interval for beta | 0.880 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.389 | ||||
| Upperbound of 95% confidence interval for alpha | 1.362 | ||||
| Treynor index (mean / b) | 1.269 | ||||
| Jensen alpha (a) | 0.487 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.579 | ||||
| SD | 0.803 | ||||
| Sharpe ratio (Glass type estimate) | 0.721 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.721 | ||||
| df | 864.000 | ||||
| t | 1.311 | ||||
| p | 0.095 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.358 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.800 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.358 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.800 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.112 | ||||
| Upside Potential Ratio | 7.025 | ||||
| Upside part of mean | 3.656 | ||||
| Downside part of mean | -3.078 | ||||
| Upside SD | 0.611 | ||||
| Downside SD | 0.520 | ||||
| N nonnegative terms | 454.000 | ||||
| N negative terms | 411.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 865.000 | ||||
| Mean of predictor | 0.534 | ||||
| Mean of criterion | 0.579 | ||||
| SD of predictor | 0.333 | ||||
| SD of criterion | 0.803 | ||||
| Covariance | 0.080 | ||||
| r | 0.299 | ||||
| b (slope, estimate of beta) | 0.720 | ||||
| a (intercept, estimate of alpha) | 0.194 | ||||
| Mean Square Error | 0.587 | ||||
| DF error | 863.000 | ||||
| t(b) | 9.190 | ||||
| p(b) | -0.000 | ||||
| t(a) | 0.458 | ||||
| p(a) | 0.323 | ||||
| Lowerbound of 95% confidence interval for beta | 0.566 | ||||
| Upperbound of 95% confidence interval for beta | 0.874 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.638 | ||||
| Upperbound of 95% confidence interval for alpha | 1.026 | ||||
| Treynor index (mean / b) | 0.804 | ||||
| Jensen alpha (a) | 0.194 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.076 | ||||
| Expected Shortfall on VaR | 0.095 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 865.000 | ||||
| Minimum | 0.730 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.015 | ||||
| Maximum | 1.575 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.052 | ||||
| Inter Quartile Range | 0.026 | ||||
| Number outliers low | 40.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.890 | ||||
| Number of outliers high | 42.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.147 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.458 | ||||
| VaR(95%) (moments method) | 0.038 | ||||
| Expected Shortfall (moments method) | 0.080 | ||||
| Extreme Value Index (regression method) | 0.281 | ||||
| VaR(95%) (regression method) | 0.032 | ||||
| Expected Shortfall (regression method) | 0.054 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 51.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.051 | ||||
| Quartile 3 | 0.164 | ||||
| Maximum | 0.417 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.026 | ||||
| Mean of quarter 3 | 0.091 | ||||
| Mean of quarter 4 | 0.258 | ||||
| Inter Quartile Range | 0.155 | ||||
| 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 | 0.020 | ||||
| Mean of outliers high | 0.417 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.332 | ||||
| VaR(95%) (moments method) | 0.282 | ||||
| Expected Shortfall (moments method) | 0.324 | ||||
| Extreme Value Index (regression method) | 0.115 | ||||
| VaR(95%) (regression method) | 0.263 | ||||
| Expected Shortfall (regression method) | 0.335 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 2.066 | ||||
| Compounded annual return (geometric extrapolation) | 0.864 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.071 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.354 | ||||
| Compounded annual return / Expected Shortfall lognormal | 9.093 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.425 | ||||
| SD | 0.548 | ||||
| Sharpe ratio (Glass type estimate) | 0.776 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.771 | ||||
| df | 130.000 | ||||
| t | 0.549 | ||||
| p | 0.476 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.999 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.548 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.002 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.545 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.100 | ||||
| Upside Potential Ratio | 9.123 | ||||
| Upside part of mean | 3.526 | ||||
| Downside part of mean | -3.101 | ||||
| Upside SD | 0.386 | ||||
| Downside SD | 0.387 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.231 | ||||
| Mean of criterion | 0.425 | ||||
| SD of predictor | 0.471 | ||||
| SD of criterion | 0.548 | ||||
| Covariance | 0.181 | ||||
| r | 0.702 | ||||
| b (slope, estimate of beta) | 0.817 | ||||
| a (intercept, estimate of alpha) | -0.581 | ||||
| Mean Square Error | 0.153 | ||||
| DF error | 129.000 | ||||
| t(b) | 11.204 | ||||
| p(b) | 0.093 | ||||
| t(a) | -1.036 | ||||
| p(a) | 0.558 | ||||
| Lowerbound of 95% confidence interval for beta | 0.673 | ||||
| Upperbound of 95% confidence interval for beta | 0.962 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.691 | ||||
| Upperbound of 95% confidence interval for alpha | 0.529 | ||||
| Treynor index (mean / b) | 0.520 | ||||
| Jensen alpha (a) | -0.581 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.275 | ||||
| SD | 0.551 | ||||
| Sharpe ratio (Glass type estimate) | 0.499 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.496 | ||||
| df | 130.000 | ||||
| t | 0.353 | ||||
| p | 0.485 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.274 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.271 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.276 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.269 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.688 | ||||
| Upside Potential Ratio | 8.637 | ||||
| Upside part of mean | 3.454 | ||||
| Downside part of mean | -3.179 | ||||
| Upside SD | 0.376 | ||||
| Downside SD | 0.400 | ||||
| N nonnegative terms | 67.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.118 | ||||
| Mean of criterion | 0.275 | ||||
| SD of predictor | 0.473 | ||||
| SD of criterion | 0.551 | ||||
| Covariance | 0.183 | ||||
| r | 0.703 | ||||
| b (slope, estimate of beta) | 0.820 | ||||
| a (intercept, estimate of alpha) | -0.641 | ||||
| Mean Square Error | 0.154 | ||||
| DF error | 129.000 | ||||
| t(b) | 11.241 | ||||
| p(b) | 0.093 | ||||
| t(a) | -1.141 | ||||
| p(a) | 0.564 | ||||
| Lowerbound of 95% confidence interval for beta | 0.675 | ||||
| Upperbound of 95% confidence interval for beta | 0.964 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.753 | ||||
| Upperbound of 95% confidence interval for alpha | 0.470 | ||||
| Treynor index (mean / b) | 0.335 | ||||
| Jensen alpha (a) | -0.641 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.067 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.897 | ||||
| Quartile 1 | 0.983 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.093 | ||||
| Mean of quarter 1 | 0.959 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.043 | ||||
| Inter Quartile Range | 0.036 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.909 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.082 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.109 | ||||
| VaR(95%) (moments method) | 0.039 | ||||
| Expected Shortfall (moments method) | 0.051 | ||||
| Extreme Value Index (regression method) | 0.206 | ||||
| VaR(95%) (regression method) | 0.038 | ||||
| Expected Shortfall (regression method) | 0.057 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.025 | ||||
| Quartile 3 | 0.067 | ||||
| Maximum | 0.278 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.057 | ||||
| Mean of quarter 4 | 0.219 | ||||
| Inter Quartile Range | 0.060 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.222 | ||||
| Mean of outliers high | 0.219 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -6.727 | ||||
| VaR(95%) (moments method) | 0.155 | ||||
| Expected Shortfall (moments method) | 0.155 | ||||
| Extreme Value Index (regression method) | -0.627 | ||||
| VaR(95%) (regression method) | 0.322 | ||||
| Expected Shortfall (regression method) | 0.370 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.346 | ||||
| Compounded annual return (geometric extrapolation) | 0.376 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.350 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.719 | ||||
| Compounded annual return / Expected Shortfall lognormal | 5.630 | ||||