Advanced Statistics: PIPALERT
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 | 0.187 | ||||
| SD | 0.529 | ||||
| Sharpe ratio (Glass type estimate) | 0.353 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.351 | ||||
| df | 95.000 | ||||
| t | 1.000 | ||||
| p | 0.160 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.342 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.047 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.344 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.045 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.568 | ||||
| Upside Potential Ratio | 1.931 | ||||
| Upside part of mean | 0.635 | ||||
| Downside part of mean | -0.449 | ||||
| Upside SD | 0.414 | ||||
| Downside SD | 0.329 | ||||
| N nonnegative terms | 57.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.188 | ||||
| Mean of criterion | 0.187 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.529 | ||||
| Covariance | 0.031 | ||||
| r | 0.252 | ||||
| b (slope, estimate of beta) | 0.576 | ||||
| a (intercept, estimate of alpha) | 0.079 | ||||
| Mean Square Error | 0.264 | ||||
| DF error | 94.000 | ||||
| t(b) | 2.529 | ||||
| p(b) | 0.007 | ||||
| t(a) | 0.421 | ||||
| p(a) | 0.337 | ||||
| Lowerbound of 95% confidence interval for beta | 0.124 | ||||
| Upperbound of 95% confidence interval for beta | 1.028 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.292 | ||||
| Upperbound of 95% confidence interval for alpha | 0.449 | ||||
| Treynor index (mean / b) | 0.324 | ||||
| Jensen alpha (a) | 0.079 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.047 | ||||
| SD | 0.541 | ||||
| Sharpe ratio (Glass type estimate) | 0.087 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.086 | ||||
| df | 95.000 | ||||
| t | 0.246 | ||||
| p | 0.403 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.606 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.780 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.607 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.779 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.113 | ||||
| Upside Potential Ratio | 1.359 | ||||
| Upside part of mean | 0.568 | ||||
| Downside part of mean | -0.521 | ||||
| Upside SD | 0.339 | ||||
| Downside SD | 0.418 | ||||
| N nonnegative terms | 57.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.161 | ||||
| Mean of criterion | 0.047 | ||||
| SD of predictor | 0.223 | ||||
| SD of criterion | 0.541 | ||||
| Covariance | 0.033 | ||||
| r | 0.276 | ||||
| b (slope, estimate of beta) | 0.668 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.273 | ||||
| DF error | 94.000 | ||||
| t(b) | 2.784 | ||||
| p(b) | 0.003 | ||||
| t(a) | -0.320 | ||||
| p(a) | 0.625 | ||||
| Lowerbound of 95% confidence interval for beta | 0.192 | ||||
| Upperbound of 95% confidence interval for beta | 1.144 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.435 | ||||
| Upperbound of 95% confidence interval for alpha | 0.314 | ||||
| Treynor index (mean / b) | 0.070 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.223 | ||||
| Expected Shortfall on VaR | 0.271 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.073 | ||||
| Expected Shortfall on VaR | 0.161 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 96.000 | ||||
| Minimum | 0.480 | ||||
| Quartile 1 | 0.965 | ||||
| Median | 1.021 | ||||
| Quartile 3 | 1.056 | ||||
| Maximum | 1.795 | ||||
| Mean of quarter 1 | 0.862 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.040 | ||||
| Mean of quarter 4 | 1.175 | ||||
| Inter Quartile Range | 0.092 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.052 | ||||
| Mean of outliers low | 0.654 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.073 | ||||
| Mean of outliers high | 1.365 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.412 | ||||
| VaR(95%) (moments method) | 0.125 | ||||
| Expected Shortfall (moments method) | 0.253 | ||||
| Extreme Value Index (regression method) | 0.383 | ||||
| VaR(95%) (regression method) | 0.119 | ||||
| Expected Shortfall (regression method) | 0.230 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.044 | ||||
| Median | 0.381 | ||||
| Quartile 3 | 0.515 | ||||
| Maximum | 0.592 | ||||
| Mean of quarter 1 | 0.021 | ||||
| Mean of quarter 2 | 0.215 | ||||
| Mean of quarter 3 | 0.510 | ||||
| Mean of quarter 4 | 0.556 | ||||
| Inter Quartile Range | 0.471 | ||||
| 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) | 0.134 | ||||
| Compounded annual return (geometric extrapolation) | 0.095 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.161 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.171 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.351 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.227 | ||||
| SD | 0.607 | ||||
| Sharpe ratio (Glass type estimate) | 0.374 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.374 | ||||
| df | 2109.000 | ||||
| t | 1.060 | ||||
| p | 0.145 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.317 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.064 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.317 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.064 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.583 | ||||
| Upside Potential Ratio | 5.411 | ||||
| Upside part of mean | 2.107 | ||||
| Downside part of mean | -1.880 | ||||
| Upside SD | 0.466 | ||||
| Downside SD | 0.389 | ||||
| N nonnegative terms | 955.000 | ||||
| N negative terms | 1155.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2110.000 | ||||
| Mean of predictor | 0.208 | ||||
| Mean of criterion | 0.227 | ||||
| SD of predictor | 0.280 | ||||
| SD of criterion | 0.607 | ||||
| Covariance | 0.015 | ||||
| r | 0.086 | ||||
| b (slope, estimate of beta) | 0.187 | ||||
| a (intercept, estimate of alpha) | 0.188 | ||||
| Mean Square Error | 0.366 | ||||
| DF error | 2108.000 | ||||
| t(b) | 3.978 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.880 | ||||
| p(a) | 0.189 | ||||
| Lowerbound of 95% confidence interval for beta | 0.095 | ||||
| Upperbound of 95% confidence interval for beta | 0.280 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.231 | ||||
| Upperbound of 95% confidence interval for alpha | 0.606 | ||||
| Treynor index (mean / b) | 1.211 | ||||
| Jensen alpha (a) | 0.188 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.046 | ||||
| SD | 0.603 | ||||
| Sharpe ratio (Glass type estimate) | 0.077 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.077 | ||||
| df | 2109.000 | ||||
| t | 0.218 | ||||
| p | 0.414 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.614 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.768 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.614 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.768 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.104 | ||||
| Upside Potential Ratio | 4.536 | ||||
| Upside part of mean | 2.017 | ||||
| Downside part of mean | -1.970 | ||||
| Upside SD | 0.408 | ||||
| Downside SD | 0.445 | ||||
| N nonnegative terms | 955.000 | ||||
| N negative terms | 1155.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2110.000 | ||||
| Mean of predictor | 0.169 | ||||
| Mean of criterion | 0.046 | ||||
| SD of predictor | 0.281 | ||||
| SD of criterion | 0.603 | ||||
| Covariance | 0.019 | ||||
| r | 0.110 | ||||
| b (slope, estimate of beta) | 0.236 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.360 | ||||
| DF error | 2108.000 | ||||
| t(b) | 5.073 | ||||
| p(b) | 0.000 | ||||
| t(a) | 0.031 | ||||
| p(a) | 0.488 | ||||
| Lowerbound of 95% confidence interval for beta | 0.145 | ||||
| Upperbound of 95% confidence interval for beta | 0.327 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.408 | ||||
| Upperbound of 95% confidence interval for alpha | 0.421 | ||||
| Treynor index (mean / b) | 0.197 | ||||
| Jensen alpha (a) | 0.007 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.074 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2110.000 | ||||
| Minimum | 0.573 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.747 | ||||
| Mean of quarter 1 | 0.973 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.030 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 203.000 | ||||
| Percentage of outliers low | 0.096 | ||||
| Mean of outliers low | 0.946 | ||||
| Number of outliers high | 203.000 | ||||
| Percentage of outliers high | 0.096 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.713 | ||||
| VaR(95%) (moments method) | 0.023 | ||||
| Expected Shortfall (moments method) | 0.090 | ||||
| Extreme Value Index (regression method) | 0.412 | ||||
| VaR(95%) (regression method) | 0.023 | ||||
| Expected Shortfall (regression method) | 0.049 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.027 | ||||
| Maximum | 0.624 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.248 | ||||
| Inter Quartile Range | 0.025 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.190 | ||||
| Mean of outliers high | 0.317 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.711 | ||||
| VaR(95%) (moments method) | 0.191 | ||||
| Expected Shortfall (moments method) | 0.770 | ||||
| Extreme Value Index (regression method) | -0.216 | ||||
| VaR(95%) (regression method) | 0.276 | ||||
| Expected Shortfall (regression method) | 0.380 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.133 | ||||
| Compounded annual return (geometric extrapolation) | 0.095 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.152 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.381 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.284 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.484 | ||||
| SD | 0.366 | ||||
| Sharpe ratio (Glass type estimate) | 1.321 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.313 | ||||
| df | 130.000 | ||||
| t | 0.934 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.458 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.095 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.463 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.090 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.180 | ||||
| Upside Potential Ratio | 9.169 | ||||
| Upside part of mean | 2.034 | ||||
| Downside part of mean | -1.551 | ||||
| Upside SD | 0.291 | ||||
| Downside SD | 0.222 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.122 | ||||
| Mean of criterion | 0.484 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.366 | ||||
| Covariance | 0.001 | ||||
| r | 0.008 | ||||
| b (slope, estimate of beta) | 0.008 | ||||
| a (intercept, estimate of alpha) | 0.474 | ||||
| Mean Square Error | 0.135 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.092 | ||||
| p(b) | 0.495 | ||||
| t(a) | 0.896 | ||||
| p(a) | 0.450 | ||||
| Lowerbound of 95% confidence interval for beta | -0.170 | ||||
| Upperbound of 95% confidence interval for beta | 0.186 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.573 | ||||
| Upperbound of 95% confidence interval for alpha | 1.522 | ||||
| Treynor index (mean / b) | 58.368 | ||||
| Jensen alpha (a) | 0.474 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.417 | ||||
| SD | 0.363 | ||||
| Sharpe ratio (Glass type estimate) | 1.151 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.145 | ||||
| df | 130.000 | ||||
| t | 0.814 | ||||
| p | 0.464 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.626 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.925 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.631 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.920 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.841 | ||||
| Upside Potential Ratio | 8.792 | ||||
| Upside part of mean | 1.993 | ||||
| Downside part of mean | -1.576 | ||||
| Upside SD | 0.282 | ||||
| Downside SD | 0.227 | ||||
| N nonnegative terms | 50.000 | ||||
| N negative terms | 81.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.055 | ||||
| Mean of criterion | 0.417 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.363 | ||||
| Covariance | -0.001 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | 0.422 | ||||
| Mean Square Error | 0.132 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.052 | ||||
| p(b) | 0.503 | ||||
| t(a) | 0.807 | ||||
| p(a) | 0.455 | ||||
| Lowerbound of 95% confidence interval for beta | -0.180 | ||||
| Upperbound of 95% confidence interval for beta | 0.170 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.613 | ||||
| Upperbound of 95% confidence interval for alpha | 1.457 | ||||
| Treynor index (mean / b) | -90.448 | ||||
| Jensen alpha (a) | 0.422 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.931 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.009 | ||||
| Maximum | 1.101 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.029 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 11.000 | ||||
| Percentage of outliers low | 0.084 | ||||
| Mean of outliers low | 0.959 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.099 | ||||
| Mean of outliers high | 1.047 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.344 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | 0.019 | ||||
| Extreme Value Index (regression method) | -0.123 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | 0.035 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.027 | ||||
| Quartile 3 | 0.074 | ||||
| Maximum | 0.201 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | 0.019 | ||||
| Mean of quarter 3 | 0.036 | ||||
| Mean of quarter 4 | 0.125 | ||||
| Inter Quartile Range | 0.056 | ||||
| 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 | 0.100 | ||||
| Mean of outliers high | 0.201 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.388 | ||||
| VaR(95%) (moments method) | 0.155 | ||||
| Expected Shortfall (moments method) | 0.259 | ||||
| Extreme Value Index (regression method) | 5.274 | ||||
| VaR(95%) (regression method) | 0.588 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.519 | ||||
| Compounded annual return (geometric extrapolation) | 0.586 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.917 | ||||
| Compounded annual return / average of 25% largest draw downs | 4.682 | ||||
| Compounded annual return / Expected Shortfall lognormal | 13.451 | ||||