Advanced Statistics: Mo Pips
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 | 0.167 | ||||
| SD | 0.402 | ||||
| Sharpe ratio (Glass type estimate) | 0.415 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.407 | ||||
| df | 36.000 | ||||
| t | 0.729 | ||||
| p | 0.235 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.708 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.533 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.713 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.527 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.777 | ||||
| Upside Potential Ratio | 2.620 | ||||
| Upside part of mean | 0.563 | ||||
| Downside part of mean | -0.396 | ||||
| Upside SD | 0.337 | ||||
| Downside SD | 0.215 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.544 | ||||
| Mean of criterion | 0.167 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.402 | ||||
| Covariance | -0.039 | ||||
| r | -0.361 | ||||
| b (slope, estimate of beta) | -0.542 | ||||
| a (intercept, estimate of alpha) | 0.462 | ||||
| Mean Square Error | 0.145 | ||||
| DF error | 35.000 | ||||
| t(b) | -2.290 | ||||
| p(b) | 0.986 | ||||
| t(a) | 1.832 | ||||
| p(a) | 0.038 | ||||
| Lowerbound of 95% confidence interval for beta | -1.022 | ||||
| Upperbound of 95% confidence interval for beta | -0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.050 | ||||
| Upperbound of 95% confidence interval for alpha | 0.973 | ||||
| Treynor index (mean / b) | -0.308 | ||||
| Jensen alpha (a) | 0.462 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.094 | ||||
| SD | 0.378 | ||||
| Sharpe ratio (Glass type estimate) | 0.249 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.244 | ||||
| df | 36.000 | ||||
| t | 0.437 | ||||
| p | 0.332 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.870 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.365 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.874 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.361 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.401 | ||||
| Upside Potential Ratio | 2.194 | ||||
| Upside part of mean | 0.515 | ||||
| Downside part of mean | -0.421 | ||||
| Upside SD | 0.291 | ||||
| Downside SD | 0.235 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 37.000 | ||||
| Mean of predictor | 0.500 | ||||
| Mean of criterion | 0.094 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.378 | ||||
| Covariance | -0.034 | ||||
| r | -0.369 | ||||
| b (slope, estimate of beta) | -0.569 | ||||
| a (intercept, estimate of alpha) | 0.378 | ||||
| Mean Square Error | 0.127 | ||||
| DF error | 35.000 | ||||
| t(b) | -2.350 | ||||
| p(b) | 0.988 | ||||
| t(a) | 1.602 | ||||
| p(a) | 0.059 | ||||
| Lowerbound of 95% confidence interval for beta | -1.061 | ||||
| Upperbound of 95% confidence interval for beta | -0.077 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.101 | ||||
| Upperbound of 95% confidence interval for alpha | 0.858 | ||||
| Treynor index (mean / b) | -0.165 | ||||
| Jensen alpha (a) | 0.378 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.158 | ||||
| Expected Shortfall on VaR | 0.195 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.073 | ||||
| Expected Shortfall on VaR | 0.137 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 37.000 | ||||
| Minimum | 0.754 | ||||
| Quartile 1 | 0.945 | ||||
| Median | 1.026 | ||||
| Quartile 3 | 1.059 | ||||
| Maximum | 1.469 | ||||
| Mean of quarter 1 | 0.901 | ||||
| Mean of quarter 2 | 0.986 | ||||
| Mean of quarter 3 | 1.041 | ||||
| Mean of quarter 4 | 1.156 | ||||
| Inter Quartile Range | 0.114 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.027 | ||||
| Mean of outliers low | 0.754 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 1.469 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.147 | ||||
| VaR(95%) (moments method) | 0.108 | ||||
| Expected Shortfall (moments method) | 0.152 | ||||
| Extreme Value Index (regression method) | 0.557 | ||||
| VaR(95%) (regression method) | 0.097 | ||||
| Expected Shortfall (regression method) | 0.184 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.136 | ||||
| Median | 0.195 | ||||
| Quartile 3 | 0.221 | ||||
| Maximum | 0.246 | ||||
| Mean of quarter 1 | 0.070 | ||||
| Mean of quarter 2 | 0.195 | ||||
| Mean of quarter 3 | 0.221 | ||||
| Mean of quarter 4 | 0.246 | ||||
| Inter Quartile Range | 0.085 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.004 | ||||
| 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) | 0.172 | ||||
| Compounded annual return (geometric extrapolation) | 0.148 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.602 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.602 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.761 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.165 | ||||
| SD | 0.383 | ||||
| Sharpe ratio (Glass type estimate) | 0.431 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.431 | ||||
| df | 818.000 | ||||
| t | 0.763 | ||||
| p | 0.223 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.677 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.540 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.678 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.540 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.644 | ||||
| Upside Potential Ratio | 8.183 | ||||
| Upside part of mean | 2.098 | ||||
| Downside part of mean | -1.933 | ||||
| Upside SD | 0.284 | ||||
| Downside SD | 0.256 | ||||
| N nonnegative terms | 407.000 | ||||
| N negative terms | 412.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 819.000 | ||||
| Mean of predictor | 0.583 | ||||
| Mean of criterion | 0.165 | ||||
| SD of predictor | 0.347 | ||||
| SD of criterion | 0.383 | ||||
| Covariance | -0.022 | ||||
| r | -0.164 | ||||
| b (slope, estimate of beta) | -0.181 | ||||
| a (intercept, estimate of alpha) | 0.271 | ||||
| Mean Square Error | 0.143 | ||||
| DF error | 817.000 | ||||
| t(b) | -4.743 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.259 | ||||
| p(a) | 0.104 | ||||
| Lowerbound of 95% confidence interval for beta | -0.255 | ||||
| Upperbound of 95% confidence interval for beta | -0.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.151 | ||||
| Upperbound of 95% confidence interval for alpha | 0.692 | ||||
| Treynor index (mean / b) | -0.914 | ||||
| Jensen alpha (a) | 0.271 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.092 | ||||
| SD | 0.382 | ||||
| Sharpe ratio (Glass type estimate) | 0.241 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.241 | ||||
| df | 818.000 | ||||
| t | 0.427 | ||||
| p | 0.335 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.867 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.350 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.868 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.350 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.348 | ||||
| Upside Potential Ratio | 7.778 | ||||
| Upside part of mean | 2.059 | ||||
| Downside part of mean | -1.967 | ||||
| Upside SD | 0.275 | ||||
| Downside SD | 0.265 | ||||
| N nonnegative terms | 407.000 | ||||
| N negative terms | 412.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 819.000 | ||||
| Mean of predictor | 0.524 | ||||
| Mean of criterion | 0.092 | ||||
| SD of predictor | 0.341 | ||||
| SD of criterion | 0.382 | ||||
| Covariance | -0.021 | ||||
| r | -0.165 | ||||
| b (slope, estimate of beta) | -0.185 | ||||
| a (intercept, estimate of alpha) | 0.189 | ||||
| Mean Square Error | 0.142 | ||||
| DF error | 817.000 | ||||
| t(b) | -4.777 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.882 | ||||
| p(a) | 0.189 | ||||
| Lowerbound of 95% confidence interval for beta | -0.261 | ||||
| Upperbound of 95% confidence interval for beta | -0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.232 | ||||
| Upperbound of 95% confidence interval for alpha | 0.610 | ||||
| Treynor index (mean / b) | -0.499 | ||||
| Jensen alpha (a) | 0.189 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.047 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 819.000 | ||||
| Minimum | 0.840 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.010 | ||||
| Maximum | 1.136 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.019 | ||||
| Number outliers low | 31.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 31.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.069 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.192 | ||||
| VaR(95%) (moments method) | 0.024 | ||||
| Expected Shortfall (moments method) | 0.037 | ||||
| Extreme Value Index (regression method) | 0.122 | ||||
| VaR(95%) (regression method) | 0.024 | ||||
| Expected Shortfall (regression method) | 0.036 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.027 | ||||
| Quartile 3 | 0.225 | ||||
| Maximum | 0.381 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.125 | ||||
| Mean of quarter 4 | 0.283 | ||||
| Inter Quartile Range | 0.215 | ||||
| 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) | -0.272 | ||||
| VaR(95%) (moments method) | 0.315 | ||||
| Expected Shortfall (moments method) | 0.355 | ||||
| Extreme Value Index (regression method) | 0.727 | ||||
| VaR(95%) (regression method) | 0.291 | ||||
| Expected Shortfall (regression method) | 0.529 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.170 | ||||
| Compounded annual return (geometric extrapolation) | 0.146 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.383 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.516 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.094 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.088 | ||||
| SD | 0.271 | ||||
| Sharpe ratio (Glass type estimate) | -0.323 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.321 | ||||
| df | 130.000 | ||||
| t | -0.228 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.094 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.450 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.093 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.451 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.462 | ||||
| Upside Potential Ratio | 8.111 | ||||
| Upside part of mean | 1.539 | ||||
| Downside part of mean | -1.626 | ||||
| Upside SD | 0.193 | ||||
| Downside SD | 0.190 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.114 | ||||
| Mean of criterion | -0.088 | ||||
| SD of predictor | 0.474 | ||||
| SD of criterion | 0.271 | ||||
| Covariance | -0.051 | ||||
| r | -0.397 | ||||
| b (slope, estimate of beta) | -0.228 | ||||
| a (intercept, estimate of alpha) | 0.166 | ||||
| Mean Square Error | 0.062 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.920 | ||||
| p(b) | 0.746 | ||||
| t(a) | 0.465 | ||||
| p(a) | 0.474 | ||||
| Lowerbound of 95% confidence interval for beta | -0.319 | ||||
| Upperbound of 95% confidence interval for beta | -0.136 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.541 | ||||
| Upperbound of 95% confidence interval for alpha | 0.873 | ||||
| Treynor index (mean / b) | 0.385 | ||||
| Jensen alpha (a) | 0.166 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.124 | ||||
| SD | 0.271 | ||||
| Sharpe ratio (Glass type estimate) | -0.458 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.455 | ||||
| df | 130.000 | ||||
| t | -0.324 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.229 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.316 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.227 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.317 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.645 | ||||
| Upside Potential Ratio | 7.904 | ||||
| Upside part of mean | 1.520 | ||||
| Downside part of mean | -1.644 | ||||
| Upside SD | 0.190 | ||||
| Downside SD | 0.192 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.000 | ||||
| Mean of criterion | -0.124 | ||||
| SD of predictor | 0.477 | ||||
| SD of criterion | 0.271 | ||||
| Covariance | -0.050 | ||||
| r | -0.391 | ||||
| b (slope, estimate of beta) | -0.222 | ||||
| a (intercept, estimate of alpha) | 0.098 | ||||
| Mean Square Error | 0.063 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.818 | ||||
| p(b) | 0.742 | ||||
| t(a) | 0.274 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | -0.313 | ||||
| Upperbound of 95% confidence interval for beta | -0.131 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.609 | ||||
| Upperbound of 95% confidence interval for alpha | 0.805 | ||||
| Treynor index (mean / b) | 0.558 | ||||
| Jensen alpha (a) | 0.098 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.957 | ||||
| Quartile 1 | 0.990 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.044 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.021 | ||||
| Inter Quartile Range | 0.018 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.023 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.040 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.009 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | 0.027 | ||||
| Extreme Value Index (regression method) | -0.129 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.030 | ||||
| Maximum | 0.220 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.128 | ||||
| Inter Quartile Range | 0.021 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.220 | ||||
| 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) | -0.078 | ||||
| Compounded annual return (geometric extrapolation) | -0.077 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.350 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.602 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.236 | ||||