Advanced Statistics: mtc-H1
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 | 0.112 | ||||
| SD | 0.315 | ||||
| Sharpe ratio (Glass type estimate) | 0.357 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.350 | ||||
| df | 42.000 | ||||
| t | 0.676 | ||||
| p | 0.252 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.683 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.393 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.688 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.389 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.571 | ||||
| Upside Potential Ratio | 2.494 | ||||
| Upside part of mean | 0.491 | ||||
| Downside part of mean | -0.379 | ||||
| Upside SD | 0.243 | ||||
| Downside SD | 0.197 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.502 | ||||
| Mean of criterion | 0.112 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.315 | ||||
| Covariance | -0.040 | ||||
| r | -0.412 | ||||
| b (slope, estimate of beta) | -0.421 | ||||
| a (intercept, estimate of alpha) | 0.324 | ||||
| Mean Square Error | 0.084 | ||||
| DF error | 41.000 | ||||
| t(b) | -2.898 | ||||
| p(b) | 0.997 | ||||
| t(a) | 1.906 | ||||
| p(a) | 0.032 | ||||
| Lowerbound of 95% confidence interval for beta | -0.715 | ||||
| Upperbound of 95% confidence interval for beta | -0.128 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.019 | ||||
| Upperbound of 95% confidence interval for alpha | 0.667 | ||||
| Treynor index (mean / b) | -0.267 | ||||
| Jensen alpha (a) | 0.324 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.065 | ||||
| SD | 0.310 | ||||
| Sharpe ratio (Glass type estimate) | 0.208 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.204 | ||||
| df | 42.000 | ||||
| t | 0.394 | ||||
| p | 0.348 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.830 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.243 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.832 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.241 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.309 | ||||
| Upside Potential Ratio | 2.220 | ||||
| Upside part of mean | 0.463 | ||||
| Downside part of mean | -0.398 | ||||
| Upside SD | 0.225 | ||||
| Downside SD | 0.208 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.447 | ||||
| Mean of criterion | 0.065 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.310 | ||||
| Covariance | -0.038 | ||||
| r | -0.414 | ||||
| b (slope, estimate of beta) | -0.428 | ||||
| a (intercept, estimate of alpha) | 0.256 | ||||
| Mean Square Error | 0.082 | ||||
| DF error | 41.000 | ||||
| t(b) | -2.913 | ||||
| p(b) | 0.997 | ||||
| t(a) | 1.555 | ||||
| p(a) | 0.064 | ||||
| Lowerbound of 95% confidence interval for beta | -0.725 | ||||
| Upperbound of 95% confidence interval for beta | -0.131 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.076 | ||||
| Upperbound of 95% confidence interval for alpha | 0.588 | ||||
| Treynor index (mean / b) | -0.151 | ||||
| Jensen alpha (a) | 0.256 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.132 | ||||
| Expected Shortfall on VaR | 0.164 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.064 | ||||
| Expected Shortfall on VaR | 0.120 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.854 | ||||
| Quartile 1 | 0.941 | ||||
| Median | 1.016 | ||||
| Quartile 3 | 1.065 | ||||
| Maximum | 1.231 | ||||
| Mean of quarter 1 | 0.898 | ||||
| Mean of quarter 2 | 0.989 | ||||
| Mean of quarter 3 | 1.044 | ||||
| Mean of quarter 4 | 1.125 | ||||
| Inter Quartile Range | 0.124 | ||||
| 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) | -1.085 | ||||
| VaR(95%) (moments method) | 0.112 | ||||
| Expected Shortfall (moments method) | 0.118 | ||||
| Extreme Value Index (regression method) | -0.631 | ||||
| VaR(95%) (regression method) | 0.118 | ||||
| Expected Shortfall (regression method) | 0.130 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.060 | ||||
| Median | 0.191 | ||||
| Quartile 3 | 0.212 | ||||
| Maximum | 0.254 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | 0.129 | ||||
| Mean of quarter 3 | 0.210 | ||||
| Mean of quarter 4 | 0.234 | ||||
| Inter Quartile Range | 0.152 | ||||
| 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) | 0.133 | ||||
| Compounded annual return (geometric extrapolation) | 0.115 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.452 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.490 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.701 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.117 | ||||
| SD | 0.326 | ||||
| Sharpe ratio (Glass type estimate) | 0.358 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.358 | ||||
| df | 943.000 | ||||
| t | 0.680 | ||||
| p | 0.248 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.674 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.391 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.675 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.391 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.525 | ||||
| Upside Potential Ratio | 8.587 | ||||
| Upside part of mean | 1.909 | ||||
| Downside part of mean | -1.793 | ||||
| Upside SD | 0.238 | ||||
| Downside SD | 0.222 | ||||
| N nonnegative terms | 480.000 | ||||
| N negative terms | 464.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 944.000 | ||||
| Mean of predictor | 0.523 | ||||
| Mean of criterion | 0.117 | ||||
| SD of predictor | 0.358 | ||||
| SD of criterion | 0.326 | ||||
| Covariance | -0.018 | ||||
| r | -0.155 | ||||
| b (slope, estimate of beta) | -0.141 | ||||
| a (intercept, estimate of alpha) | 0.190 | ||||
| Mean Square Error | 0.104 | ||||
| DF error | 942.000 | ||||
| t(b) | -4.813 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.118 | ||||
| p(a) | 0.132 | ||||
| Lowerbound of 95% confidence interval for beta | -0.198 | ||||
| Upperbound of 95% confidence interval for beta | -0.083 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | 0.524 | ||||
| Treynor index (mean / b) | -0.828 | ||||
| Jensen alpha (a) | 0.190 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.064 | ||||
| SD | 0.325 | ||||
| Sharpe ratio (Glass type estimate) | 0.197 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.197 | ||||
| df | 943.000 | ||||
| t | 0.374 | ||||
| p | 0.354 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.836 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.229 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.836 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.229 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.282 | ||||
| Upside Potential Ratio | 8.300 | ||||
| Upside part of mean | 1.881 | ||||
| Downside part of mean | -1.818 | ||||
| Upside SD | 0.232 | ||||
| Downside SD | 0.227 | ||||
| N nonnegative terms | 480.000 | ||||
| N negative terms | 464.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 944.000 | ||||
| Mean of predictor | 0.456 | ||||
| Mean of criterion | 0.064 | ||||
| SD of predictor | 0.370 | ||||
| SD of criterion | 0.325 | ||||
| Covariance | -0.018 | ||||
| r | -0.149 | ||||
| b (slope, estimate of beta) | -0.131 | ||||
| a (intercept, estimate of alpha) | 0.124 | ||||
| Mean Square Error | 0.103 | ||||
| DF error | 942.000 | ||||
| t(b) | -4.639 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.729 | ||||
| p(a) | 0.233 | ||||
| Lowerbound of 95% confidence interval for beta | -0.187 | ||||
| Upperbound of 95% confidence interval for beta | -0.076 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.209 | ||||
| Upperbound of 95% confidence interval for alpha | 0.457 | ||||
| Treynor index (mean / b) | -0.487 | ||||
| Jensen alpha (a) | 0.124 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 944.000 | ||||
| Minimum | 0.924 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.011 | ||||
| Maximum | 1.122 | ||||
| Mean of quarter 1 | 0.976 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.020 | ||||
| Number outliers low | 25.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.948 | ||||
| Number of outliers high | 25.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.060 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.007 | ||||
| VaR(95%) (moments method) | 0.022 | ||||
| Expected Shortfall (moments method) | 0.029 | ||||
| Extreme Value Index (regression method) | -0.026 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.029 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 18.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.056 | ||||
| Quartile 3 | 0.115 | ||||
| Maximum | 0.325 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.031 | ||||
| Mean of quarter 3 | 0.072 | ||||
| Mean of quarter 4 | 0.236 | ||||
| Inter Quartile Range | 0.102 | ||||
| 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 | 0.111 | ||||
| Mean of outliers high | 0.300 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -11.313 | ||||
| VaR(95%) (moments method) | 0.225 | ||||
| Expected Shortfall (moments method) | 0.225 | ||||
| Extreme Value Index (regression method) | -1.036 | ||||
| VaR(95%) (regression method) | 0.291 | ||||
| Expected Shortfall (regression method) | 0.310 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.132 | ||||
| Compounded annual return (geometric extrapolation) | 0.114 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.350 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.482 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.831 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.285 | ||||
| SD | 0.205 | ||||
| Sharpe ratio (Glass type estimate) | -1.388 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.380 | ||||
| df | 130.000 | ||||
| t | -0.981 | ||||
| p | 0.543 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.162 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.392 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.157 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.397 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.669 | ||||
| Upside Potential Ratio | 5.651 | ||||
| Upside part of mean | 0.964 | ||||
| Downside part of mean | -1.248 | ||||
| Upside SD | 0.114 | ||||
| Downside SD | 0.170 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.299 | ||||
| Mean of criterion | -0.285 | ||||
| SD of predictor | 0.395 | ||||
| SD of criterion | 0.205 | ||||
| Covariance | -0.016 | ||||
| r | -0.201 | ||||
| b (slope, estimate of beta) | -0.104 | ||||
| a (intercept, estimate of alpha) | -0.149 | ||||
| Mean Square Error | 0.041 | ||||
| DF error | 129.000 | ||||
| t(b) | -2.325 | ||||
| p(b) | 0.627 | ||||
| t(a) | -0.513 | ||||
| p(a) | 0.529 | ||||
| Lowerbound of 95% confidence interval for beta | -0.193 | ||||
| Upperbound of 95% confidence interval for beta | -0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.725 | ||||
| Upperbound of 95% confidence interval for alpha | 0.427 | ||||
| Treynor index (mean / b) | 2.733 | ||||
| Jensen alpha (a) | -0.149 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.306 | ||||
| SD | 0.207 | ||||
| Sharpe ratio (Glass type estimate) | -1.480 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.471 | ||||
| df | 130.000 | ||||
| t | -1.046 | ||||
| p | 0.546 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.254 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.301 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.249 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.307 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.765 | ||||
| Upside Potential Ratio | 5.526 | ||||
| Upside part of mean | 0.957 | ||||
| Downside part of mean | -1.263 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.173 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.218 | ||||
| Mean of criterion | -0.306 | ||||
| SD of predictor | 0.398 | ||||
| SD of criterion | 0.207 | ||||
| Covariance | -0.016 | ||||
| r | -0.190 | ||||
| b (slope, estimate of beta) | -0.099 | ||||
| a (intercept, estimate of alpha) | -0.185 | ||||
| Mean Square Error | 0.041 | ||||
| DF error | 129.000 | ||||
| t(b) | -2.197 | ||||
| p(b) | 0.620 | ||||
| t(a) | -0.633 | ||||
| p(a) | 0.535 | ||||
| Lowerbound of 95% confidence interval for beta | -0.188 | ||||
| Upperbound of 95% confidence interval for beta | -0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.766 | ||||
| Upperbound of 95% confidence interval for alpha | 0.395 | ||||
| Treynor index (mean / b) | 3.096 | ||||
| Jensen alpha (a) | -0.185 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.950 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.032 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.076 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.028 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.116 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.018 | ||||
| Extreme Value Index (regression method) | -0.228 | ||||
| VaR(95%) (regression method) | 0.020 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.054 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.103 | ||||
| Maximum | 0.160 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.071 | ||||
| Mean of quarter 3 | 0.084 | ||||
| Mean of quarter 4 | 0.160 | ||||
| Inter Quartile Range | 0.049 | ||||
| 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) | -0.245 | ||||
| Compounded annual return (geometric extrapolation) | -0.230 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.435 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.435 | ||||
| Compounded annual return / Expected Shortfall lognormal | -8.492 | ||||