Advanced Statistics: (52547431)
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 | 0.123 | ||||
| SD | 0.151 | ||||
| Sharpe ratio (Glass type estimate) | 0.814 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.805 | ||||
| df | 67.000 | ||||
| t | 1.939 | ||||
| p | 0.028 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.023 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.646 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.029 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.640 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.609 | ||||
| Upside Potential Ratio | 3.167 | ||||
| Upside part of mean | 0.242 | ||||
| Downside part of mean | -0.119 | ||||
| Upside SD | 0.134 | ||||
| Downside SD | 0.077 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.296 | ||||
| Mean of criterion | 0.123 | ||||
| SD of predictor | 0.197 | ||||
| SD of criterion | 0.151 | ||||
| Covariance | 0.027 | ||||
| r | 0.891 | ||||
| b (slope, estimate of beta) | 0.682 | ||||
| a (intercept, estimate of alpha) | -0.079 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 66.000 | ||||
| t(b) | 15.930 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.490 | ||||
| p(a) | 0.992 | ||||
| Lowerbound of 95% confidence interval for beta | 0.597 | ||||
| Upperbound of 95% confidence interval for beta | 0.768 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.142 | ||||
| Upperbound of 95% confidence interval for alpha | -0.016 | ||||
| Treynor index (mean / b) | 0.180 | ||||
| Jensen alpha (a) | -0.079 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.111 | ||||
| SD | 0.148 | ||||
| Sharpe ratio (Glass type estimate) | 0.753 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.744 | ||||
| df | 67.000 | ||||
| t | 1.792 | ||||
| p | 0.039 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.083 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.583 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.089 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.577 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.398 | ||||
| Upside Potential Ratio | 2.931 | ||||
| Upside part of mean | 0.233 | ||||
| Downside part of mean | -0.122 | ||||
| Upside SD | 0.127 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.273 | ||||
| Mean of criterion | 0.111 | ||||
| SD of predictor | 0.191 | ||||
| SD of criterion | 0.148 | ||||
| Covariance | 0.025 | ||||
| r | 0.888 | ||||
| b (slope, estimate of beta) | 0.688 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 66.000 | ||||
| t(b) | 15.688 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.468 | ||||
| p(a) | 0.992 | ||||
| Lowerbound of 95% confidence interval for beta | 0.600 | ||||
| Upperbound of 95% confidence interval for beta | 0.775 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | -0.015 | ||||
| Treynor index (mean / b) | 0.162 | ||||
| Jensen alpha (a) | -0.077 | ||||
| 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 | 0.076 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.878 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.006 | ||||
| Quartile 3 | 1.031 | ||||
| Maximum | 1.145 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.017 | ||||
| Mean of quarter 4 | 1.071 | ||||
| Inter Quartile Range | 0.038 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.878 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.074 | ||||
| Mean of outliers high | 1.119 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.331 | ||||
| VaR(95%) (moments method) | 0.024 | ||||
| Expected Shortfall (moments method) | 0.030 | ||||
| Extreme Value Index (regression method) | 0.196 | ||||
| VaR(95%) (regression method) | 0.030 | ||||
| Expected Shortfall (regression method) | 0.051 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 11.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.020 | ||||
| Median | 0.029 | ||||
| Quartile 3 | 0.058 | ||||
| Maximum | 0.122 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.024 | ||||
| Mean of quarter 3 | 0.047 | ||||
| Mean of quarter 4 | 0.096 | ||||
| Inter Quartile Range | 0.038 | ||||
| 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 | 0.122 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -16.083 | ||||
| VaR(95%) (moments method) | 0.101 | ||||
| Expected Shortfall (moments method) | 0.101 | ||||
| Extreme Value Index (regression method) | -1.826 | ||||
| VaR(95%) (regression method) | 0.144 | ||||
| Expected Shortfall (regression method) | 0.147 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.249 | ||||
| Compounded annual return (geometric extrapolation) | 0.168 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.380 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.757 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.222 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.151 | ||||
| SD | 0.204 | ||||
| Sharpe ratio (Glass type estimate) | 0.741 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.740 | ||||
| df | 1486.000 | ||||
| t | 1.765 | ||||
| p | 0.477 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.083 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.564 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.083 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.563 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.968 | ||||
| Upside Potential Ratio | 6.115 | ||||
| Upside part of mean | 0.956 | ||||
| Downside part of mean | -0.805 | ||||
| Upside SD | 0.132 | ||||
| Downside SD | 0.156 | ||||
| N nonnegative terms | 820.000 | ||||
| N negative terms | 667.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1487.000 | ||||
| Mean of predictor | 0.342 | ||||
| Mean of criterion | 0.151 | ||||
| SD of predictor | 0.293 | ||||
| SD of criterion | 0.204 | ||||
| Covariance | 0.050 | ||||
| r | 0.835 | ||||
| b (slope, estimate of beta) | 0.583 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 1485.000 | ||||
| t(b) | 58.537 | ||||
| p(b) | 0.039 | ||||
| t(a) | -1.012 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | 0.564 | ||||
| Upperbound of 95% confidence interval for beta | 0.603 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.141 | ||||
| Upperbound of 95% confidence interval for alpha | 0.045 | ||||
| Treynor index (mean / b) | 0.260 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.130 | ||||
| SD | 0.212 | ||||
| Sharpe ratio (Glass type estimate) | 0.612 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.612 | ||||
| df | 1486.000 | ||||
| t | 1.458 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.211 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.435 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.211 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.435 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.774 | ||||
| Upside Potential Ratio | 5.662 | ||||
| Upside part of mean | 0.948 | ||||
| Downside part of mean | -0.818 | ||||
| Upside SD | 0.130 | ||||
| Downside SD | 0.167 | ||||
| N nonnegative terms | 820.000 | ||||
| N negative terms | 667.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1487.000 | ||||
| Mean of predictor | 0.297 | ||||
| Mean of criterion | 0.130 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.212 | ||||
| Covariance | 0.054 | ||||
| r | 0.846 | ||||
| b (slope, estimate of beta) | 0.592 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.013 | ||||
| DF error | 1485.000 | ||||
| t(b) | 61.034 | ||||
| p(b) | 0.036 | ||||
| t(a) | -0.973 | ||||
| p(a) | 0.516 | ||||
| Lowerbound of 95% confidence interval for beta | 0.573 | ||||
| Upperbound of 95% confidence interval for beta | 0.611 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | 0.047 | ||||
| Treynor index (mean / b) | 0.219 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1487.000 | ||||
| Minimum | 0.761 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.001 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.013 | ||||
| Inter Quartile Range | 0.007 | ||||
| Number outliers low | 91.000 | ||||
| Percentage of outliers low | 0.061 | ||||
| Mean of outliers low | 0.973 | ||||
| Number of outliers high | 93.000 | ||||
| Percentage of outliers high | 0.063 | ||||
| Mean of outliers high | 1.026 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.525 | ||||
| VaR(95%) (moments method) | 0.010 | ||||
| Expected Shortfall (moments method) | 0.024 | ||||
| Extreme Value Index (regression method) | 0.366 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 62.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.015 | ||||
| Quartile 3 | 0.032 | ||||
| Maximum | 0.242 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.021 | ||||
| Mean of quarter 4 | 0.085 | ||||
| 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 | 6.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 0.151 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.504 | ||||
| VaR(95%) (moments method) | 0.094 | ||||
| Expected Shortfall (moments method) | 0.208 | ||||
| Extreme Value Index (regression method) | 0.417 | ||||
| VaR(95%) (regression method) | 0.093 | ||||
| Expected Shortfall (regression method) | 0.180 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.296 | ||||
| Compounded annual return (geometric extrapolation) | 0.189 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.783 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.233 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.258 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.607 | ||||
| SD | 0.369 | ||||
| Sharpe ratio (Glass type estimate) | 1.646 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.636 | ||||
| df | 130.000 | ||||
| t | 1.164 | ||||
| p | 0.449 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.136 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.422 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.142 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.415 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.474 | ||||
| Upside Potential Ratio | 10.143 | ||||
| Upside part of mean | 2.489 | ||||
| Downside part of mean | -1.882 | ||||
| Upside SD | 0.276 | ||||
| Downside SD | 0.245 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.000 | ||||
| Mean of criterion | 0.607 | ||||
| SD of predictor | 0.480 | ||||
| SD of criterion | 0.369 | ||||
| Covariance | 0.160 | ||||
| r | 0.903 | ||||
| b (slope, estimate of beta) | 0.693 | ||||
| a (intercept, estimate of alpha) | -0.086 | ||||
| Mean Square Error | 0.025 | ||||
| DF error | 129.000 | ||||
| t(b) | 23.844 | ||||
| p(b) | 0.018 | ||||
| t(a) | -0.379 | ||||
| p(a) | 0.521 | ||||
| Lowerbound of 95% confidence interval for beta | 0.636 | ||||
| Upperbound of 95% confidence interval for beta | 0.751 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.535 | ||||
| Upperbound of 95% confidence interval for alpha | 0.363 | ||||
| Treynor index (mean / b) | 0.876 | ||||
| Jensen alpha (a) | -0.086 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.539 | ||||
| SD | 0.368 | ||||
| Sharpe ratio (Glass type estimate) | 1.467 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.459 | ||||
| df | 130.000 | ||||
| t | 1.038 | ||||
| p | 0.455 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.313 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 4.242 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.319 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 4.236 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.152 | ||||
| Upside Potential Ratio | 9.786 | ||||
| Upside part of mean | 2.452 | ||||
| Downside part of mean | -1.913 | ||||
| Upside SD | 0.269 | ||||
| Downside SD | 0.251 | ||||
| N nonnegative terms | 80.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.885 | ||||
| Mean of criterion | 0.539 | ||||
| SD of predictor | 0.478 | ||||
| SD of criterion | 0.368 | ||||
| Covariance | 0.158 | ||||
| r | 0.901 | ||||
| b (slope, estimate of beta) | 0.693 | ||||
| a (intercept, estimate of alpha) | -0.073 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 129.000 | ||||
| t(b) | 23.622 | ||||
| p(b) | 0.018 | ||||
| t(a) | -0.323 | ||||
| p(a) | 0.518 | ||||
| Lowerbound of 95% confidence interval for beta | 0.635 | ||||
| Upperbound of 95% confidence interval for beta | 0.751 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.524 | ||||
| Upperbound of 95% confidence interval for alpha | 0.377 | ||||
| Treynor index (mean / b) | 0.779 | ||||
| Jensen alpha (a) | -0.073 | ||||
| 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%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.935 | ||||
| Quartile 1 | 0.991 | ||||
| Median | 1.005 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 1.107 | ||||
| Mean of quarter 1 | 0.974 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.009 | ||||
| Mean of quarter 4 | 1.028 | ||||
| Inter Quartile Range | 0.023 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.946 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.082 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.031 | ||||
| VaR(95%) (moments method) | 0.023 | ||||
| Expected Shortfall (moments method) | 0.031 | ||||
| Extreme Value Index (regression method) | -0.208 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.036 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.013 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.054 | ||||
| Maximum | 0.195 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.018 | ||||
| Mean of quarter 3 | 0.043 | ||||
| Mean of quarter 4 | 0.139 | ||||
| Inter Quartile Range | 0.041 | ||||
| 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 | 0.195 | ||||
| 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) | 0.677 | ||||
| Compounded annual return (geometric extrapolation) | 0.792 | ||||
| Calmar ratio (compounded annual return / max draw down) | 4.054 | ||||
| Compounded annual return / average of 25% largest draw downs | 5.691 | ||||
| Compounded annual return / Expected Shortfall lognormal | 18.099 | ||||