Advanced Statistics: Topaz NQ100 M
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 | 0.171 | ||||
| SD | 0.247 | ||||
| Sharpe ratio (Glass type estimate) | 0.692 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.687 | ||||
| df | 122.000 | ||||
| t | 2.214 | ||||
| p | 0.402 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.072 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.309 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.069 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.306 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.190 | ||||
| Upside Potential Ratio | 2.632 | ||||
| Upside part of mean | 0.377 | ||||
| Downside part of mean | -0.207 | ||||
| Upside SD | 0.206 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 123.000 | ||||
| Mean of predictor | 0.132 | ||||
| Mean of criterion | 0.171 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.247 | ||||
| Covariance | 0.020 | ||||
| r | 0.354 | ||||
| b (slope, estimate of beta) | 0.379 | ||||
| a (intercept, estimate of alpha) | 0.121 | ||||
| Mean Square Error | 0.054 | ||||
| DF error | 121.000 | ||||
| t(b) | 4.166 | ||||
| p(b) | 0.279 | ||||
| t(a) | 1.646 | ||||
| p(a) | 0.406 | ||||
| Lowerbound of 95% confidence interval for beta | 0.199 | ||||
| Upperbound of 95% confidence interval for beta | 0.559 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.025 | ||||
| Upperbound of 95% confidence interval for alpha | 0.266 | ||||
| Treynor index (mean / b) | 0.451 | ||||
| Jensen alpha (a) | 0.121 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.140 | ||||
| SD | 0.240 | ||||
| Sharpe ratio (Glass type estimate) | 0.583 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.580 | ||||
| df | 122.000 | ||||
| t | 1.867 | ||||
| p | 0.417 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.034 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.199 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.037 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.196 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.913 | ||||
| Upside Potential Ratio | 2.327 | ||||
| Upside part of mean | 0.357 | ||||
| Downside part of mean | -0.217 | ||||
| Upside SD | 0.188 | ||||
| Downside SD | 0.154 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 123.000 | ||||
| Mean of predictor | 0.104 | ||||
| Mean of criterion | 0.140 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.240 | ||||
| Covariance | 0.022 | ||||
| r | 0.391 | ||||
| b (slope, estimate of beta) | 0.405 | ||||
| a (intercept, estimate of alpha) | 0.098 | ||||
| Mean Square Error | 0.049 | ||||
| DF error | 121.000 | ||||
| t(b) | 4.678 | ||||
| p(b) | 0.257 | ||||
| t(a) | 1.400 | ||||
| p(a) | 0.420 | ||||
| Lowerbound of 95% confidence interval for beta | 0.234 | ||||
| Upperbound of 95% confidence interval for beta | 0.577 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.041 | ||||
| Upperbound of 95% confidence interval for alpha | 0.236 | ||||
| Treynor index (mean / b) | 0.346 | ||||
| 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%) | 0.097 | ||||
| Expected Shortfall on VaR | 0.123 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.075 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 123.000 | ||||
| Minimum | 0.828 | ||||
| Quartile 1 | 0.993 | ||||
| Median | 1.021 | ||||
| Quartile 3 | 1.047 | ||||
| Maximum | 1.339 | ||||
| Mean of quarter 1 | 0.938 | ||||
| Mean of quarter 2 | 1.004 | ||||
| Mean of quarter 3 | 1.034 | ||||
| Mean of quarter 4 | 1.096 | ||||
| Inter Quartile Range | 0.054 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.065 | ||||
| Mean of outliers low | 0.865 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.041 | ||||
| Mean of outliers high | 1.223 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.159 | ||||
| VaR(95%) (moments method) | 0.032 | ||||
| Expected Shortfall (moments method) | 0.044 | ||||
| Extreme Value Index (regression method) | -0.445 | ||||
| VaR(95%) (regression method) | 0.055 | ||||
| Expected Shortfall (regression method) | 0.068 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 13.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.035 | ||||
| Median | 0.102 | ||||
| Quartile 3 | 0.172 | ||||
| Maximum | 0.328 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.070 | ||||
| Mean of quarter 3 | 0.158 | ||||
| Mean of quarter 4 | 0.295 | ||||
| Inter Quartile Range | 0.137 | ||||
| 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) | -22.777 | ||||
| VaR(95%) (moments method) | 0.268 | ||||
| Expected Shortfall (moments method) | 0.268 | ||||
| Extreme Value Index (regression method) | -1.387 | ||||
| VaR(95%) (regression method) | 0.290 | ||||
| Expected Shortfall (regression method) | 0.297 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.547 | ||||
| Compounded annual return (geometric extrapolation) | 0.202 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.616 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.685 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.646 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.460 | ||||
| SD | 1.040 | ||||
| Sharpe ratio (Glass type estimate) | 0.442 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.442 | ||||
| df | 2693.000 | ||||
| t | 1.419 | ||||
| p | 0.078 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.169 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.054 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.169 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.054 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.194 | ||||
| Upside Potential Ratio | 5.117 | ||||
| Upside part of mean | 1.972 | ||||
| Downside part of mean | -1.512 | ||||
| Upside SD | 0.966 | ||||
| Downside SD | 0.385 | ||||
| N nonnegative terms | 1212.000 | ||||
| N negative terms | 1482.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2694.000 | ||||
| Mean of predictor | 0.205 | ||||
| Mean of criterion | 0.460 | ||||
| SD of predictor | 0.432 | ||||
| SD of criterion | 1.040 | ||||
| Covariance | -0.005 | ||||
| r | -0.012 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | 0.466 | ||||
| Mean Square Error | 1.081 | ||||
| DF error | 2692.000 | ||||
| t(b) | -0.625 | ||||
| p(b) | 0.734 | ||||
| t(a) | 1.436 | ||||
| p(a) | 0.076 | ||||
| Lowerbound of 95% confidence interval for beta | -0.120 | ||||
| Upperbound of 95% confidence interval for beta | 0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.170 | ||||
| Upperbound of 95% confidence interval for alpha | 1.102 | ||||
| Treynor index (mean / b) | -15.854 | ||||
| Jensen alpha (a) | 0.466 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.140 | ||||
| SD | 0.764 | ||||
| Sharpe ratio (Glass type estimate) | 0.183 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.183 | ||||
| df | 2693.000 | ||||
| t | 0.586 | ||||
| p | 0.279 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.429 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.794 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.429 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.794 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.259 | ||||
| Upside Potential Ratio | 3.278 | ||||
| Upside part of mean | 1.763 | ||||
| Downside part of mean | -1.623 | ||||
| Upside SD | 0.543 | ||||
| Downside SD | 0.538 | ||||
| N nonnegative terms | 1212.000 | ||||
| N negative terms | 1482.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2694.000 | ||||
| Mean of predictor | 0.112 | ||||
| Mean of criterion | 0.140 | ||||
| SD of predictor | 0.433 | ||||
| SD of criterion | 0.764 | ||||
| Covariance | 0.012 | ||||
| r | 0.036 | ||||
| b (slope, estimate of beta) | 0.063 | ||||
| a (intercept, estimate of alpha) | 0.133 | ||||
| Mean Square Error | 0.583 | ||||
| DF error | 2692.000 | ||||
| t(b) | 1.845 | ||||
| p(b) | 0.033 | ||||
| t(a) | 0.556 | ||||
| p(a) | 0.289 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.129 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.335 | ||||
| Upperbound of 95% confidence interval for alpha | 0.600 | ||||
| Treynor index (mean / b) | 2.224 | ||||
| Jensen alpha (a) | 0.133 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.074 | ||||
| Expected Shortfall on VaR | 0.092 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2694.000 | ||||
| Minimum | 0.255 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.004 | ||||
| Maximum | 3.859 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.029 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 329.000 | ||||
| Percentage of outliers low | 0.122 | ||||
| Mean of outliers low | 0.959 | ||||
| Number of outliers high | 339.000 | ||||
| Percentage of outliers high | 0.126 | ||||
| Mean of outliers high | 1.051 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.142 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.553 | ||||
| VaR(95%) (regression method) | 0.015 | ||||
| Expected Shortfall (regression method) | 0.043 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 72.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.018 | ||||
| Maximum | 0.749 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.145 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.181 | ||||
| Mean of outliers high | 0.191 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.830 | ||||
| VaR(95%) (moments method) | 0.113 | ||||
| Expected Shortfall (moments method) | 0.747 | ||||
| Extreme Value Index (regression method) | 0.559 | ||||
| VaR(95%) (regression method) | 0.154 | ||||
| Expected Shortfall (regression method) | 0.444 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.545 | ||||
| Compounded annual return (geometric extrapolation) | 0.201 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.269 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.387 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.186 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.034 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.442 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.935 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.444 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8725605454110504.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | -63475219277818617382274267611136.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.000 | ||||
| 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) | 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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| Mean of quarter 1 | NA | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | NA | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||