Advanced Statistics: Sigma TF
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 | -0.025 | ||||
| SD | 0.053 | ||||
| Sharpe ratio (Glass type estimate) | -0.463 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.457 | ||||
| df | 53.000 | ||||
| t | -0.983 | ||||
| p | 0.835 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.389 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.467 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.385 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.471 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.738 | ||||
| Upside Potential Ratio | 0.991 | ||||
| Upside part of mean | 0.033 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.041 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.325 | ||||
| Mean of criterion | -0.025 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.053 | ||||
| Covariance | 0.000 | ||||
| r | 0.001 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 52.000 | ||||
| t(b) | 0.010 | ||||
| p(b) | 0.496 | ||||
| t(a) | -0.919 | ||||
| p(a) | 0.819 | ||||
| Lowerbound of 95% confidence interval for beta | -0.056 | ||||
| Upperbound of 95% confidence interval for beta | 0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.029 | ||||
| Treynor index (mean / b) | -91.468 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.052 | ||||
| Sharpe ratio (Glass type estimate) | -0.492 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.485 | ||||
| df | 53.000 | ||||
| t | -1.044 | ||||
| p | 0.849 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.419 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.439 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.414 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.443 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.759 | ||||
| Upside Potential Ratio | 0.940 | ||||
| Upside part of mean | 0.032 | ||||
| Downside part of mean | -0.058 | ||||
| Upside SD | 0.040 | ||||
| Downside SD | 0.034 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 54.000 | ||||
| Mean of predictor | 0.289 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.246 | ||||
| SD of criterion | 0.052 | ||||
| Covariance | 0.000 | ||||
| r | 0.006 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.026 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 52.000 | ||||
| t(b) | 0.042 | ||||
| p(b) | 0.483 | ||||
| t(a) | -0.992 | ||||
| p(a) | 0.837 | ||||
| Lowerbound of 95% confidence interval for beta | -0.058 | ||||
| Upperbound of 95% confidence interval for beta | 0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.079 | ||||
| Upperbound of 95% confidence interval for alpha | 0.027 | ||||
| Treynor index (mean / b) | -20.987 | ||||
| Jensen alpha (a) | -0.026 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 54.000 | ||||
| Minimum | 0.940 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.062 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.056 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.074 | ||||
| Mean of outliers high | 1.041 | ||||
| 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) | 1.290 | ||||
| VaR(95%) (regression method) | 0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.010 | ||||
| Quartile 1 | 0.023 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.048 | ||||
| Maximum | 0.061 | ||||
| Mean of quarter 1 | 0.010 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.061 | ||||
| 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 | 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) | 0.019 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.302 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.302 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.560 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.023 | ||||
| SD | 0.081 | ||||
| Sharpe ratio (Glass type estimate) | -0.282 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.282 | ||||
| df | 1198.000 | ||||
| t | -0.604 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.199 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.634 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.199 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.634 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.446 | ||||
| Upside Potential Ratio | 2.454 | ||||
| Upside part of mean | 0.126 | ||||
| Downside part of mean | -0.149 | ||||
| Upside SD | 0.063 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 1164.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1199.000 | ||||
| Mean of predictor | 0.360 | ||||
| Mean of criterion | -0.023 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.081 | ||||
| Covariance | -0.000 | ||||
| r | -0.003 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1197.000 | ||||
| t(b) | -0.095 | ||||
| p(b) | 0.502 | ||||
| t(a) | -0.594 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.097 | ||||
| Upperbound of 95% confidence interval for alpha | 0.052 | ||||
| Treynor index (mean / b) | 27.340 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.080 | ||||
| Sharpe ratio (Glass type estimate) | -0.325 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.324 | ||||
| df | 1198.000 | ||||
| t | -0.694 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.241 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.592 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.241 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.592 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.502 | ||||
| Upside Potential Ratio | 2.382 | ||||
| Upside part of mean | 0.124 | ||||
| Downside part of mean | -0.150 | ||||
| Upside SD | 0.061 | ||||
| Downside SD | 0.052 | ||||
| N nonnegative terms | 35.000 | ||||
| N negative terms | 1164.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1199.000 | ||||
| Mean of predictor | 0.324 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.268 | ||||
| SD of criterion | 0.080 | ||||
| Covariance | -0.000 | ||||
| r | -0.002 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.026 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1197.000 | ||||
| t(b) | -0.063 | ||||
| p(b) | 0.501 | ||||
| t(a) | -0.687 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | -0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.048 | ||||
| Treynor index (mean / b) | 47.567 | ||||
| Jensen alpha (a) | -0.026 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1199.000 | ||||
| Minimum | 0.956 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.066 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 29.000 | ||||
| Percentage of outliers low | 0.024 | ||||
| Mean of outliers low | 0.983 | ||||
| Number of outliers high | 36.000 | ||||
| Percentage of outliers high | 0.030 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -8.529 | ||||
| VaR(95%) (moments method) | -1.959 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.552 | ||||
| VaR(95%) (regression method) | -0.017 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.035 | ||||
| Quartile 3 | 0.060 | ||||
| Maximum | 0.158 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.052 | ||||
| Mean of quarter 4 | 0.112 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.158 | ||||
| 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) | 0.019 | ||||
| Compounded annual return (geometric extrapolation) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.114 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.161 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.753 | ||||
| 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 | 1.020 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.462 | ||||
| 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 | 0.912 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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) | -8734948273721003.000 | ||||
| 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) | 479671815440661972184422122782720.000 | ||||
| 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 | ||||