Advanced Statistics: Trending Profits
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 | -0.059 | ||||
| SD | 0.086 | ||||
| Sharpe ratio (Glass type estimate) | -0.678 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.667 | ||||
| df | 47.000 | ||||
| t | -1.357 | ||||
| p | 0.909 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.664 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.315 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.657 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.322 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.775 | ||||
| Upside Potential Ratio | 0.403 | ||||
| Upside part of mean | 0.031 | ||||
| Downside part of mean | -0.089 | ||||
| Upside SD | 0.043 | ||||
| Downside SD | 0.076 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.447 | ||||
| Mean of criterion | -0.059 | ||||
| SD of predictor | 0.266 | ||||
| SD of criterion | 0.086 | ||||
| Covariance | -0.001 | ||||
| r | -0.039 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 46.000 | ||||
| t(b) | -0.264 | ||||
| p(b) | 0.604 | ||||
| t(a) | -1.090 | ||||
| p(a) | 0.859 | ||||
| Lowerbound of 95% confidence interval for beta | -0.109 | ||||
| Upperbound of 95% confidence interval for beta | 0.084 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.151 | ||||
| Upperbound of 95% confidence interval for alpha | 0.045 | ||||
| Treynor index (mean / b) | 4.637 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.062 | ||||
| SD | 0.090 | ||||
| Sharpe ratio (Glass type estimate) | -0.692 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.680 | ||||
| df | 47.000 | ||||
| t | -1.383 | ||||
| p | 0.913 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.678 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.302 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.670 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.309 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.771 | ||||
| Upside Potential Ratio | 0.365 | ||||
| Upside part of mean | 0.030 | ||||
| Downside part of mean | -0.092 | ||||
| Upside SD | 0.042 | ||||
| Downside SD | 0.081 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 46.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 48.000 | ||||
| Mean of predictor | 0.405 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.258 | ||||
| SD of criterion | 0.090 | ||||
| Covariance | -0.001 | ||||
| r | -0.038 | ||||
| b (slope, estimate of beta) | -0.013 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 46.000 | ||||
| t(b) | -0.255 | ||||
| p(b) | 0.600 | ||||
| t(a) | -1.139 | ||||
| p(a) | 0.870 | ||||
| Lowerbound of 95% confidence interval for beta | -0.117 | ||||
| Upperbound of 95% confidence interval for beta | 0.090 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.158 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | 4.756 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.047 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.860 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.068 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.104 | ||||
| Mean of outliers low | 0.962 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.083 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.979 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 2.127 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.181 | ||||
| Quartile 1 | 0.181 | ||||
| Median | 0.181 | ||||
| Quartile 3 | 0.181 | ||||
| Maximum | 0.181 | ||||
| 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 | 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) | -0.018 | ||||
| Compounded annual return (geometric extrapolation) | -0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.100 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.318 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | -0.671 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.670 | ||||
| df | 1063.000 | ||||
| t | -1.351 | ||||
| p | 0.526 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.643 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.303 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.643 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.303 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.049 | ||||
| Upside Potential Ratio | 1.736 | ||||
| Upside part of mean | 0.097 | ||||
| Downside part of mean | -0.155 | ||||
| Upside SD | 0.067 | ||||
| Downside SD | 0.056 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 1035.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1064.000 | ||||
| Mean of predictor | 0.494 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.352 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 1062.000 | ||||
| t(b) | -0.114 | ||||
| p(b) | 0.502 | ||||
| t(a) | -1.336 | ||||
| p(a) | 0.520 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.143 | ||||
| Upperbound of 95% confidence interval for alpha | 0.027 | ||||
| Treynor index (mean / b) | 67.265 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.062 | ||||
| SD | 0.086 | ||||
| Sharpe ratio (Glass type estimate) | -0.720 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.720 | ||||
| df | 1063.000 | ||||
| t | -1.452 | ||||
| p | 0.528 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.693 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.253 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.693 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.253 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.094 | ||||
| Upside Potential Ratio | 1.663 | ||||
| Upside part of mean | 0.094 | ||||
| Downside part of mean | -0.156 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 29.000 | ||||
| N negative terms | 1035.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1064.000 | ||||
| Mean of predictor | 0.433 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.345 | ||||
| SD of criterion | 0.086 | ||||
| Covariance | -0.000 | ||||
| r | -0.004 | ||||
| b (slope, estimate of beta) | -0.001 | ||||
| a (intercept, estimate of alpha) | -0.062 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 1062.000 | ||||
| t(b) | -0.116 | ||||
| p(b) | 0.502 | ||||
| t(a) | -1.438 | ||||
| p(a) | 0.522 | ||||
| Lowerbound of 95% confidence interval for beta | -0.016 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.146 | ||||
| Upperbound of 95% confidence interval for alpha | 0.023 | ||||
| Treynor index (mean / b) | 69.792 | ||||
| Jensen alpha (a) | -0.062 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1064.000 | ||||
| Minimum | 0.943 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.088 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 45.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.990 | ||||
| Number of outliers high | 29.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.530 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.234 | ||||
| Quartile 1 | 0.234 | ||||
| Median | 0.234 | ||||
| Quartile 3 | 0.234 | ||||
| Maximum | 0.234 | ||||
| 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 | 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) | -0.017 | ||||
| Compounded annual return (geometric extrapolation) | -0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.077 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.606 | ||||
| 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 | 1.017 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.456 | ||||
| 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 | 0.913 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.455 | ||||
| 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) | -8732641674508891.000 | ||||
| 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) | 87274103893816440201269968109568.000 | ||||
| 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 | ||||