Advanced Statistics: The Profit Pipeline
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 | -0.107 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -1.795 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.750 | ||||
| df | 30.000 | ||||
| t | -2.885 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.083 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.482 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.047 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.453 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.615 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.107 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.066 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.588 | ||||
| Mean of criterion | -0.107 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.003 | ||||
| r | 0.148 | ||||
| b (slope, estimate of beta) | 0.031 | ||||
| a (intercept, estimate of alpha) | -0.125 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 29.000 | ||||
| t(b) | 0.803 | ||||
| p(b) | 0.214 | ||||
| t(a) | -2.872 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.214 | ||||
| Upperbound of 95% confidence interval for alpha | -0.036 | ||||
| Treynor index (mean / b) | -3.494 | ||||
| Jensen alpha (a) | -0.125 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.109 | ||||
| SD | 0.062 | ||||
| Sharpe ratio (Glass type estimate) | -1.766 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.722 | ||||
| df | 30.000 | ||||
| t | -2.839 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.052 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.455 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.017 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.427 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.594 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.068 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 31.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.536 | ||||
| Mean of criterion | -0.109 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.062 | ||||
| Covariance | 0.002 | ||||
| r | 0.140 | ||||
| b (slope, estimate of beta) | 0.032 | ||||
| a (intercept, estimate of alpha) | -0.126 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 29.000 | ||||
| t(b) | 0.759 | ||||
| p(b) | 0.227 | ||||
| t(a) | -2.822 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.053 | ||||
| Upperbound of 95% confidence interval for beta | 0.117 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.217 | ||||
| Upperbound of 95% confidence interval for alpha | -0.035 | ||||
| Treynor index (mean / b) | -3.457 | ||||
| Jensen alpha (a) | -0.126 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.038 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.031 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.923 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.980 | ||||
| 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 | 3.000 | ||||
| Percentage of outliers low | 0.097 | ||||
| Mean of outliers low | 0.946 | ||||
| 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) | -1.203 | ||||
| VaR(95%) (regression method) | 0.064 | ||||
| Expected Shortfall (regression method) | 0.082 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.155 | ||||
| Quartile 1 | 0.155 | ||||
| Median | 0.155 | ||||
| Quartile 3 | 0.155 | ||||
| Maximum | 0.155 | ||||
| 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) | -0.060 | ||||
| Compounded annual return (geometric extrapolation) | -0.063 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.407 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.406 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.105 | ||||
| SD | 0.065 | ||||
| Sharpe ratio (Glass type estimate) | -1.609 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.608 | ||||
| df | 693.000 | ||||
| t | -2.619 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.816 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.402 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.815 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.400 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.992 | ||||
| Upside Potential Ratio | 1.333 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.176 | ||||
| Upside SD | 0.039 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 676.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 694.000 | ||||
| Mean of predictor | 0.621 | ||||
| Mean of criterion | -0.105 | ||||
| SD of predictor | 0.365 | ||||
| SD of criterion | 0.065 | ||||
| Covariance | 0.000 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.106 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 692.000 | ||||
| t(b) | 0.141 | ||||
| p(b) | 0.444 | ||||
| t(a) | -2.618 | ||||
| p(a) | 0.995 | ||||
| Lowerbound of 95% confidence interval for beta | -0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | -0.026 | ||||
| Treynor index (mean / b) | -109.491 | ||||
| Jensen alpha (a) | -0.106 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.107 | ||||
| SD | 0.066 | ||||
| Sharpe ratio (Glass type estimate) | -1.636 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.634 | ||||
| df | 693.000 | ||||
| t | -2.662 | ||||
| p | 0.996 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.842 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.428 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.841 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.426 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.004 | ||||
| Upside Potential Ratio | 1.301 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.177 | ||||
| Upside SD | 0.038 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 676.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 694.000 | ||||
| Mean of predictor | 0.554 | ||||
| Mean of criterion | -0.107 | ||||
| SD of predictor | 0.362 | ||||
| SD of criterion | 0.066 | ||||
| Covariance | 0.000 | ||||
| r | 0.005 | ||||
| b (slope, estimate of beta) | 0.001 | ||||
| a (intercept, estimate of alpha) | -0.108 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 692.000 | ||||
| t(b) | 0.130 | ||||
| p(b) | 0.448 | ||||
| t(a) | -2.661 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | -0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.014 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.188 | ||||
| Upperbound of 95% confidence interval for alpha | -0.028 | ||||
| Treynor index (mean / b) | -119.275 | ||||
| Jensen alpha (a) | -0.108 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| 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 | 694.000 | ||||
| Minimum | 0.956 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.042 | ||||
| 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 | 30.000 | ||||
| Percentage of outliers low | 0.043 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 19.000 | ||||
| Percentage of outliers high | 0.027 | ||||
| Mean of outliers high | 1.010 | ||||
| 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) | 0.012 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.155 | ||||
| Quartile 1 | 0.155 | ||||
| Median | 0.155 | ||||
| Quartile 3 | 0.155 | ||||
| Maximum | 0.155 | ||||
| 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) | -0.058 | ||||
| Compounded annual return (geometric extrapolation) | -0.061 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.397 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -7.029 | ||||
| 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 | 0.847 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| 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 | 0.744 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| 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) | -8754648264555237.000 | ||||
| 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) | 175760898557837839179808996589568.000 | ||||
| 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 | ||||