Advanced Statistics: Piston
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 | -0.000 | ||||
| SD | 0.096 | ||||
| Sharpe ratio (Glass type estimate) | -0.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.000 | ||||
| df | 46.000 | ||||
| t | -0.000 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.990 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.990 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.990 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.990 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.000 | ||||
| Upside Potential Ratio | 1.525 | ||||
| Upside part of mean | 0.085 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.077 | ||||
| Downside SD | 0.056 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.452 | ||||
| Mean of criterion | -0.000 | ||||
| SD of predictor | 0.304 | ||||
| SD of criterion | 0.096 | ||||
| Covariance | 0.001 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.016 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 45.000 | ||||
| t(b) | 0.333 | ||||
| p(b) | 0.370 | ||||
| t(a) | -0.133 | ||||
| p(a) | 0.553 | ||||
| Lowerbound of 95% confidence interval for beta | -0.079 | ||||
| Upperbound of 95% confidence interval for beta | 0.110 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.114 | ||||
| Upperbound of 95% confidence interval for alpha | 0.100 | ||||
| Treynor index (mean / b) | -0.001 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.094 | ||||
| Sharpe ratio (Glass type estimate) | -0.047 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.046 | ||||
| df | 46.000 | ||||
| t | -0.092 | ||||
| p | 0.537 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.037 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.944 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.036 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.945 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.076 | ||||
| Upside Potential Ratio | 1.433 | ||||
| Upside part of mean | 0.082 | ||||
| Downside part of mean | -0.087 | ||||
| Upside SD | 0.073 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 47.000 | ||||
| Mean of predictor | 0.404 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.272 | ||||
| SD of criterion | 0.094 | ||||
| Covariance | 0.002 | ||||
| r | 0.068 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 45.000 | ||||
| t(b) | 0.457 | ||||
| p(b) | 0.325 | ||||
| t(a) | -0.266 | ||||
| p(a) | 0.604 | ||||
| Lowerbound of 95% confidence interval for beta | -0.080 | ||||
| Upperbound of 95% confidence interval for beta | 0.127 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | 0.091 | ||||
| Treynor index (mean / b) | -0.186 | ||||
| Jensen alpha (a) | -0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 47.000 | ||||
| Minimum | 0.938 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.105 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.031 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.128 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.213 | ||||
| Mean of outliers high | 1.037 | ||||
| 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) | -1.109 | ||||
| VaR(95%) (regression method) | 0.027 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.025 | ||||
| Median | 0.048 | ||||
| Quartile 3 | 0.071 | ||||
| Maximum | 0.094 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.094 | ||||
| Inter Quartile Range | 0.046 | ||||
| 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) | 0.043 | ||||
| Compounded annual return (geometric extrapolation) | 0.040 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.432 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.432 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.737 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.001 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | -0.007 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.007 | ||||
| df | 1027.000 | ||||
| t | -0.015 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.997 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.982 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.997 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.982 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.011 | ||||
| Upside Potential Ratio | 4.434 | ||||
| Upside part of mean | 0.252 | ||||
| Downside part of mean | -0.253 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 126.000 | ||||
| N negative terms | 902.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1028.000 | ||||
| Mean of predictor | 0.459 | ||||
| Mean of criterion | -0.001 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | 0.001 | ||||
| r | 0.048 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 1026.000 | ||||
| t(b) | 1.543 | ||||
| p(b) | 0.476 | ||||
| t(a) | -0.162 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.094 | ||||
| Upperbound of 95% confidence interval for alpha | 0.080 | ||||
| Treynor index (mean / b) | -0.046 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | -0.051 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.051 | ||||
| df | 1027.000 | ||||
| t | -0.101 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.041 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.938 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.041 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.938 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.077 | ||||
| Upside Potential Ratio | 4.342 | ||||
| Upside part of mean | 0.250 | ||||
| Downside part of mean | -0.255 | ||||
| Upside SD | 0.065 | ||||
| Downside SD | 0.058 | ||||
| N nonnegative terms | 126.000 | ||||
| N negative terms | 902.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1028.000 | ||||
| Mean of predictor | 0.414 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | 0.001 | ||||
| r | 0.048 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.010 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 1026.000 | ||||
| t(b) | 1.542 | ||||
| p(b) | 0.476 | ||||
| t(a) | -0.232 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.097 | ||||
| Upperbound of 95% confidence interval for alpha | 0.076 | ||||
| Treynor index (mean / b) | -0.319 | ||||
| Jensen alpha (a) | -0.010 | ||||
| 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%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1028.000 | ||||
| Minimum | 0.957 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.060 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.004 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 126.000 | ||||
| Percentage of outliers low | 0.123 | ||||
| Mean of outliers low | 0.993 | ||||
| Number of outliers high | 128.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 1.008 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.078 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.004 | ||||
| Extreme Value Index (regression method) | 0.137 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.018 | ||||
| Median | 0.028 | ||||
| Quartile 3 | 0.033 | ||||
| Maximum | 0.124 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.024 | ||||
| Mean of quarter 3 | 0.032 | ||||
| Mean of quarter 4 | 0.079 | ||||
| Inter Quartile Range | 0.015 | ||||
| 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 | 0.124 | ||||
| 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) | 0.043 | ||||
| Compounded annual return (geometric extrapolation) | 0.040 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.325 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.511 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.646 | ||||
| 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 | 1.023 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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 | 0.911 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.471 | ||||
| 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) | -8737343857939799.000 | ||||
| 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) | 92187662800871547817645349797888.000 | ||||
| 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 | ||||