Advanced Statistics: Price Action
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 | -0.006 | ||||
| SD | 0.058 | ||||
| Sharpe ratio (Glass type estimate) | -0.109 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.107 | ||||
| df | 60.000 | ||||
| t | -0.245 | ||||
| p | 0.596 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.978 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.761 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.977 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.762 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.192 | ||||
| Upside Potential Ratio | 1.495 | ||||
| Upside part of mean | 0.049 | ||||
| Downside part of mean | -0.055 | ||||
| Upside SD | 0.047 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.343 | ||||
| Mean of criterion | -0.006 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.058 | ||||
| Covariance | 0.001 | ||||
| r | 0.072 | ||||
| b (slope, estimate of beta) | 0.018 | ||||
| a (intercept, estimate of alpha) | -0.012 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.553 | ||||
| p(b) | 0.291 | ||||
| t(a) | -0.441 | ||||
| p(a) | 0.669 | ||||
| Lowerbound of 95% confidence interval for beta | -0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.069 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | -0.355 | ||||
| Jensen alpha (a) | -0.012 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.008 | ||||
| SD | 0.057 | ||||
| Sharpe ratio (Glass type estimate) | -0.138 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.137 | ||||
| df | 60.000 | ||||
| t | -0.312 | ||||
| p | 0.622 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.008 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.732 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.006 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.733 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.236 | ||||
| Upside Potential Ratio | 1.429 | ||||
| Upside part of mean | 0.048 | ||||
| Downside part of mean | -0.056 | ||||
| Upside SD | 0.046 | ||||
| Downside SD | 0.033 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.312 | ||||
| Mean of criterion | -0.008 | ||||
| SD of predictor | 0.221 | ||||
| SD of criterion | 0.057 | ||||
| Covariance | 0.001 | ||||
| r | 0.080 | ||||
| b (slope, estimate of beta) | 0.021 | ||||
| a (intercept, estimate of alpha) | -0.014 | ||||
| Mean Square Error | 0.003 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.617 | ||||
| p(b) | 0.270 | ||||
| t(a) | -0.522 | ||||
| p(a) | 0.698 | ||||
| Lowerbound of 95% confidence interval for beta | -0.046 | ||||
| Upperbound of 95% confidence interval for beta | 0.088 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.069 | ||||
| Upperbound of 95% confidence interval for alpha | 0.041 | ||||
| Treynor index (mean / b) | -0.383 | ||||
| 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%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.948 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.089 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.148 | ||||
| Mean of outliers high | 1.031 | ||||
| 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) | 0.981 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.473 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.034 | ||||
| Quartile 3 | 0.050 | ||||
| Maximum | 0.067 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.067 | ||||
| Inter Quartile Range | 0.033 | ||||
| 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) | 0.040 | ||||
| Compounded annual return (geometric extrapolation) | 0.037 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.551 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.551 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.081 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.090 | ||||
| Sharpe ratio (Glass type estimate) | -0.044 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.044 | ||||
| df | 1332.000 | ||||
| t | -0.099 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.913 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.825 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.913 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.825 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.066 | ||||
| Upside Potential Ratio | 3.650 | ||||
| Upside part of mean | 0.218 | ||||
| Downside part of mean | -0.222 | ||||
| Upside SD | 0.067 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 112.000 | ||||
| N negative terms | 1221.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1333.000 | ||||
| Mean of predictor | 0.379 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.090 | ||||
| Covariance | 0.003 | ||||
| r | 0.098 | ||||
| b (slope, estimate of beta) | 0.030 | ||||
| a (intercept, estimate of alpha) | -0.015 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 1331.000 | ||||
| t(b) | 3.583 | ||||
| p(b) | 0.438 | ||||
| t(a) | -0.382 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.046 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | 0.063 | ||||
| Treynor index (mean / b) | -0.133 | ||||
| Jensen alpha (a) | -0.015 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.008 | ||||
| SD | 0.089 | ||||
| Sharpe ratio (Glass type estimate) | -0.089 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.089 | ||||
| df | 1332.000 | ||||
| t | -0.200 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.958 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.780 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.958 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.780 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.131 | ||||
| Upside Potential Ratio | 3.568 | ||||
| Upside part of mean | 0.216 | ||||
| Downside part of mean | -0.224 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 112.000 | ||||
| N negative terms | 1221.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1333.000 | ||||
| Mean of predictor | 0.335 | ||||
| Mean of criterion | -0.008 | ||||
| SD of predictor | 0.297 | ||||
| SD of criterion | 0.089 | ||||
| Covariance | 0.003 | ||||
| r | 0.097 | ||||
| b (slope, estimate of beta) | 0.029 | ||||
| a (intercept, estimate of alpha) | -0.018 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 1331.000 | ||||
| t(b) | 3.552 | ||||
| p(b) | 0.438 | ||||
| t(a) | -0.447 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 0.013 | ||||
| Upperbound of 95% confidence interval for beta | 0.045 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.095 | ||||
| Upperbound of 95% confidence interval for alpha | 0.060 | ||||
| Treynor index (mean / b) | -0.272 | ||||
| Jensen alpha (a) | -0.018 | ||||
| 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 | 0.006 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1333.000 | ||||
| Minimum | 0.958 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.048 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.003 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 85.000 | ||||
| Percentage of outliers low | 0.064 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 113.000 | ||||
| Percentage of outliers high | 0.085 | ||||
| Mean of outliers high | 1.010 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.598 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | -0.099 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 14.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.025 | ||||
| Quartile 3 | 0.051 | ||||
| Maximum | 0.073 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.017 | ||||
| Mean of quarter 3 | 0.033 | ||||
| Mean of quarter 4 | 0.063 | ||||
| Inter Quartile Range | 0.042 | ||||
| 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) | -1.173 | ||||
| VaR(95%) (moments method) | 0.069 | ||||
| Expected Shortfall (moments method) | 0.071 | ||||
| Extreme Value Index (regression method) | -0.328 | ||||
| VaR(95%) (regression method) | 0.072 | ||||
| Expected Shortfall (regression method) | 0.078 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.040 | ||||
| Compounded annual return (geometric extrapolation) | 0.037 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.503 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.581 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.235 | ||||
| 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 | 1.098 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.507 | ||||
| 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 | 0.968 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.510 | ||||
| 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) | -8739395158544910.000 | ||||
| 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) | -94262966976249458212515730161664.000 | ||||
| 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 | ||||