Advanced Statistics: 7months2profit
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.062 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -1.043 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.032 | ||||
| df | 72.000 | ||||
| t | -2.572 | ||||
| p | 0.994 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.852 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.227 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.844 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.219 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.226 | ||||
| Upside Potential Ratio | 0.284 | ||||
| Upside part of mean | 0.014 | ||||
| Downside part of mean | -0.077 | ||||
| Upside SD | 0.035 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.279 | ||||
| Mean of criterion | -0.062 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.003 | ||||
| r | 0.135 | ||||
| b (slope, estimate of beta) | 0.025 | ||||
| a (intercept, estimate of alpha) | -0.069 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 71.000 | ||||
| t(b) | 1.147 | ||||
| p(b) | 0.128 | ||||
| t(a) | -2.781 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.069 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | -0.020 | ||||
| Treynor index (mean / b) | -2.461 | ||||
| Jensen alpha (a) | -0.069 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.064 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -1.062 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.051 | ||||
| df | 72.000 | ||||
| t | -2.620 | ||||
| p | 0.995 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.872 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.246 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.864 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.238 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.216 | ||||
| Upside Potential Ratio | 0.261 | ||||
| Upside part of mean | 0.014 | ||||
| Downside part of mean | -0.078 | ||||
| Upside SD | 0.034 | ||||
| Downside SD | 0.053 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 72.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 73.000 | ||||
| Mean of predictor | 0.226 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.317 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.003 | ||||
| r | 0.136 | ||||
| b (slope, estimate of beta) | 0.026 | ||||
| a (intercept, estimate of alpha) | -0.070 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 71.000 | ||||
| t(b) | 1.153 | ||||
| p(b) | 0.126 | ||||
| t(a) | -2.806 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | -0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.070 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | -0.020 | ||||
| Treynor index (mean / b) | -2.482 | ||||
| Jensen alpha (a) | -0.070 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.033 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.042 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 73.000 | ||||
| Minimum | 0.907 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.091 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.082 | ||||
| Mean of outliers low | 0.966 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.015 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -47.441 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | -0.491 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.174 | ||||
| Quartile 1 | 0.174 | ||||
| Median | 0.174 | ||||
| Quartile 3 | 0.174 | ||||
| Maximum | 0.174 | ||||
| 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) | -0.019 | ||||
| Compounded annual return (geometric extrapolation) | -0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.114 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.489 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.003 | ||||
| SD | 0.353 | ||||
| Sharpe ratio (Glass type estimate) | -0.007 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.007 | ||||
| df | 1593.000 | ||||
| t | -0.018 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.802 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.787 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.802 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.787 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.011 | ||||
| Upside Potential Ratio | 2.345 | ||||
| Upside part of mean | 0.537 | ||||
| Downside part of mean | -0.540 | ||||
| Upside SD | 0.269 | ||||
| Downside SD | 0.229 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 1542.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1594.000 | ||||
| Mean of predictor | 0.379 | ||||
| Mean of criterion | -0.003 | ||||
| SD of predictor | 0.557 | ||||
| SD of criterion | 0.353 | ||||
| Covariance | 0.063 | ||||
| r | 0.318 | ||||
| b (slope, estimate of beta) | 0.202 | ||||
| a (intercept, estimate of alpha) | -0.079 | ||||
| Mean Square Error | 0.112 | ||||
| DF error | 1592.000 | ||||
| t(b) | 13.404 | ||||
| p(b) | 0.341 | ||||
| t(a) | -0.581 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.172 | ||||
| Upperbound of 95% confidence interval for beta | 0.232 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.346 | ||||
| Upperbound of 95% confidence interval for alpha | 0.188 | ||||
| Treynor index (mean / b) | -0.013 | ||||
| Jensen alpha (a) | -0.079 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.064 | ||||
| SD | 0.350 | ||||
| Sharpe ratio (Glass type estimate) | -0.183 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.183 | ||||
| df | 1593.000 | ||||
| t | -0.451 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.977 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.612 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.977 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.612 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.259 | ||||
| Upside Potential Ratio | 2.048 | ||||
| Upside part of mean | 0.505 | ||||
| Downside part of mean | -0.569 | ||||
| Upside SD | 0.248 | ||||
| Downside SD | 0.246 | ||||
| N nonnegative terms | 52.000 | ||||
| N negative terms | 1542.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1594.000 | ||||
| Mean of predictor | 0.226 | ||||
| Mean of criterion | -0.064 | ||||
| SD of predictor | 0.551 | ||||
| SD of criterion | 0.350 | ||||
| Covariance | 0.062 | ||||
| r | 0.323 | ||||
| b (slope, estimate of beta) | 0.205 | ||||
| a (intercept, estimate of alpha) | -0.110 | ||||
| Mean Square Error | 0.110 | ||||
| DF error | 1592.000 | ||||
| t(b) | 13.614 | ||||
| p(b) | 0.339 | ||||
| t(a) | -0.822 | ||||
| p(a) | 0.510 | ||||
| Lowerbound of 95% confidence interval for beta | 0.176 | ||||
| Upperbound of 95% confidence interval for beta | 0.235 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.374 | ||||
| Upperbound of 95% confidence interval for alpha | 0.153 | ||||
| Treynor index (mean / b) | -0.312 | ||||
| Jensen alpha (a) | -0.110 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.044 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1594.000 | ||||
| Minimum | 0.823 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.273 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 93.000 | ||||
| Percentage of outliers low | 0.058 | ||||
| Mean of outliers low | 0.967 | ||||
| Number of outliers high | 85.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.039 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -3.525 | ||||
| VaR(95%) (moments method) | -0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.204 | ||||
| VaR(95%) (regression method) | -0.012 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.181 | ||||
| Quartile 1 | 0.191 | ||||
| Median | 0.202 | ||||
| Quartile 3 | 0.225 | ||||
| Maximum | 0.247 | ||||
| Mean of quarter 1 | 0.181 | ||||
| Mean of quarter 2 | 0.202 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.247 | ||||
| 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) | -0.019 | ||||
| Compounded annual return (geometric extrapolation) | -0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.080 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.080 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.450 | ||||
| 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 | 1.048 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.499 | ||||
| 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 | 0.921 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.503 | ||||
| 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) | -8743560943805765.000 | ||||
| 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) | -122352209001556876654539257675776.000 | ||||
| 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 | ||||