Advanced Statistics: Online Investing AI M6
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 | -0.069 | ||||
| SD | 0.043 | ||||
| Sharpe ratio (Glass type estimate) | -1.604 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.585 | ||||
| df | 64.000 | ||||
| t | -3.732 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.484 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.711 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.470 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.699 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.483 | ||||
| Upside Potential Ratio | 0.068 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.072 | ||||
| Upside SD | 0.007 | ||||
| Downside SD | 0.047 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.272 | ||||
| Mean of criterion | -0.069 | ||||
| SD of predictor | 0.327 | ||||
| SD of criterion | 0.043 | ||||
| Covariance | 0.003 | ||||
| r | 0.225 | ||||
| b (slope, estimate of beta) | 0.030 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 63.000 | ||||
| t(b) | 1.834 | ||||
| p(b) | 0.036 | ||||
| t(a) | -4.126 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.062 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.115 | ||||
| Upperbound of 95% confidence interval for alpha | -0.040 | ||||
| Treynor index (mean / b) | -2.327 | ||||
| Jensen alpha (a) | -0.077 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.070 | ||||
| SD | 0.045 | ||||
| Sharpe ratio (Glass type estimate) | -1.573 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.554 | ||||
| df | 64.000 | ||||
| t | -3.660 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.452 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.682 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.438 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.670 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.457 | ||||
| Upside Potential Ratio | 0.065 | ||||
| Upside part of mean | 0.003 | ||||
| Downside part of mean | -0.073 | ||||
| Upside SD | 0.007 | ||||
| Downside SD | 0.048 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 64.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.218 | ||||
| Mean of criterion | -0.070 | ||||
| SD of predictor | 0.319 | ||||
| SD of criterion | 0.045 | ||||
| Covariance | 0.003 | ||||
| r | 0.230 | ||||
| b (slope, estimate of beta) | 0.032 | ||||
| a (intercept, estimate of alpha) | -0.077 | ||||
| Mean Square Error | 0.002 | ||||
| DF error | 63.000 | ||||
| t(b) | 1.877 | ||||
| p(b) | 0.033 | ||||
| t(a) | -4.026 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.066 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.115 | ||||
| Upperbound of 95% confidence interval for alpha | -0.039 | ||||
| Treynor index (mean / b) | -2.183 | ||||
| Jensen alpha (a) | -0.077 | ||||
| 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 | 0.032 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 65.000 | ||||
| Minimum | 0.927 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.021 | ||||
| Mean of quarter 1 | 0.991 | ||||
| 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 | 5.000 | ||||
| Percentage of outliers low | 0.077 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -23.162 | ||||
| VaR(95%) (moments method) | -0.015 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -1.729 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | 0.063 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.132 | ||||
| Quartile 1 | 0.132 | ||||
| Median | 0.132 | ||||
| Quartile 3 | 0.132 | ||||
| Maximum | 0.132 | ||||
| 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) | -0.024 | ||||
| Compounded annual return (geometric extrapolation) | -0.026 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.195 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.807 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.057 | ||||
| SD | 0.160 | ||||
| Sharpe ratio (Glass type estimate) | -0.357 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.357 | ||||
| df | 1429.000 | ||||
| t | -0.835 | ||||
| p | 0.514 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.196 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.482 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.196 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.482 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.527 | ||||
| Upside Potential Ratio | 1.912 | ||||
| Upside part of mean | 0.207 | ||||
| Downside part of mean | -0.264 | ||||
| Upside SD | 0.118 | ||||
| Downside SD | 0.108 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 1371.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1430.000 | ||||
| Mean of predictor | 0.400 | ||||
| Mean of criterion | -0.057 | ||||
| SD of predictor | 0.526 | ||||
| SD of criterion | 0.160 | ||||
| Covariance | 0.025 | ||||
| r | 0.300 | ||||
| b (slope, estimate of beta) | 0.091 | ||||
| a (intercept, estimate of alpha) | -0.094 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1428.000 | ||||
| t(b) | 11.881 | ||||
| p(b) | 0.350 | ||||
| t(a) | -1.431 | ||||
| p(a) | 0.519 | ||||
| Lowerbound of 95% confidence interval for beta | 0.076 | ||||
| Upperbound of 95% confidence interval for beta | 0.106 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.222 | ||||
| Upperbound of 95% confidence interval for alpha | 0.035 | ||||
| Treynor index (mean / b) | -0.626 | ||||
| Jensen alpha (a) | -0.094 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.070 | ||||
| SD | 0.159 | ||||
| Sharpe ratio (Glass type estimate) | -0.439 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.439 | ||||
| df | 1429.000 | ||||
| t | -1.026 | ||||
| p | 0.517 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.278 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.400 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.278 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.400 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.621 | ||||
| Upside Potential Ratio | 1.786 | ||||
| Upside part of mean | 0.201 | ||||
| Downside part of mean | -0.271 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.112 | ||||
| N nonnegative terms | 59.000 | ||||
| N negative terms | 1371.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1430.000 | ||||
| Mean of predictor | 0.261 | ||||
| Mean of criterion | -0.070 | ||||
| SD of predictor | 0.526 | ||||
| SD of criterion | 0.159 | ||||
| Covariance | 0.025 | ||||
| r | 0.298 | ||||
| b (slope, estimate of beta) | 0.090 | ||||
| a (intercept, estimate of alpha) | -0.093 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 1428.000 | ||||
| t(b) | 11.777 | ||||
| p(b) | 0.351 | ||||
| t(a) | -1.435 | ||||
| p(a) | 0.519 | ||||
| Lowerbound of 95% confidence interval for beta | 0.075 | ||||
| Upperbound of 95% confidence interval for beta | 0.105 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.221 | ||||
| Upperbound of 95% confidence interval for alpha | 0.034 | ||||
| Treynor index (mean / b) | -0.776 | ||||
| Jensen alpha (a) | -0.093 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1430.000 | ||||
| Minimum | 0.892 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.152 | ||||
| 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 | 86.000 | ||||
| Percentage of outliers low | 0.060 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 70.000 | ||||
| Percentage of outliers high | 0.049 | ||||
| Mean of outliers high | 1.016 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.047 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.598 | ||||
| VaR(95%) (regression method) | -0.001 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.042 | ||||
| Quartile 1 | 0.068 | ||||
| Median | 0.094 | ||||
| Quartile 3 | 0.120 | ||||
| Maximum | 0.146 | ||||
| Mean of quarter 1 | 0.042 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.146 | ||||
| Inter Quartile Range | 0.052 | ||||
| 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) | -0.024 | ||||
| Compounded annual return (geometric extrapolation) | -0.025 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.174 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.174 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.254 | ||||
| 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 | 1.772 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.657 | ||||
| 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 | 1.553 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.657 | ||||
| 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) | -8706652154478112.000 | ||||
| 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) | -265025440816047616298751633653760.000 | ||||
| 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 | ||||