Advanced Statistics: VIVALDI Seasonal Trends
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 | -0.032 | ||||
| SD | 0.154 | ||||
| Sharpe ratio (Glass type estimate) | -0.211 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.209 | ||||
| df | 95.000 | ||||
| t | -0.596 | ||||
| p | 0.724 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.904 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.483 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.903 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.484 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.429 | ||||
| Upside Potential Ratio | 0.927 | ||||
| Upside part of mean | 0.070 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.133 | ||||
| Downside SD | 0.076 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.121 | ||||
| Mean of criterion | -0.032 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.154 | ||||
| Covariance | 0.005 | ||||
| r | 0.136 | ||||
| b (slope, estimate of beta) | 0.087 | ||||
| a (intercept, estimate of alpha) | -0.043 | ||||
| Mean Square Error | 0.023 | ||||
| DF error | 94.000 | ||||
| t(b) | 1.336 | ||||
| p(b) | 0.092 | ||||
| t(a) | -0.784 | ||||
| p(a) | 0.783 | ||||
| Lowerbound of 95% confidence interval for beta | -0.042 | ||||
| Upperbound of 95% confidence interval for beta | 0.215 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.152 | ||||
| Upperbound of 95% confidence interval for alpha | 0.066 | ||||
| Treynor index (mean / b) | -0.375 | ||||
| Jensen alpha (a) | -0.043 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.141 | ||||
| Sharpe ratio (Glass type estimate) | -0.303 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.300 | ||||
| df | 95.000 | ||||
| t | -0.856 | ||||
| p | 0.803 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.996 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.392 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.995 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.394 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.531 | ||||
| Upside Potential Ratio | 0.777 | ||||
| Upside part of mean | 0.062 | ||||
| Downside part of mean | -0.105 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.080 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 91.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 96.000 | ||||
| Mean of predictor | 0.091 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.243 | ||||
| SD of criterion | 0.141 | ||||
| Covariance | 0.006 | ||||
| r | 0.185 | ||||
| b (slope, estimate of beta) | 0.108 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 94.000 | ||||
| t(b) | 1.829 | ||||
| p(b) | 0.035 | ||||
| t(a) | -1.060 | ||||
| p(a) | 0.854 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.225 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.151 | ||||
| Upperbound of 95% confidence interval for alpha | 0.046 | ||||
| Treynor index (mean / b) | -0.396 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.084 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 96.000 | ||||
| Minimum | 0.838 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.353 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 16.000 | ||||
| Percentage of outliers low | 0.167 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.064 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -45.285 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.405 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.178 | ||||
| Quartile 1 | 0.198 | ||||
| Median | 0.217 | ||||
| Quartile 3 | 0.237 | ||||
| Maximum | 0.256 | ||||
| Mean of quarter 1 | 0.178 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.256 | ||||
| Inter Quartile Range | 0.039 | ||||
| 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) | 0.001 | ||||
| Compounded annual return (geometric extrapolation) | 0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.005 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.005 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.015 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.019 | ||||
| SD | 0.355 | ||||
| Sharpe ratio (Glass type estimate) | 0.054 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.054 | ||||
| df | 2114.000 | ||||
| t | 0.154 | ||||
| p | 0.439 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.636 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.744 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.636 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.744 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.083 | ||||
| Upside Potential Ratio | 2.131 | ||||
| Upside part of mean | 0.493 | ||||
| Downside part of mean | -0.473 | ||||
| Upside SD | 0.269 | ||||
| Downside SD | 0.231 | ||||
| N nonnegative terms | 170.000 | ||||
| N negative terms | 1945.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2115.000 | ||||
| Mean of predictor | 0.260 | ||||
| Mean of criterion | 0.019 | ||||
| SD of predictor | 0.606 | ||||
| SD of criterion | 0.355 | ||||
| Covariance | 0.062 | ||||
| r | 0.287 | ||||
| b (slope, estimate of beta) | 0.168 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.115 | ||||
| DF error | 2113.000 | ||||
| t(b) | 13.778 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.205 | ||||
| p(a) | 0.581 | ||||
| Lowerbound of 95% confidence interval for beta | 0.144 | ||||
| Upperbound of 95% confidence interval for beta | 0.192 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.259 | ||||
| Upperbound of 95% confidence interval for alpha | 0.210 | ||||
| Treynor index (mean / b) | 0.114 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.043 | ||||
| SD | 0.353 | ||||
| Sharpe ratio (Glass type estimate) | -0.121 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.121 | ||||
| df | 2114.000 | ||||
| t | -0.344 | ||||
| p | 0.635 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.811 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.569 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.811 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.569 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.163 | ||||
| Upside Potential Ratio | 1.766 | ||||
| Upside part of mean | 0.462 | ||||
| Downside part of mean | -0.505 | ||||
| Upside SD | 0.237 | ||||
| Downside SD | 0.262 | ||||
| N nonnegative terms | 170.000 | ||||
| N negative terms | 1945.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2115.000 | ||||
| Mean of predictor | 0.081 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.598 | ||||
| SD of criterion | 0.353 | ||||
| Covariance | 0.062 | ||||
| r | 0.292 | ||||
| b (slope, estimate of beta) | 0.172 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.114 | ||||
| DF error | 2113.000 | ||||
| t(b) | 14.033 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.477 | ||||
| p(a) | 0.683 | ||||
| Lowerbound of 95% confidence interval for beta | 0.148 | ||||
| Upperbound of 95% confidence interval for beta | 0.196 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.290 | ||||
| Upperbound of 95% confidence interval for alpha | 0.176 | ||||
| Treynor index (mean / b) | -0.248 | ||||
| Jensen alpha (a) | -0.057 | ||||
| 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%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2115.000 | ||||
| Minimum | 0.721 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.371 | ||||
| Mean of quarter 1 | 0.993 | ||||
| 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 | 179.000 | ||||
| Percentage of outliers low | 0.085 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 201.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 1.020 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.684 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| 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 | 7.000 | ||||
| Minimum | 0.092 | ||||
| Quartile 1 | 0.231 | ||||
| Median | 0.252 | ||||
| Quartile 3 | 0.280 | ||||
| Maximum | 0.298 | ||||
| Mean of quarter 1 | 0.158 | ||||
| Mean of quarter 2 | 0.245 | ||||
| Mean of quarter 3 | 0.278 | ||||
| Mean of quarter 4 | 0.290 | ||||
| Inter Quartile Range | 0.049 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.143 | ||||
| Mean of outliers low | 0.092 | ||||
| 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) | 0.001 | ||||
| Compounded annual return (geometric extrapolation) | 0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.004 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.004 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.028 | ||||
| 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 | 1.018 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.701 | ||||
| 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 | 0.781 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.685 | ||||
| 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) | -8777843073111519.000 | ||||
| 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) | 340183656210919403860714336550912.000 | ||||
| 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 | ||||