Advanced Statistics: Darlingtonia californica Google
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 | -0.024 | ||||
| SD | 0.071 | ||||
| Sharpe ratio (Glass type estimate) | -0.331 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.327 | ||||
| df | 67.000 | ||||
| t | -0.788 | ||||
| p | 0.783 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.155 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.496 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.152 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.498 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.586 | ||||
| Upside Potential Ratio | 0.999 | ||||
| Upside part of mean | 0.040 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.040 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.255 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.277 | ||||
| SD of criterion | 0.071 | ||||
| Covariance | -0.002 | ||||
| r | -0.114 | ||||
| b (slope, estimate of beta) | -0.029 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 66.000 | ||||
| t(b) | -0.929 | ||||
| p(b) | 0.822 | ||||
| t(a) | -0.520 | ||||
| p(a) | 0.697 | ||||
| Lowerbound of 95% confidence interval for beta | -0.092 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.046 | ||||
| Treynor index (mean / b) | 0.806 | ||||
| Jensen alpha (a) | -0.016 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.070 | ||||
| Sharpe ratio (Glass type estimate) | -0.372 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.368 | ||||
| df | 67.000 | ||||
| t | -0.886 | ||||
| p | 0.811 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.197 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.455 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.194 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.458 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.624 | ||||
| Upside Potential Ratio | 0.925 | ||||
| Upside part of mean | 0.038 | ||||
| Downside part of mean | -0.064 | ||||
| Upside SD | 0.056 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 65.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 68.000 | ||||
| Mean of predictor | 0.215 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.070 | ||||
| Covariance | -0.002 | ||||
| r | -0.106 | ||||
| b (slope, estimate of beta) | -0.027 | ||||
| a (intercept, estimate of alpha) | -0.020 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 66.000 | ||||
| t(b) | -0.864 | ||||
| p(b) | 0.805 | ||||
| t(a) | -0.672 | ||||
| p(a) | 0.748 | ||||
| Lowerbound of 95% confidence interval for beta | -0.089 | ||||
| Upperbound of 95% confidence interval for beta | 0.035 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.080 | ||||
| Upperbound of 95% confidence interval for alpha | 0.040 | ||||
| Treynor index (mean / b) | 0.970 | ||||
| Jensen alpha (a) | -0.020 | ||||
| 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 | 0.043 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 68.000 | ||||
| Minimum | 0.919 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.112 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.074 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.074 | ||||
| Mean of outliers high | 1.048 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -57.984 | ||||
| VaR(95%) (moments method) | -0.203 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.277 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.043 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.018 | ||||
| Quartile 1 | 0.039 | ||||
| Median | 0.060 | ||||
| Quartile 3 | 0.082 | ||||
| Maximum | 0.103 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.103 | ||||
| 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) | 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) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.177 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.177 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.427 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.221 | ||||
| Sharpe ratio (Glass type estimate) | -0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.009 | ||||
| df | 1503.000 | ||||
| t | -0.023 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.827 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.809 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.827 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.809 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.015 | ||||
| Upside Potential Ratio | 2.159 | ||||
| Upside part of mean | 0.310 | ||||
| Downside part of mean | -0.312 | ||||
| Upside SD | 0.168 | ||||
| Downside SD | 0.143 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 1457.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1504.000 | ||||
| Mean of predictor | 0.388 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.566 | ||||
| SD of criterion | 0.221 | ||||
| Covariance | -0.048 | ||||
| r | -0.385 | ||||
| b (slope, estimate of beta) | -0.150 | ||||
| a (intercept, estimate of alpha) | 0.056 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 1502.000 | ||||
| t(b) | -16.153 | ||||
| p(b) | 0.692 | ||||
| t(a) | 0.659 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | -0.168 | ||||
| Upperbound of 95% confidence interval for beta | -0.132 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.111 | ||||
| Upperbound of 95% confidence interval for alpha | 0.223 | ||||
| Treynor index (mean / b) | 0.014 | ||||
| Jensen alpha (a) | 0.056 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.026 | ||||
| SD | 0.219 | ||||
| Sharpe ratio (Glass type estimate) | -0.119 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.119 | ||||
| df | 1503.000 | ||||
| t | -0.286 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.937 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.699 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.937 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.699 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.173 | ||||
| Upside Potential Ratio | 1.957 | ||||
| Upside part of mean | 0.297 | ||||
| Downside part of mean | -0.323 | ||||
| Upside SD | 0.158 | ||||
| Downside SD | 0.152 | ||||
| N nonnegative terms | 47.000 | ||||
| N negative terms | 1457.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1504.000 | ||||
| Mean of predictor | 0.230 | ||||
| Mean of criterion | -0.026 | ||||
| SD of predictor | 0.563 | ||||
| SD of criterion | 0.219 | ||||
| Covariance | -0.048 | ||||
| r | -0.387 | ||||
| b (slope, estimate of beta) | -0.151 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.041 | ||||
| DF error | 1502.000 | ||||
| t(b) | -16.274 | ||||
| p(b) | 0.694 | ||||
| t(a) | 0.100 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | -0.169 | ||||
| Upperbound of 95% confidence interval for beta | -0.133 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.157 | ||||
| Upperbound of 95% confidence interval for alpha | 0.174 | ||||
| Treynor index (mean / b) | 0.174 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.028 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.004 | ||||
| Expected Shortfall on VaR | 0.009 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1504.000 | ||||
| Minimum | 0.859 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.178 | ||||
| Mean of quarter 1 | 0.996 | ||||
| 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 | 52.000 | ||||
| Percentage of outliers low | 0.035 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 57.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -7.401 | ||||
| VaR(95%) (moments method) | -0.011 | ||||
| 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 | 7.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.039 | ||||
| Median | 0.064 | ||||
| Quartile 3 | 0.151 | ||||
| Maximum | 0.168 | ||||
| Mean of quarter 1 | 0.018 | ||||
| Mean of quarter 2 | 0.059 | ||||
| Mean of quarter 3 | 0.141 | ||||
| Mean of quarter 4 | 0.165 | ||||
| Inter Quartile Range | 0.112 | ||||
| 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) | 0.018 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.107 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.109 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.651 | ||||
| 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 | 0.860 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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 | 0.748 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.473 | ||||
| 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) | -8757797784499335.000 | ||||
| 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) | -76184281186555457652580461576192.000 | ||||
| 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 | ||||