Advanced Statistics: LameSister2
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 | 0.048 | ||||
| SD | 0.364 | ||||
| Sharpe ratio (Glass type estimate) | 0.131 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.130 | ||||
| df | 64.000 | ||||
| t | 0.306 | ||||
| p | 0.380 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.712 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.973 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.713 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.972 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.174 | ||||
| Upside Potential Ratio | 0.742 | ||||
| Upside part of mean | 0.204 | ||||
| Downside part of mean | -0.156 | ||||
| Upside SD | 0.236 | ||||
| Downside SD | 0.275 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.310 | ||||
| Mean of criterion | 0.048 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.364 | ||||
| Covariance | 0.015 | ||||
| r | 0.174 | ||||
| b (slope, estimate of beta) | 0.271 | ||||
| a (intercept, estimate of alpha) | -0.036 | ||||
| Mean Square Error | 0.131 | ||||
| DF error | 63.000 | ||||
| t(b) | 1.403 | ||||
| p(b) | 0.083 | ||||
| t(a) | -0.216 | ||||
| p(a) | 0.585 | ||||
| Lowerbound of 95% confidence interval for beta | -0.115 | ||||
| Upperbound of 95% confidence interval for beta | 0.656 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.369 | ||||
| Upperbound of 95% confidence interval for alpha | 0.297 | ||||
| Treynor index (mean / b) | 0.177 | ||||
| Jensen alpha (a) | -0.036 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.483 | ||||
| Sharpe ratio (Glass type estimate) | -0.091 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.090 | ||||
| df | 64.000 | ||||
| t | -0.212 | ||||
| p | 0.584 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.933 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.751 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.932 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.752 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.101 | ||||
| Upside Potential Ratio | 0.416 | ||||
| Upside part of mean | 0.181 | ||||
| Downside part of mean | -0.225 | ||||
| Upside SD | 0.202 | ||||
| Downside SD | 0.434 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 65.000 | ||||
| Mean of predictor | 0.279 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.233 | ||||
| SD of criterion | 0.483 | ||||
| Covariance | 0.029 | ||||
| r | 0.260 | ||||
| b (slope, estimate of beta) | 0.540 | ||||
| a (intercept, estimate of alpha) | -0.194 | ||||
| Mean Square Error | 0.221 | ||||
| DF error | 63.000 | ||||
| t(b) | 2.140 | ||||
| p(b) | 0.018 | ||||
| t(a) | -0.910 | ||||
| p(a) | 0.817 | ||||
| Lowerbound of 95% confidence interval for beta | 0.036 | ||||
| Upperbound of 95% confidence interval for beta | 1.044 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.621 | ||||
| Upperbound of 95% confidence interval for alpha | 0.233 | ||||
| Treynor index (mean / b) | -0.082 | ||||
| Jensen alpha (a) | -0.194 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.208 | ||||
| Expected Shortfall on VaR | 0.252 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.094 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 65.000 | ||||
| Minimum | 0.365 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.451 | ||||
| Mean of quarter 1 | 0.963 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.071 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.046 | ||||
| Mean of outliers low | 0.788 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.154 | ||||
| Mean of outliers high | 1.113 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.159 | ||||
| Median | 0.317 | ||||
| Quartile 3 | 0.476 | ||||
| Maximum | 0.635 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.635 | ||||
| Inter Quartile Range | 0.317 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.040 | ||||
| SD | 0.391 | ||||
| Sharpe ratio (Glass type estimate) | 0.102 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.102 | ||||
| df | 1421.000 | ||||
| t | 0.238 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.739 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.943 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.739 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.943 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.145 | ||||
| Upside Potential Ratio | 1.693 | ||||
| Upside part of mean | 0.466 | ||||
| Downside part of mean | -0.426 | ||||
| Upside SD | 0.278 | ||||
| Downside SD | 0.275 | ||||
| N nonnegative terms | 81.000 | ||||
| N negative terms | 1341.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1422.000 | ||||
| Mean of predictor | 0.329 | ||||
| Mean of criterion | 0.040 | ||||
| SD of predictor | 0.314 | ||||
| SD of criterion | 0.391 | ||||
| Covariance | 0.013 | ||||
| r | 0.109 | ||||
| b (slope, estimate of beta) | 0.135 | ||||
| a (intercept, estimate of alpha) | -0.005 | ||||
| Mean Square Error | 0.151 | ||||
| DF error | 1420.000 | ||||
| t(b) | 4.117 | ||||
| p(b) | 0.446 | ||||
| t(a) | -0.027 | ||||
| p(a) | 0.500 | ||||
| Lowerbound of 95% confidence interval for beta | 0.071 | ||||
| Upperbound of 95% confidence interval for beta | 0.200 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.333 | ||||
| Upperbound of 95% confidence interval for alpha | 0.324 | ||||
| Treynor index (mean / b) | 0.295 | ||||
| Jensen alpha (a) | -0.005 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.426 | ||||
| Sharpe ratio (Glass type estimate) | -0.103 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.103 | ||||
| df | 1421.000 | ||||
| t | -0.241 | ||||
| p | 0.504 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.945 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.738 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.944 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.738 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.124 | ||||
| Upside Potential Ratio | 1.227 | ||||
| Upside part of mean | 0.435 | ||||
| Downside part of mean | -0.479 | ||||
| Upside SD | 0.237 | ||||
| Downside SD | 0.354 | ||||
| N nonnegative terms | 81.000 | ||||
| N negative terms | 1341.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1422.000 | ||||
| Mean of predictor | 0.277 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.325 | ||||
| SD of criterion | 0.426 | ||||
| Covariance | 0.020 | ||||
| r | 0.146 | ||||
| b (slope, estimate of beta) | 0.192 | ||||
| a (intercept, estimate of alpha) | -0.097 | ||||
| Mean Square Error | 0.178 | ||||
| DF error | 1420.000 | ||||
| t(b) | 5.574 | ||||
| p(b) | 0.427 | ||||
| t(a) | -0.536 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | 0.124 | ||||
| Upperbound of 95% confidence interval for beta | 0.259 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.453 | ||||
| Upperbound of 95% confidence interval for alpha | 0.259 | ||||
| Treynor index (mean / b) | -0.229 | ||||
| Jensen alpha (a) | -0.097 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1422.000 | ||||
| Minimum | 0.516 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.538 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.007 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 75.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.972 | ||||
| Number of outliers high | 81.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 1.031 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.311 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.400 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.000 | ||||
| Maximum | 0.641 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | 0.000 | ||||
| Mean of quarter 4 | 0.321 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.143 | ||||
| Mean of outliers high | 0.641 | ||||
| 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) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.041 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.368 | ||||
| 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 | 0.971 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.371 | ||||
| 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) | -8686076459478296.000 | ||||
| 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) | 86891801255631086728257128628224.000 | ||||
| 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 | ||||