Advanced Statistics: Blue Lobster Fund
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 | 0.093 | ||||
| SD | 0.573 | ||||
| Sharpe ratio (Glass type estimate) | 0.163 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.161 | ||||
| df | 66.000 | ||||
| t | 0.385 | ||||
| p | 0.351 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.668 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.992 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.669 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.991 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.323 | ||||
| Upside Potential Ratio | 1.205 | ||||
| Upside part of mean | 0.348 | ||||
| Downside part of mean | -0.255 | ||||
| Upside SD | 0.491 | ||||
| Downside SD | 0.289 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.204 | ||||
| Mean of criterion | 0.093 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 0.573 | ||||
| Covariance | 0.028 | ||||
| r | 0.179 | ||||
| b (slope, estimate of beta) | 0.372 | ||||
| a (intercept, estimate of alpha) | 0.017 | ||||
| Mean Square Error | 0.323 | ||||
| DF error | 65.000 | ||||
| t(b) | 1.467 | ||||
| p(b) | 0.074 | ||||
| t(a) | 0.071 | ||||
| p(a) | 0.472 | ||||
| Lowerbound of 95% confidence interval for beta | -0.134 | ||||
| Upperbound of 95% confidence interval for beta | 0.878 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.474 | ||||
| Upperbound of 95% confidence interval for alpha | 0.509 | ||||
| Treynor index (mean / b) | 0.251 | ||||
| Jensen alpha (a) | 0.017 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.527 | ||||
| Sharpe ratio (Glass type estimate) | -0.083 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.082 | ||||
| df | 66.000 | ||||
| t | -0.197 | ||||
| p | 0.578 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.913 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.747 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.912 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.747 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.111 | ||||
| Upside Potential Ratio | 0.691 | ||||
| Upside part of mean | 0.272 | ||||
| Downside part of mean | -0.316 | ||||
| Upside SD | 0.343 | ||||
| Downside SD | 0.394 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 57.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.165 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.278 | ||||
| SD of criterion | 0.527 | ||||
| Covariance | 0.011 | ||||
| r | 0.078 | ||||
| b (slope, estimate of beta) | 0.147 | ||||
| a (intercept, estimate of alpha) | -0.068 | ||||
| Mean Square Error | 0.280 | ||||
| DF error | 65.000 | ||||
| t(b) | 0.629 | ||||
| p(b) | 0.266 | ||||
| t(a) | -0.300 | ||||
| p(a) | 0.617 | ||||
| Lowerbound of 95% confidence interval for beta | -0.321 | ||||
| Upperbound of 95% confidence interval for beta | 0.615 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.522 | ||||
| Upperbound of 95% confidence interval for alpha | 0.386 | ||||
| Treynor index (mean / b) | -0.298 | ||||
| Jensen alpha (a) | -0.068 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.224 | ||||
| Expected Shortfall on VaR | 0.271 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.146 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 67.000 | ||||
| Minimum | 0.444 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.101 | ||||
| Mean of quarter 1 | 0.929 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.116 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.134 | ||||
| Mean of outliers low | 0.865 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.194 | ||||
| Mean of outliers high | 1.152 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.693 | ||||
| VaR(95%) (moments method) | 0.006 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.536 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.159 | ||||
| Median | 0.303 | ||||
| Quartile 3 | 0.498 | ||||
| Maximum | 0.693 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.303 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.693 | ||||
| Inter Quartile Range | 0.339 | ||||
| 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 | 1.149 | ||||
| SD | 1.841 | ||||
| Sharpe ratio (Glass type estimate) | 0.624 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.624 | ||||
| df | 1472.000 | ||||
| t | 1.480 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.203 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.451 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.203 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.451 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.534 | ||||
| Upside Potential Ratio | 4.233 | ||||
| Upside part of mean | 3.171 | ||||
| Downside part of mean | -2.022 | ||||
| Upside SD | 1.683 | ||||
| Downside SD | 0.749 | ||||
| N nonnegative terms | 161.000 | ||||
| N negative terms | 1312.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1473.000 | ||||
| Mean of predictor | 0.494 | ||||
| Mean of criterion | 1.149 | ||||
| SD of predictor | 0.713 | ||||
| SD of criterion | 1.841 | ||||
| Covariance | -0.394 | ||||
| r | -0.301 | ||||
| b (slope, estimate of beta) | -0.776 | ||||
| a (intercept, estimate of alpha) | 1.533 | ||||
| Mean Square Error | 3.087 | ||||
| DF error | 1471.000 | ||||
| t(b) | -12.084 | ||||
| p(b) | 0.688 | ||||
| t(a) | 2.067 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | -0.902 | ||||
| Upperbound of 95% confidence interval for beta | -0.650 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 2.987 | ||||
| Treynor index (mean / b) | -1.480 | ||||
| Jensen alpha (a) | 1.533 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 1.488 | ||||
| Sharpe ratio (Glass type estimate) | -0.030 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.029 | ||||
| df | 1472.000 | ||||
| t | -0.070 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.856 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.797 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.856 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.797 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.043 | ||||
| Upside Potential Ratio | 2.332 | ||||
| Upside part of mean | 2.402 | ||||
| Downside part of mean | -2.446 | ||||
| Upside SD | 1.073 | ||||
| Downside SD | 1.030 | ||||
| N nonnegative terms | 161.000 | ||||
| N negative terms | 1312.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1473.000 | ||||
| Mean of predictor | 0.247 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.703 | ||||
| SD of criterion | 1.488 | ||||
| Covariance | -0.368 | ||||
| r | -0.352 | ||||
| b (slope, estimate of beta) | -0.745 | ||||
| a (intercept, estimate of alpha) | 0.140 | ||||
| Mean Square Error | 1.942 | ||||
| DF error | 1471.000 | ||||
| t(b) | -14.418 | ||||
| p(b) | 0.719 | ||||
| t(a) | 0.238 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.846 | ||||
| Upperbound of 95% confidence interval for beta | -0.644 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.013 | ||||
| Upperbound of 95% confidence interval for alpha | 1.293 | ||||
| Treynor index (mean / b) | 0.059 | ||||
| Jensen alpha (a) | 0.140 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.140 | ||||
| Expected Shortfall on VaR | 0.172 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.056 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1473.000 | ||||
| Minimum | 0.342 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.951 | ||||
| Mean of quarter 1 | 0.970 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.049 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 158.000 | ||||
| Percentage of outliers low | 0.107 | ||||
| Mean of outliers low | 0.929 | ||||
| Number of outliers high | 165.000 | ||||
| Percentage of outliers high | 0.112 | ||||
| Mean of outliers high | 1.108 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.766 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| 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 | 10.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.064 | ||||
| Median | 0.087 | ||||
| Quartile 3 | 0.348 | ||||
| Maximum | 0.693 | ||||
| Mean of quarter 1 | 0.027 | ||||
| Mean of quarter 2 | 0.071 | ||||
| Mean of quarter 3 | 0.105 | ||||
| Mean of quarter 4 | 0.590 | ||||
| Inter Quartile Range | 0.284 | ||||
| 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) | -91.172 | ||||
| VaR(95%) (moments method) | 0.622 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -3.314 | ||||
| VaR(95%) (regression method) | 0.937 | ||||
| Expected Shortfall (regression method) | 0.939 | ||||
| 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 | 0.001 | ||||
| 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 | 1.721 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.687 | ||||
| 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 | 1.483 | ||||
| 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) | -8721511327553513.000 | ||||
| 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) | -136194616586240409900401219862528.000 | ||||
| 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 | ||||