Advanced Statistics: lamesister4
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 | 0.124 | ||||
| SD | 0.316 | ||||
| Sharpe ratio (Glass type estimate) | 0.392 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.384 | ||||
| df | 39.000 | ||||
| t | 0.715 | ||||
| p | 0.239 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.688 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.466 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.693 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.461 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.387 | ||||
| Upside Potential Ratio | 2.564 | ||||
| Upside part of mean | 0.229 | ||||
| Downside part of mean | -0.105 | ||||
| Upside SD | 0.301 | ||||
| Downside SD | 0.089 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.551 | ||||
| Mean of criterion | 0.124 | ||||
| SD of predictor | 0.267 | ||||
| SD of criterion | 0.316 | ||||
| Covariance | 0.004 | ||||
| r | 0.048 | ||||
| b (slope, estimate of beta) | 0.056 | ||||
| a (intercept, estimate of alpha) | 0.093 | ||||
| Mean Square Error | 0.102 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.293 | ||||
| p(b) | 0.385 | ||||
| t(a) | 0.454 | ||||
| p(a) | 0.326 | ||||
| Lowerbound of 95% confidence interval for beta | -0.332 | ||||
| Upperbound of 95% confidence interval for beta | 0.444 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.321 | ||||
| Upperbound of 95% confidence interval for alpha | 0.506 | ||||
| Treynor index (mean / b) | 2.201 | ||||
| Jensen alpha (a) | 0.093 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.084 | ||||
| SD | 0.266 | ||||
| Sharpe ratio (Glass type estimate) | 0.317 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.311 | ||||
| df | 39.000 | ||||
| t | 0.578 | ||||
| p | 0.283 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.761 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.391 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.765 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.386 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.890 | ||||
| Upside Potential Ratio | 2.039 | ||||
| Upside part of mean | 0.193 | ||||
| Downside part of mean | -0.109 | ||||
| Upside SD | 0.246 | ||||
| Downside SD | 0.095 | ||||
| N nonnegative terms | 3.000 | ||||
| N negative terms | 37.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 40.000 | ||||
| Mean of predictor | 0.505 | ||||
| Mean of criterion | 0.084 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.266 | ||||
| Covariance | 0.005 | ||||
| r | 0.070 | ||||
| b (slope, estimate of beta) | 0.072 | ||||
| a (intercept, estimate of alpha) | 0.048 | ||||
| Mean Square Error | 0.072 | ||||
| DF error | 38.000 | ||||
| t(b) | 0.431 | ||||
| p(b) | 0.335 | ||||
| t(a) | 0.282 | ||||
| p(a) | 0.390 | ||||
| Lowerbound of 95% confidence interval for beta | -0.267 | ||||
| Upperbound of 95% confidence interval for beta | 0.411 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.296 | ||||
| Upperbound of 95% confidence interval for alpha | 0.392 | ||||
| Treynor index (mean / b) | 1.170 | ||||
| Jensen alpha (a) | 0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.113 | ||||
| Expected Shortfall on VaR | 0.140 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 40.000 | ||||
| Minimum | 0.865 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.520 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.077 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.050 | ||||
| Mean of outliers low | 0.893 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.075 | ||||
| Mean of outliers high | 1.258 | ||||
| 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) | -1.483 | ||||
| VaR(95%) (regression method) | 0.084 | ||||
| Expected Shortfall (regression method) | 0.149 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.079 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.107 | ||||
| Quartile 3 | 0.121 | ||||
| Maximum | 0.135 | ||||
| Mean of quarter 1 | 0.079 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.135 | ||||
| Inter Quartile Range | 0.028 | ||||
| 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) | 0.160 | ||||
| Compounded annual return (geometric extrapolation) | 0.137 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.015 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.015 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.977 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.097 | ||||
| SD | 0.163 | ||||
| Sharpe ratio (Glass type estimate) | 0.598 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.597 | ||||
| df | 873.000 | ||||
| t | 1.091 | ||||
| p | 0.138 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.476 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.671 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.476 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.671 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.040 | ||||
| Upside Potential Ratio | 3.593 | ||||
| Upside part of mean | 0.336 | ||||
| Downside part of mean | -0.239 | ||||
| Upside SD | 0.133 | ||||
| Downside SD | 0.094 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 836.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 874.000 | ||||
| Mean of predictor | 0.565 | ||||
| Mean of criterion | 0.097 | ||||
| SD of predictor | 0.354 | ||||
| SD of criterion | 0.163 | ||||
| Covariance | 0.001 | ||||
| r | 0.010 | ||||
| b (slope, estimate of beta) | 0.004 | ||||
| a (intercept, estimate of alpha) | 0.095 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 872.000 | ||||
| t(b) | 0.281 | ||||
| p(b) | 0.389 | ||||
| t(a) | 1.058 | ||||
| p(a) | 0.145 | ||||
| Lowerbound of 95% confidence interval for beta | -0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.035 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.081 | ||||
| Upperbound of 95% confidence interval for alpha | 0.271 | ||||
| Treynor index (mean / b) | 22.205 | ||||
| Jensen alpha (a) | 0.095 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.084 | ||||
| SD | 0.162 | ||||
| Sharpe ratio (Glass type estimate) | 0.521 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.521 | ||||
| df | 873.000 | ||||
| t | 0.952 | ||||
| p | 0.171 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.552 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.595 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.552 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.594 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.864 | ||||
| Upside Potential Ratio | 3.362 | ||||
| Upside part of mean | 0.328 | ||||
| Downside part of mean | -0.244 | ||||
| Upside SD | 0.129 | ||||
| Downside SD | 0.098 | ||||
| N nonnegative terms | 38.000 | ||||
| N negative terms | 836.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 874.000 | ||||
| Mean of predictor | 0.499 | ||||
| Mean of criterion | 0.084 | ||||
| SD of predictor | 0.368 | ||||
| SD of criterion | 0.162 | ||||
| Covariance | 0.001 | ||||
| r | 0.011 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | 0.082 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 872.000 | ||||
| t(b) | 0.318 | ||||
| p(b) | 0.375 | ||||
| t(a) | 0.922 | ||||
| p(a) | 0.178 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.034 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.256 | ||||
| Treynor index (mean / b) | 17.798 | ||||
| Jensen alpha (a) | 0.082 | ||||
| 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 | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 874.000 | ||||
| Minimum | 0.879 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.129 | ||||
| Mean of quarter 1 | 0.997 | ||||
| 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 | 32.000 | ||||
| Percentage of outliers low | 0.037 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 38.000 | ||||
| Percentage of outliers high | 0.043 | ||||
| Mean of outliers high | 1.030 | ||||
| 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) | -0.038 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.053 | ||||
| Quartile 3 | 0.112 | ||||
| Maximum | 0.235 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.026 | ||||
| Mean of quarter 3 | 0.092 | ||||
| Mean of quarter 4 | 0.176 | ||||
| Inter Quartile Range | 0.095 | ||||
| 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) | 0.160 | ||||
| Compounded annual return (geometric extrapolation) | 0.137 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.582 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.779 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.823 | ||||
| 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 | 0.983 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.494 | ||||
| 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 | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.496 | ||||
| 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) | -8749461669369125.000 | ||||
| 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) | 324922294959613071559342367440896.000 | ||||
| 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 | ||||