Advanced Statistics: Poppintito
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 | 0.042 | ||||
| SD | 0.277 | ||||
| Sharpe ratio (Glass type estimate) | 0.152 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.150 | ||||
| df | 76.000 | ||||
| t | 0.384 | ||||
| p | 0.351 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.623 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.925 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.624 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.924 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.748 | ||||
| Upside Potential Ratio | 1.900 | ||||
| Upside part of mean | 0.107 | ||||
| Downside part of mean | -0.065 | ||||
| Upside SD | 0.270 | ||||
| Downside SD | 0.056 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 77.000 | ||||
| Mean of predictor | 0.156 | ||||
| Mean of criterion | 0.042 | ||||
| SD of predictor | 0.244 | ||||
| SD of criterion | 0.277 | ||||
| Covariance | 0.001 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | 0.040 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 75.000 | ||||
| t(b) | 0.076 | ||||
| p(b) | 0.470 | ||||
| t(a) | 0.361 | ||||
| p(a) | 0.359 | ||||
| Lowerbound of 95% confidence interval for beta | -0.251 | ||||
| Upperbound of 95% confidence interval for beta | 0.271 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.183 | ||||
| Upperbound of 95% confidence interval for alpha | 0.264 | ||||
| Treynor index (mean / b) | 4.240 | ||||
| Jensen alpha (a) | 0.040 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.015 | ||||
| SD | 0.215 | ||||
| Sharpe ratio (Glass type estimate) | 0.069 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.069 | ||||
| df | 76.000 | ||||
| t | 0.176 | ||||
| p | 0.430 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.705 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.843 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.705 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.843 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.249 | ||||
| Upside Potential Ratio | 1.352 | ||||
| Upside part of mean | 0.081 | ||||
| Downside part of mean | -0.066 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 75.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 77.000 | ||||
| Mean of predictor | 0.125 | ||||
| Mean of criterion | 0.015 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.215 | ||||
| Covariance | 0.001 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | 0.014 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 75.000 | ||||
| t(b) | 0.111 | ||||
| p(b) | 0.456 | ||||
| t(a) | 0.157 | ||||
| p(a) | 0.438 | ||||
| Lowerbound of 95% confidence interval for beta | -0.189 | ||||
| Upperbound of 95% confidence interval for beta | 0.211 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.159 | ||||
| Upperbound of 95% confidence interval for alpha | 0.186 | ||||
| Treynor index (mean / b) | 1.340 | ||||
| Jensen alpha (a) | 0.014 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.096 | ||||
| Expected Shortfall on VaR | 0.119 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 77.000 | ||||
| Minimum | 0.865 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.688 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.036 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.930 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.026 | ||||
| Mean of outliers high | 1.346 | ||||
| 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) | 3.779 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.037 | ||||
| Median | 0.070 | ||||
| Quartile 3 | 0.102 | ||||
| Maximum | 0.135 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.135 | ||||
| Inter Quartile Range | 0.065 | ||||
| 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) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.061 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.450 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.450 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.511 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.104 | ||||
| SD | 0.448 | ||||
| Sharpe ratio (Glass type estimate) | 0.233 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.233 | ||||
| df | 1696.000 | ||||
| t | 0.593 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.537 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.003 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.537 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.003 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.457 | ||||
| Upside Potential Ratio | 1.498 | ||||
| Upside part of mean | 0.342 | ||||
| Downside part of mean | -0.238 | ||||
| Upside SD | 0.385 | ||||
| Downside SD | 0.228 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 1671.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1697.000 | ||||
| Mean of predictor | 0.262 | ||||
| Mean of criterion | 0.104 | ||||
| SD of predictor | 0.545 | ||||
| SD of criterion | 0.448 | ||||
| Covariance | 0.012 | ||||
| r | 0.050 | ||||
| b (slope, estimate of beta) | 0.041 | ||||
| a (intercept, estimate of alpha) | 0.094 | ||||
| Mean Square Error | 0.200 | ||||
| DF error | 1695.000 | ||||
| t(b) | 2.046 | ||||
| p(b) | 0.468 | ||||
| t(a) | 0.533 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | 0.002 | ||||
| Upperbound of 95% confidence interval for beta | 0.080 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.251 | ||||
| Upperbound of 95% confidence interval for alpha | 0.439 | ||||
| Treynor index (mean / b) | 2.560 | ||||
| Jensen alpha (a) | 0.094 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.014 | ||||
| SD | 0.420 | ||||
| Sharpe ratio (Glass type estimate) | 0.034 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.034 | ||||
| df | 1696.000 | ||||
| t | 0.087 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.736 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.804 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.736 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.804 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.051 | ||||
| Upside Potential Ratio | 1.009 | ||||
| Upside part of mean | 0.287 | ||||
| Downside part of mean | -0.273 | ||||
| Upside SD | 0.309 | ||||
| Downside SD | 0.284 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 1671.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1697.000 | ||||
| Mean of predictor | 0.115 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.542 | ||||
| SD of criterion | 0.420 | ||||
| Covariance | 0.012 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.041 | ||||
| a (intercept, estimate of alpha) | 0.010 | ||||
| Mean Square Error | 0.176 | ||||
| DF error | 1695.000 | ||||
| t(b) | 2.194 | ||||
| p(b) | 0.466 | ||||
| t(a) | 0.059 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 0.004 | ||||
| Upperbound of 95% confidence interval for beta | 0.078 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.313 | ||||
| Upperbound of 95% confidence interval for alpha | 0.333 | ||||
| Treynor index (mean / b) | 0.350 | ||||
| Jensen alpha (a) | 0.010 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.042 | ||||
| Expected Shortfall on VaR | 0.052 | ||||
| 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 | 1697.000 | ||||
| Minimum | 0.611 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.663 | ||||
| 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 | 27.000 | ||||
| Percentage of outliers low | 0.016 | ||||
| Mean of outliers low | 0.953 | ||||
| Number of outliers high | 26.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.085 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.196 | ||||
| VaR(95%) (moments method) | -0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.416 | ||||
| VaR(95%) (regression method) | -0.009 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.093 | ||||
| Median | 0.126 | ||||
| Quartile 3 | 0.387 | ||||
| Maximum | 0.427 | ||||
| Mean of quarter 1 | 0.048 | ||||
| Mean of quarter 2 | 0.126 | ||||
| Mean of quarter 3 | 0.387 | ||||
| Mean of quarter 4 | 0.427 | ||||
| Inter Quartile Range | 0.294 | ||||
| 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) | 0.071 | ||||
| Compounded annual return (geometric extrapolation) | 0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.141 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.141 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.157 | ||||
| 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 | 0.911 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.548 | ||||
| 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 | 0.758 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.557 | ||||
| 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) | -8768622436308638.000 | ||||
| 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) | -2573187519378046219049006096449536.000 | ||||
| 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 | ||||