Advanced Statistics: TheSpeculator
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 | -0.127 | ||||
| SD | 0.082 | ||||
| Sharpe ratio (Glass type estimate) | -1.545 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.512 | ||||
| df | 35.000 | ||||
| t | -2.676 | ||||
| p | 0.994 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.723 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.348 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.698 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.326 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.428 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.127 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.089 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.571 | ||||
| Mean of criterion | -0.127 | ||||
| SD of predictor | 0.393 | ||||
| SD of criterion | 0.082 | ||||
| Covariance | 0.004 | ||||
| r | 0.109 | ||||
| b (slope, estimate of beta) | 0.023 | ||||
| a (intercept, estimate of alpha) | -0.140 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.637 | ||||
| p(b) | 0.264 | ||||
| t(a) | -2.691 | ||||
| p(a) | 0.995 | ||||
| Lowerbound of 95% confidence interval for beta | -0.050 | ||||
| Upperbound of 95% confidence interval for beta | 0.095 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.246 | ||||
| Upperbound of 95% confidence interval for alpha | -0.034 | ||||
| Treynor index (mean / b) | -5.595 | ||||
| Jensen alpha (a) | -0.140 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.131 | ||||
| SD | 0.087 | ||||
| Sharpe ratio (Glass type estimate) | -1.510 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.477 | ||||
| df | 35.000 | ||||
| t | -2.615 | ||||
| p | 0.993 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.685 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.315 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.660 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.294 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.400 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.131 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.093 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 36.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 36.000 | ||||
| Mean of predictor | 0.491 | ||||
| Mean of criterion | -0.131 | ||||
| SD of predictor | 0.361 | ||||
| SD of criterion | 0.087 | ||||
| Covariance | 0.003 | ||||
| r | 0.099 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.142 | ||||
| Mean Square Error | 0.008 | ||||
| DF error | 34.000 | ||||
| t(b) | 0.583 | ||||
| p(b) | 0.282 | ||||
| t(a) | -2.622 | ||||
| p(a) | 0.994 | ||||
| Lowerbound of 95% confidence interval for beta | -0.059 | ||||
| Upperbound of 95% confidence interval for beta | 0.107 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.253 | ||||
| Upperbound of 95% confidence interval for alpha | -0.032 | ||||
| Treynor index (mean / b) | -5.478 | ||||
| Jensen alpha (a) | -0.142 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.051 | ||||
| Expected Shortfall on VaR | 0.060 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.037 | ||||
| Expected Shortfall on VaR | 0.072 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 36.000 | ||||
| Minimum | 0.884 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.972 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.111 | ||||
| Mean of outliers low | 0.938 | ||||
| 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) | -0.334 | ||||
| VaR(95%) (regression method) | 0.066 | ||||
| Expected Shortfall (regression method) | 0.108 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.229 | ||||
| Quartile 1 | 0.229 | ||||
| Median | 0.229 | ||||
| Quartile 3 | 0.229 | ||||
| Maximum | 0.229 | ||||
| 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 | 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) | -0.076 | ||||
| Compounded annual return (geometric extrapolation) | -0.083 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.363 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.373 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.125 | ||||
| SD | 0.094 | ||||
| Sharpe ratio (Glass type estimate) | -1.321 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.319 | ||||
| df | 799.000 | ||||
| t | -2.308 | ||||
| p | 0.989 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.444 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.197 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.443 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.196 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.676 | ||||
| Upside Potential Ratio | 1.501 | ||||
| Upside part of mean | 0.112 | ||||
| Downside part of mean | -0.236 | ||||
| Upside SD | 0.059 | ||||
| Downside SD | 0.074 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 782.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 800.000 | ||||
| Mean of predictor | 0.588 | ||||
| Mean of criterion | -0.125 | ||||
| SD of predictor | 0.352 | ||||
| SD of criterion | 0.094 | ||||
| Covariance | -0.000 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.124 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 798.000 | ||||
| t(b) | -0.194 | ||||
| p(b) | 0.577 | ||||
| t(a) | -2.274 | ||||
| p(a) | 0.988 | ||||
| Lowerbound of 95% confidence interval for beta | -0.020 | ||||
| Upperbound of 95% confidence interval for beta | 0.017 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.230 | ||||
| Upperbound of 95% confidence interval for alpha | -0.017 | ||||
| Treynor index (mean / b) | 67.696 | ||||
| Jensen alpha (a) | -0.124 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.129 | ||||
| SD | 0.095 | ||||
| Sharpe ratio (Glass type estimate) | -1.364 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.362 | ||||
| df | 799.000 | ||||
| t | -2.383 | ||||
| p | 0.991 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.487 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -0.240 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.486 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.239 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.706 | ||||
| Upside Potential Ratio | 1.452 | ||||
| Upside part of mean | 0.110 | ||||
| Downside part of mean | -0.239 | ||||
| Upside SD | 0.057 | ||||
| Downside SD | 0.076 | ||||
| N nonnegative terms | 18.000 | ||||
| N negative terms | 782.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 800.000 | ||||
| Mean of predictor | 0.524 | ||||
| Mean of criterion | -0.129 | ||||
| SD of predictor | 0.359 | ||||
| SD of criterion | 0.095 | ||||
| Covariance | -0.000 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.128 | ||||
| Mean Square Error | 0.009 | ||||
| DF error | 798.000 | ||||
| t(b) | -0.207 | ||||
| p(b) | 0.582 | ||||
| t(a) | -2.353 | ||||
| p(a) | 0.991 | ||||
| Lowerbound of 95% confidence interval for beta | -0.020 | ||||
| Upperbound of 95% confidence interval for beta | 0.016 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.235 | ||||
| Upperbound of 95% confidence interval for alpha | -0.021 | ||||
| Treynor index (mean / b) | 66.967 | ||||
| Jensen alpha (a) | -0.128 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| 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 | 800.000 | ||||
| Minimum | 0.953 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.063 | ||||
| Mean of quarter 1 | 0.997 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.002 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 32.000 | ||||
| Percentage of outliers low | 0.040 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 18.000 | ||||
| Percentage of outliers high | 0.022 | ||||
| Mean of outliers high | 1.019 | ||||
| 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) | -0.515 | ||||
| VaR(95%) (regression method) | -0.003 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.244 | ||||
| Quartile 1 | 0.244 | ||||
| Median | 0.244 | ||||
| Quartile 3 | 0.244 | ||||
| Maximum | 0.244 | ||||
| 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 | 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) | -0.075 | ||||
| Compounded annual return (geometric extrapolation) | -0.082 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.335 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.539 | ||||
| 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 | 1.003 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.481 | ||||
| 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 | 0.885 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.485 | ||||
| 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) | -8743864592128845.000 | ||||
| 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) | -973558312276865529674265782124544.000 | ||||
| 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 | ||||