Advanced Statistics:
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 | 0.252 | ||||
| SD | 1.289 | ||||
| Sharpe ratio (Glass type estimate) | 0.195 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.192 | ||||
| df | 52.000 | ||||
| t | 0.410 | ||||
| p | 0.342 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.739 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.128 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.741 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.126 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.696 | ||||
| Upside Potential Ratio | 1.905 | ||||
| Upside part of mean | 0.689 | ||||
| Downside part of mean | -0.437 | ||||
| Upside SD | 1.226 | ||||
| Downside SD | 0.362 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.369 | ||||
| Mean of criterion | 0.252 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 1.289 | ||||
| Covariance | -0.125 | ||||
| r | -0.349 | ||||
| b (slope, estimate of beta) | -1.615 | ||||
| a (intercept, estimate of alpha) | 0.848 | ||||
| Mean Square Error | 1.487 | ||||
| DF error | 51.000 | ||||
| t(b) | -2.659 | ||||
| p(b) | 0.995 | ||||
| t(a) | 1.363 | ||||
| p(a) | 0.089 | ||||
| Lowerbound of 95% confidence interval for beta | -2.833 | ||||
| Upperbound of 95% confidence interval for beta | -0.396 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.401 | ||||
| Upperbound of 95% confidence interval for alpha | 2.096 | ||||
| Treynor index (mean / b) | -0.156 | ||||
| Jensen alpha (a) | 0.848 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.145 | ||||
| SD | 0.783 | ||||
| Sharpe ratio (Glass type estimate) | -0.185 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.182 | ||||
| df | 52.000 | ||||
| t | -0.389 | ||||
| p | 0.651 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.118 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.749 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.116 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.751 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.319 | ||||
| Upside Potential Ratio | 0.835 | ||||
| Upside part of mean | 0.379 | ||||
| Downside part of mean | -0.524 | ||||
| Upside SD | 0.630 | ||||
| Downside SD | 0.454 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 53.000 | ||||
| Mean of predictor | 0.326 | ||||
| Mean of criterion | -0.145 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.783 | ||||
| Covariance | -0.066 | ||||
| r | -0.308 | ||||
| b (slope, estimate of beta) | -0.878 | ||||
| a (intercept, estimate of alpha) | 0.141 | ||||
| Mean Square Error | 0.566 | ||||
| DF error | 51.000 | ||||
| t(b) | -2.313 | ||||
| p(b) | 0.988 | ||||
| t(a) | 0.373 | ||||
| p(a) | 0.355 | ||||
| Lowerbound of 95% confidence interval for beta | -1.641 | ||||
| Upperbound of 95% confidence interval for beta | -0.116 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.619 | ||||
| Upperbound of 95% confidence interval for alpha | 0.901 | ||||
| Treynor index (mean / b) | 0.165 | ||||
| Jensen alpha (a) | 0.141 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.319 | ||||
| Expected Shortfall on VaR | 0.378 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.124 | ||||
| Expected Shortfall on VaR | 0.254 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 53.000 | ||||
| Minimum | 0.542 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 3.528 | ||||
| Mean of quarter 1 | 0.875 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.235 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.151 | ||||
| Mean of outliers low | 0.782 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.057 | ||||
| Mean of outliers high | 2.017 | ||||
| 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) | -0.017 | ||||
| VaR(95%) (regression method) | 0.147 | ||||
| Expected Shortfall (regression method) | 0.265 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.881 | ||||
| Quartile 1 | 0.881 | ||||
| Median | 0.881 | ||||
| Quartile 3 | 0.881 | ||||
| Maximum | 0.881 | ||||
| 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) | -0.081 | ||||
| Compounded annual return (geometric extrapolation) | -0.096 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.109 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.254 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.197 | ||||
| SD | 0.889 | ||||
| Sharpe ratio (Glass type estimate) | 0.222 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.222 | ||||
| df | 1163.000 | ||||
| t | 0.469 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.708 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.152 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.708 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.152 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.414 | ||||
| Upside Potential Ratio | 3.409 | ||||
| Upside part of mean | 1.625 | ||||
| Downside part of mean | -1.427 | ||||
| Upside SD | 0.750 | ||||
| Downside SD | 0.477 | ||||
| N nonnegative terms | 96.000 | ||||
| N negative terms | 1068.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1164.000 | ||||
| Mean of predictor | 0.392 | ||||
| Mean of criterion | 0.197 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.889 | ||||
| Covariance | 0.027 | ||||
| r | 0.096 | ||||
| b (slope, estimate of beta) | 0.268 | ||||
| a (intercept, estimate of alpha) | 0.092 | ||||
| Mean Square Error | 0.783 | ||||
| DF error | 1162.000 | ||||
| t(b) | 3.271 | ||||
| p(b) | 0.452 | ||||
| t(a) | 0.219 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.107 | ||||
| Upperbound of 95% confidence interval for beta | 0.429 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.734 | ||||
| Upperbound of 95% confidence interval for alpha | 0.918 | ||||
| Treynor index (mean / b) | 0.736 | ||||
| Jensen alpha (a) | 0.092 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.144 | ||||
| SD | 0.810 | ||||
| Sharpe ratio (Glass type estimate) | -0.178 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.178 | ||||
| df | 1163.000 | ||||
| t | -0.376 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.108 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.752 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.108 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.752 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.262 | ||||
| Upside Potential Ratio | 2.577 | ||||
| Upside part of mean | 1.420 | ||||
| Downside part of mean | -1.564 | ||||
| Upside SD | 0.593 | ||||
| Downside SD | 0.551 | ||||
| N nonnegative terms | 96.000 | ||||
| N negative terms | 1068.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1164.000 | ||||
| Mean of predictor | 0.341 | ||||
| Mean of criterion | -0.144 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 0.810 | ||||
| Covariance | 0.025 | ||||
| r | 0.095 | ||||
| b (slope, estimate of beta) | 0.240 | ||||
| a (intercept, estimate of alpha) | -0.226 | ||||
| Mean Square Error | 0.650 | ||||
| DF error | 1162.000 | ||||
| t(b) | 3.247 | ||||
| p(b) | 0.453 | ||||
| t(a) | -0.590 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.095 | ||||
| Upperbound of 95% confidence interval for beta | 0.385 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.978 | ||||
| Upperbound of 95% confidence interval for alpha | 0.526 | ||||
| Treynor index (mean / b) | -0.601 | ||||
| Jensen alpha (a) | -0.226 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.040 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1164.000 | ||||
| Minimum | 0.618 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 2.016 | ||||
| Mean of quarter 1 | 0.979 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.025 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 106.000 | ||||
| Percentage of outliers low | 0.091 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 96.000 | ||||
| Percentage of outliers high | 0.082 | ||||
| Mean of outliers high | 1.075 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.935 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.003 | ||||
| Extreme Value Index (regression method) | 0.305 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.056 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.048 | ||||
| Quartile 1 | 0.069 | ||||
| Median | 0.205 | ||||
| Quartile 3 | 0.364 | ||||
| Maximum | 0.881 | ||||
| Mean of quarter 1 | 0.053 | ||||
| Mean of quarter 2 | 0.104 | ||||
| Mean of quarter 3 | 0.306 | ||||
| Mean of quarter 4 | 0.632 | ||||
| Inter Quartile Range | 0.295 | ||||
| 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 | 0.167 | ||||
| Mean of outliers high | 0.881 | ||||
| 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) | -0.081 | ||||
| Compounded annual return (geometric extrapolation) | -0.095 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.108 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.151 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.970 | ||||
| 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 | 1.163 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.330 | ||||
| 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 | 1.107 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.328 | ||||
| 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) | -8613406897598330.000 | ||||
| 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) | -223318429043615819920388235722752.000 | ||||
| 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 | ||||