Advanced Statistics: TryIt
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 | 2.994 | ||||
| SD | 6.787 | ||||
| Sharpe ratio (Glass type estimate) | 0.441 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.431 | ||||
| df | 32.000 | ||||
| t | 0.731 | ||||
| p | 0.235 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.749 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.625 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.756 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.617 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.970 | ||||
| Upside Potential Ratio | 4.331 | ||||
| Upside part of mean | 4.365 | ||||
| Downside part of mean | -1.371 | ||||
| Upside SD | 6.664 | ||||
| Downside SD | 1.008 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.633 | ||||
| Mean of criterion | 2.994 | ||||
| SD of predictor | 0.286 | ||||
| SD of criterion | 6.787 | ||||
| Covariance | -0.073 | ||||
| r | -0.038 | ||||
| b (slope, estimate of beta) | -0.892 | ||||
| a (intercept, estimate of alpha) | 3.558 | ||||
| Mean Square Error | 47.487 | ||||
| DF error | 31.000 | ||||
| t(b) | -0.209 | ||||
| p(b) | 0.582 | ||||
| t(a) | 0.718 | ||||
| p(a) | 0.239 | ||||
| Lowerbound of 95% confidence interval for beta | -9.591 | ||||
| Upperbound of 95% confidence interval for beta | 7.807 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.549 | ||||
| Upperbound of 95% confidence interval for alpha | 13.665 | ||||
| Treynor index (mean / b) | -3.357 | ||||
| Jensen alpha (a) | 3.558 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.558 | ||||
| SD | 3.997 | ||||
| Sharpe ratio (Glass type estimate) | -0.640 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.625 | ||||
| df | 32.000 | ||||
| t | -1.061 | ||||
| p | 0.852 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.827 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.557 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.817 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.567 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.691 | ||||
| Upside Potential Ratio | 0.326 | ||||
| Upside part of mean | 1.205 | ||||
| Downside part of mean | -3.764 | ||||
| Upside SD | 1.527 | ||||
| Downside SD | 3.702 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 29.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 33.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | -2.558 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 3.997 | ||||
| Covariance | 0.171 | ||||
| r | 0.155 | ||||
| b (slope, estimate of beta) | 2.247 | ||||
| a (intercept, estimate of alpha) | -3.858 | ||||
| Mean Square Error | 16.097 | ||||
| DF error | 31.000 | ||||
| t(b) | 0.874 | ||||
| p(b) | 0.194 | ||||
| t(a) | -1.359 | ||||
| p(a) | 0.908 | ||||
| Lowerbound of 95% confidence interval for beta | -2.996 | ||||
| Upperbound of 95% confidence interval for beta | 7.490 | ||||
| Lowerbound of 95% confidence interval for alpha | -9.650 | ||||
| Upperbound of 95% confidence interval for alpha | 1.934 | ||||
| Treynor index (mean / b) | -1.138 | ||||
| Jensen alpha (a) | -3.858 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.879 | ||||
| Expected Shortfall on VaR | 0.919 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.368 | ||||
| Expected Shortfall on VaR | 0.737 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 33.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 12.039 | ||||
| Mean of quarter 1 | 0.593 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 2.502 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.182 | ||||
| Mean of outliers low | 0.389 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.121 | ||||
| Mean of outliers high | 4.005 | ||||
| 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) | -1.032 | ||||
| VaR(95%) (regression method) | 0.523 | ||||
| Expected Shortfall (regression method) | 0.604 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.942 | ||||
| Quartile 1 | 0.957 | ||||
| Median | 0.971 | ||||
| Quartile 3 | 0.985 | ||||
| Maximum | 0.999 | ||||
| Mean of quarter 1 | 0.942 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.999 | ||||
| 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) | -0.363 | ||||
| Compounded annual return (geometric extrapolation) | -0.919 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.920 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.920 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 92.349 | ||||
| SD | 114.413 | ||||
| Sharpe ratio (Glass type estimate) | 0.807 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.806 | ||||
| df | 720.000 | ||||
| t | 1.339 | ||||
| p | 0.090 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.375 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.989 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.376 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.989 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 56.663 | ||||
| Upside Potential Ratio | 60.566 | ||||
| Upside part of mean | 98.710 | ||||
| Downside part of mean | -6.361 | ||||
| Upside SD | 114.464 | ||||
| Downside SD | 1.630 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 627.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 721.000 | ||||
| Mean of predictor | 0.631 | ||||
| Mean of criterion | 92.349 | ||||
| SD of predictor | 0.320 | ||||
| SD of criterion | 114.413 | ||||
| Covariance | 2.220 | ||||
| r | 0.061 | ||||
| b (slope, estimate of beta) | 21.685 | ||||
| a (intercept, estimate of alpha) | 78.675 | ||||
| Mean Square Error | 13060.238 | ||||
| DF error | 719.000 | ||||
| t(b) | 1.629 | ||||
| p(b) | 0.052 | ||||
| t(a) | 1.134 | ||||
| p(a) | 0.129 | ||||
| Lowerbound of 95% confidence interval for beta | -4.450 | ||||
| Upperbound of 95% confidence interval for beta | 47.821 | ||||
| Lowerbound of 95% confidence interval for alpha | -57.576 | ||||
| Upperbound of 95% confidence interval for alpha | 214.925 | ||||
| Treynor index (mean / b) | 4.259 | ||||
| Jensen alpha (a) | 78.675 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.557 | ||||
| SD | 6.356 | ||||
| Sharpe ratio (Glass type estimate) | -0.402 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.402 | ||||
| df | 720.000 | ||||
| t | -0.667 | ||||
| p | 0.748 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.584 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.780 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.583 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.780 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.552 | ||||
| Upside Potential Ratio | 1.836 | ||||
| Upside part of mean | 8.499 | ||||
| Downside part of mean | -11.056 | ||||
| Upside SD | 4.352 | ||||
| Downside SD | 4.629 | ||||
| N nonnegative terms | 94.000 | ||||
| N negative terms | 627.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 721.000 | ||||
| Mean of predictor | 0.578 | ||||
| Mean of criterion | -2.557 | ||||
| SD of predictor | 0.324 | ||||
| SD of criterion | 6.356 | ||||
| Covariance | 0.141 | ||||
| r | 0.069 | ||||
| b (slope, estimate of beta) | 1.351 | ||||
| a (intercept, estimate of alpha) | -3.337 | ||||
| Mean Square Error | 40.266 | ||||
| DF error | 719.000 | ||||
| t(b) | 1.848 | ||||
| p(b) | 0.032 | ||||
| t(a) | -0.867 | ||||
| p(a) | 0.807 | ||||
| Lowerbound of 95% confidence interval for beta | -0.084 | ||||
| Upperbound of 95% confidence interval for beta | 2.786 | ||||
| Lowerbound of 95% confidence interval for alpha | -10.893 | ||||
| Upperbound of 95% confidence interval for alpha | 4.218 | ||||
| Treynor index (mean / b) | -1.892 | ||||
| Jensen alpha (a) | -3.337 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.481 | ||||
| Expected Shortfall on VaR | 0.555 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.077 | ||||
| Expected Shortfall on VaR | 0.170 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 721.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 171.500 | ||||
| Mean of quarter 1 | 0.904 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 2.509 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 114.000 | ||||
| Percentage of outliers low | 0.158 | ||||
| Mean of outliers low | 0.847 | ||||
| Number of outliers high | 94.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 3.890 | ||||
| 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) | 0.281 | ||||
| VaR(95%) (regression method) | 0.077 | ||||
| Expected Shortfall (regression method) | 0.185 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.066 | ||||
| Median | 0.146 | ||||
| Quartile 3 | 0.438 | ||||
| Maximum | 0.999 | ||||
| Mean of quarter 1 | 0.041 | ||||
| Mean of quarter 2 | 0.100 | ||||
| Mean of quarter 3 | 0.197 | ||||
| Mean of quarter 4 | 0.838 | ||||
| Inter Quartile Range | 0.372 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.200 | ||||
| Mean of outliers high | 0.999 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -5615549.467 | ||||
| VaR(95%) (moments method) | 0.856 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -11.258 | ||||
| VaR(95%) (regression method) | 8.773 | ||||
| Expected Shortfall (regression method) | 8.773 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.363 | ||||
| Compounded annual return (geometric extrapolation) | -0.919 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.919 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.097 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.656 | ||||
| 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 | 1.031 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.467 | ||||
| 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 | 0.920 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.468 | ||||
| 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) | -8734967332242979.000 | ||||
| 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) | 1269646578256165274389656312479744.000 | ||||
| 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 | ||||