Advanced Statistics: mvp-3
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 | 0.012 | ||||
| SD | 0.519 | ||||
| Sharpe ratio (Glass type estimate) | 0.022 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.022 | ||||
| df | 79.000 | ||||
| t | 0.058 | ||||
| p | 0.477 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.737 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.781 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.737 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.781 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.036 | ||||
| Upside Potential Ratio | 1.566 | ||||
| Upside part of mean | 0.511 | ||||
| Downside part of mean | -0.500 | ||||
| Upside SD | 0.400 | ||||
| Downside SD | 0.326 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.248 | ||||
| Mean of criterion | 0.012 | ||||
| SD of predictor | 0.316 | ||||
| SD of criterion | 0.519 | ||||
| Covariance | 0.020 | ||||
| r | 0.119 | ||||
| b (slope, estimate of beta) | 0.196 | ||||
| a (intercept, estimate of alpha) | -0.037 | ||||
| Mean Square Error | 0.269 | ||||
| DF error | 78.000 | ||||
| t(b) | 1.062 | ||||
| p(b) | 0.146 | ||||
| t(a) | -0.180 | ||||
| p(a) | 0.571 | ||||
| Lowerbound of 95% confidence interval for beta | -0.172 | ||||
| Upperbound of 95% confidence interval for beta | 0.564 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.447 | ||||
| Upperbound of 95% confidence interval for alpha | 0.373 | ||||
| Treynor index (mean / b) | 0.059 | ||||
| Jensen alpha (a) | -0.037 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.118 | ||||
| SD | 0.517 | ||||
| Sharpe ratio (Glass type estimate) | -0.228 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.226 | ||||
| df | 79.000 | ||||
| t | -0.589 | ||||
| p | 0.721 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.987 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.532 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.986 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.534 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.298 | ||||
| Upside Potential Ratio | 1.133 | ||||
| Upside part of mean | 0.448 | ||||
| Downside part of mean | -0.566 | ||||
| Upside SD | 0.329 | ||||
| Downside SD | 0.396 | ||||
| N nonnegative terms | 22.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 80.000 | ||||
| Mean of predictor | 0.199 | ||||
| Mean of criterion | -0.118 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.517 | ||||
| Covariance | 0.028 | ||||
| r | 0.180 | ||||
| b (slope, estimate of beta) | 0.309 | ||||
| a (intercept, estimate of alpha) | -0.180 | ||||
| Mean Square Error | 0.262 | ||||
| DF error | 78.000 | ||||
| t(b) | 1.613 | ||||
| p(b) | 0.055 | ||||
| t(a) | -0.891 | ||||
| p(a) | 0.812 | ||||
| Lowerbound of 95% confidence interval for beta | -0.072 | ||||
| Upperbound of 95% confidence interval for beta | 0.691 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.581 | ||||
| Upperbound of 95% confidence interval for alpha | 0.222 | ||||
| Treynor index (mean / b) | -0.381 | ||||
| Jensen alpha (a) | -0.180 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.225 | ||||
| Expected Shortfall on VaR | 0.271 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.120 | ||||
| Expected Shortfall on VaR | 0.234 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 80.000 | ||||
| Minimum | 0.502 | ||||
| Quartile 1 | 0.973 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.012 | ||||
| Maximum | 1.759 | ||||
| Mean of quarter 1 | 0.847 | ||||
| Mean of quarter 2 | 0.997 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.174 | ||||
| Inter Quartile Range | 0.039 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.175 | ||||
| Mean of outliers low | 0.803 | ||||
| Number of outliers high | 14.000 | ||||
| Percentage of outliers high | 0.175 | ||||
| Mean of outliers high | 1.228 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.454 | ||||
| VaR(95%) (moments method) | 0.105 | ||||
| Expected Shortfall (moments method) | 0.127 | ||||
| Extreme Value Index (regression method) | -0.038 | ||||
| VaR(95%) (regression method) | 0.140 | ||||
| Expected Shortfall (regression method) | 0.203 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.042 | ||||
| Quartile 1 | 0.283 | ||||
| Median | 0.350 | ||||
| Quartile 3 | 0.511 | ||||
| Maximum | 0.750 | ||||
| Mean of quarter 1 | 0.163 | ||||
| Mean of quarter 2 | 0.350 | ||||
| Mean of quarter 3 | 0.511 | ||||
| Mean of quarter 4 | 0.750 | ||||
| Inter Quartile Range | 0.227 | ||||
| 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) | -0.058 | ||||
| Compounded annual return (geometric extrapolation) | -0.071 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.095 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.095 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.263 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.752 | ||||
| SD | 1.380 | ||||
| Sharpe ratio (Glass type estimate) | 0.544 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.544 | ||||
| df | 1758.000 | ||||
| t | 1.411 | ||||
| p | 0.483 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.212 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.301 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.212 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.301 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.975 | ||||
| Upside Potential Ratio | 5.583 | ||||
| Upside part of mean | 4.305 | ||||
| Downside part of mean | -3.554 | ||||
| Upside SD | 1.145 | ||||
| Downside SD | 0.771 | ||||
| N nonnegative terms | 420.000 | ||||
| N negative terms | 1339.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1759.000 | ||||
| Mean of predictor | 0.346 | ||||
| Mean of criterion | 0.752 | ||||
| SD of predictor | 0.511 | ||||
| SD of criterion | 1.380 | ||||
| Covariance | 0.185 | ||||
| r | 0.263 | ||||
| b (slope, estimate of beta) | 0.711 | ||||
| a (intercept, estimate of alpha) | 0.505 | ||||
| Mean Square Error | 1.775 | ||||
| DF error | 1757.000 | ||||
| t(b) | 11.420 | ||||
| p(b) | 0.335 | ||||
| t(a) | 0.982 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | 0.589 | ||||
| Upperbound of 95% confidence interval for beta | 0.833 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.504 | ||||
| Upperbound of 95% confidence interval for alpha | 1.515 | ||||
| Treynor index (mean / b) | 1.058 | ||||
| Jensen alpha (a) | 0.505 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.117 | ||||
| SD | 1.307 | ||||
| Sharpe ratio (Glass type estimate) | -0.090 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.090 | ||||
| df | 1758.000 | ||||
| t | -0.233 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.846 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.667 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.846 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.667 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.128 | ||||
| Upside Potential Ratio | 4.145 | ||||
| Upside part of mean | 3.810 | ||||
| Downside part of mean | -3.928 | ||||
| Upside SD | 0.929 | ||||
| Downside SD | 0.919 | ||||
| N nonnegative terms | 420.000 | ||||
| N negative terms | 1339.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1759.000 | ||||
| Mean of predictor | 0.216 | ||||
| Mean of criterion | -0.117 | ||||
| SD of predictor | 0.511 | ||||
| SD of criterion | 1.307 | ||||
| Covariance | 0.175 | ||||
| r | 0.262 | ||||
| b (slope, estimate of beta) | 0.668 | ||||
| a (intercept, estimate of alpha) | -0.262 | ||||
| Mean Square Error | 1.593 | ||||
| DF error | 1757.000 | ||||
| t(b) | 11.358 | ||||
| p(b) | 0.335 | ||||
| t(a) | -0.537 | ||||
| p(a) | 0.508 | ||||
| Lowerbound of 95% confidence interval for beta | 0.553 | ||||
| Upperbound of 95% confidence interval for beta | 0.784 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.217 | ||||
| Upperbound of 95% confidence interval for alpha | 0.694 | ||||
| Treynor index (mean / b) | -0.176 | ||||
| Jensen alpha (a) | -0.262 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.125 | ||||
| Expected Shortfall on VaR | 0.153 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.040 | ||||
| Expected Shortfall on VaR | 0.087 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1759.000 | ||||
| Minimum | 0.510 | ||||
| Quartile 1 | 0.997 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.866 | ||||
| Mean of quarter 1 | 0.946 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.066 | ||||
| Inter Quartile Range | 0.003 | ||||
| Number outliers low | 387.000 | ||||
| Percentage of outliers low | 0.220 | ||||
| Mean of outliers low | 0.940 | ||||
| Number of outliers high | 375.000 | ||||
| Percentage of outliers high | 0.213 | ||||
| Mean of outliers high | 1.077 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.927 | ||||
| VaR(95%) (moments method) | 0.026 | ||||
| Expected Shortfall (moments method) | 0.410 | ||||
| Extreme Value Index (regression method) | 0.434 | ||||
| VaR(95%) (regression method) | 0.040 | ||||
| Expected Shortfall (regression method) | 0.097 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 16.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.139 | ||||
| Median | 0.286 | ||||
| Quartile 3 | 0.421 | ||||
| Maximum | 0.801 | ||||
| Mean of quarter 1 | 0.056 | ||||
| Mean of quarter 2 | 0.207 | ||||
| Mean of quarter 3 | 0.355 | ||||
| Mean of quarter 4 | 0.608 | ||||
| Inter Quartile Range | 0.281 | ||||
| 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) | -0.731 | ||||
| VaR(95%) (moments method) | 0.688 | ||||
| Expected Shortfall (moments method) | 0.745 | ||||
| Extreme Value Index (regression method) | -0.044 | ||||
| VaR(95%) (regression method) | 0.742 | ||||
| Expected Shortfall (regression method) | 0.907 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.058 | ||||
| Compounded annual return (geometric extrapolation) | -0.071 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.088 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.116 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.461 | ||||
| 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 | 1.064 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.521 | ||||
| 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 | 0.925 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.526 | ||||
| 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) | -8747816172130090.000 | ||||
| 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) | -93275813890005126468468794720256.000 | ||||
| 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 | ||||