Advanced Statistics: MSTCOURTJESTER
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 | -0.043 | ||||
| SD | 0.060 | ||||
| Sharpe ratio (Glass type estimate) | -0.720 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.714 | ||||
| df | 83.000 | ||||
| t | -1.906 | ||||
| p | 0.970 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.467 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.031 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.462 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.035 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.837 | ||||
| Upside Potential Ratio | 0.502 | ||||
| Upside part of mean | 0.026 | ||||
| Downside part of mean | -0.069 | ||||
| Upside SD | 0.032 | ||||
| Downside SD | 0.051 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 76.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.134 | ||||
| Mean of criterion | -0.043 | ||||
| SD of predictor | 0.242 | ||||
| SD of criterion | 0.060 | ||||
| Covariance | 0.001 | ||||
| r | 0.079 | ||||
| b (slope, estimate of beta) | 0.020 | ||||
| a (intercept, estimate of alpha) | -0.046 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 82.000 | ||||
| t(b) | 0.721 | ||||
| p(b) | 0.237 | ||||
| t(a) | -1.991 | ||||
| p(a) | 0.975 | ||||
| Lowerbound of 95% confidence interval for beta | -0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.074 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.091 | ||||
| Upperbound of 95% confidence interval for alpha | -0.000 | ||||
| Treynor index (mean / b) | -2.194 | ||||
| Jensen alpha (a) | -0.046 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 0.061 | ||||
| Sharpe ratio (Glass type estimate) | -0.730 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.724 | ||||
| df | 83.000 | ||||
| t | -1.932 | ||||
| p | 0.972 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.477 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.021 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.473 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.025 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.832 | ||||
| Upside Potential Ratio | 0.468 | ||||
| Upside part of mean | 0.025 | ||||
| Downside part of mean | -0.070 | ||||
| Upside SD | 0.031 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 76.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.105 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.239 | ||||
| SD of criterion | 0.061 | ||||
| Covariance | 0.001 | ||||
| r | 0.084 | ||||
| b (slope, estimate of beta) | 0.022 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.004 | ||||
| DF error | 82.000 | ||||
| t(b) | 0.767 | ||||
| p(b) | 0.223 | ||||
| t(a) | -2.009 | ||||
| p(a) | 0.976 | ||||
| Lowerbound of 95% confidence interval for beta | -0.035 | ||||
| Upperbound of 95% confidence interval for beta | 0.078 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.093 | ||||
| Upperbound of 95% confidence interval for alpha | -0.000 | ||||
| Treynor index (mean / b) | -2.063 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.032 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.887 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.061 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.010 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.155 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 17.000 | ||||
| Percentage of outliers high | 0.202 | ||||
| Mean of outliers high | 1.013 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.390 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.001 | ||||
| Extreme Value Index (regression method) | 1.132 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.004 | ||||
| Quartile 3 | 0.048 | ||||
| Maximum | 0.116 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.048 | ||||
| Mean of quarter 4 | 0.116 | ||||
| Inter Quartile Range | 0.048 | ||||
| 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) | -0.001 | ||||
| Compounded annual return (geometric extrapolation) | -0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.006 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.006 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.017 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -0.527 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.527 | ||||
| df | 1848.000 | ||||
| t | -1.401 | ||||
| p | 0.516 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.265 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.211 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.265 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.211 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.775 | ||||
| Upside Potential Ratio | 2.530 | ||||
| Upside part of mean | 0.136 | ||||
| Downside part of mean | -0.177 | ||||
| Upside SD | 0.058 | ||||
| Downside SD | 0.054 | ||||
| N nonnegative terms | 169.000 | ||||
| N negative terms | 1680.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1849.000 | ||||
| Mean of predictor | 0.243 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.558 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.008 | ||||
| r | 0.175 | ||||
| b (slope, estimate of beta) | 0.025 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1847.000 | ||||
| t(b) | 7.647 | ||||
| p(b) | 0.389 | ||||
| t(a) | -1.628 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | 0.018 | ||||
| Upperbound of 95% confidence interval for beta | 0.031 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.105 | ||||
| Upperbound of 95% confidence interval for alpha | 0.010 | ||||
| Treynor index (mean / b) | -1.681 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.045 | ||||
| SD | 0.079 | ||||
| Sharpe ratio (Glass type estimate) | -0.568 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.568 | ||||
| df | 1848.000 | ||||
| t | -1.510 | ||||
| p | 0.518 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.306 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.170 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.306 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.170 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.818 | ||||
| Upside Potential Ratio | 2.454 | ||||
| Upside part of mean | 0.134 | ||||
| Downside part of mean | -0.179 | ||||
| Upside SD | 0.057 | ||||
| Downside SD | 0.055 | ||||
| N nonnegative terms | 169.000 | ||||
| N negative terms | 1680.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1849.000 | ||||
| Mean of predictor | 0.093 | ||||
| Mean of criterion | -0.045 | ||||
| SD of predictor | 0.547 | ||||
| SD of criterion | 0.079 | ||||
| Covariance | 0.008 | ||||
| r | 0.178 | ||||
| b (slope, estimate of beta) | 0.026 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 1847.000 | ||||
| t(b) | 7.793 | ||||
| p(b) | 0.387 | ||||
| t(a) | -1.616 | ||||
| p(a) | 0.524 | ||||
| Lowerbound of 95% confidence interval for beta | 0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.104 | ||||
| Upperbound of 95% confidence interval for alpha | 0.010 | ||||
| Treynor index (mean / b) | -1.742 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1849.000 | ||||
| Minimum | 0.933 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.077 | ||||
| Mean of quarter 1 | 0.998 | ||||
| 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 | 201.000 | ||||
| Percentage of outliers low | 0.109 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 209.000 | ||||
| Percentage of outliers high | 0.113 | ||||
| Mean of outliers high | 1.005 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.749 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.009 | ||||
| Extreme Value Index (regression method) | 0.386 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.006 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.007 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.051 | ||||
| Maximum | 0.161 | ||||
| Mean of quarter 1 | 0.008 | ||||
| Mean of quarter 2 | 0.012 | ||||
| Mean of quarter 3 | 0.031 | ||||
| Mean of quarter 4 | 0.110 | ||||
| Inter Quartile Range | 0.040 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.161 | ||||
| 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) | -0.001 | ||||
| Compounded annual return (geometric extrapolation) | -0.001 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.004 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.006 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.067 | ||||
| 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 | 0.775 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.564 | ||||
| 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 | 0.610 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.582 | ||||
| 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) | -8781226945611536.000 | ||||
| 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) | 2455317137882858996120313615351808.000 | ||||
| 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 | ||||