Advanced Statistics: Rebound Solo
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 | 0.067 | ||||
| SD | 0.162 | ||||
| Sharpe ratio (Glass type estimate) | 0.416 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.412 | ||||
| df | 82.000 | ||||
| t | 1.095 | ||||
| p | 0.138 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.333 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.163 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.335 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.160 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.786 | ||||
| Upside Potential Ratio | 2.255 | ||||
| Upside part of mean | 0.193 | ||||
| Downside part of mean | -0.126 | ||||
| Upside SD | 0.138 | ||||
| Downside SD | 0.086 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.257 | ||||
| Mean of criterion | 0.067 | ||||
| SD of predictor | 0.210 | ||||
| SD of criterion | 0.162 | ||||
| Covariance | 0.004 | ||||
| r | 0.115 | ||||
| b (slope, estimate of beta) | 0.089 | ||||
| a (intercept, estimate of alpha) | 0.045 | ||||
| Mean Square Error | 0.026 | ||||
| DF error | 81.000 | ||||
| t(b) | 1.046 | ||||
| p(b) | 0.149 | ||||
| t(a) | 0.682 | ||||
| p(a) | 0.249 | ||||
| Lowerbound of 95% confidence interval for beta | -0.080 | ||||
| Upperbound of 95% confidence interval for beta | 0.258 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.085 | ||||
| Upperbound of 95% confidence interval for alpha | 0.175 | ||||
| Treynor index (mean / b) | 0.759 | ||||
| Jensen alpha (a) | 0.045 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.055 | ||||
| SD | 0.156 | ||||
| Sharpe ratio (Glass type estimate) | 0.350 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.346 | ||||
| df | 82.000 | ||||
| t | 0.920 | ||||
| p | 0.180 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.399 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.096 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.401 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.094 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.614 | ||||
| Upside Potential Ratio | 2.065 | ||||
| Upside part of mean | 0.184 | ||||
| Downside part of mean | -0.129 | ||||
| Upside SD | 0.128 | ||||
| Downside SD | 0.089 | ||||
| N nonnegative terms | 28.000 | ||||
| N negative terms | 55.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 83.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | 0.055 | ||||
| SD of predictor | 0.201 | ||||
| SD of criterion | 0.156 | ||||
| Covariance | 0.004 | ||||
| r | 0.139 | ||||
| b (slope, estimate of beta) | 0.109 | ||||
| a (intercept, estimate of alpha) | 0.029 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 81.000 | ||||
| t(b) | 1.265 | ||||
| p(b) | 0.105 | ||||
| t(a) | 0.469 | ||||
| p(a) | 0.320 | ||||
| Lowerbound of 95% confidence interval for beta | -0.062 | ||||
| Upperbound of 95% confidence interval for beta | 0.279 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.095 | ||||
| Upperbound of 95% confidence interval for alpha | 0.154 | ||||
| Treynor index (mean / b) | 0.504 | ||||
| Jensen alpha (a) | 0.029 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.067 | ||||
| Expected Shortfall on VaR | 0.085 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 83.000 | ||||
| Minimum | 0.898 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.020 | ||||
| Maximum | 1.226 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.004 | ||||
| Mean of quarter 4 | 1.065 | ||||
| Inter Quartile Range | 0.020 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.120 | ||||
| Mean of outliers low | 0.938 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.108 | ||||
| Mean of outliers high | 1.106 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.135 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | -0.092 | ||||
| VaR(95%) (regression method) | 0.030 | ||||
| Expected Shortfall (regression method) | 0.048 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.011 | ||||
| Quartile 1 | 0.015 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.127 | ||||
| Maximum | 0.292 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.071 | ||||
| Mean of quarter 4 | 0.292 | ||||
| Inter Quartile Range | 0.112 | ||||
| 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) | 0.142 | ||||
| Compounded annual return (geometric extrapolation) | 0.104 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.355 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.355 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.226 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.089 | ||||
| SD | 0.268 | ||||
| Sharpe ratio (Glass type estimate) | 0.333 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.333 | ||||
| df | 1830.000 | ||||
| t | 0.880 | ||||
| p | 0.490 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.409 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.074 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.409 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.074 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.508 | ||||
| Upside Potential Ratio | 5.294 | ||||
| Upside part of mean | 0.931 | ||||
| Downside part of mean | -0.842 | ||||
| Upside SD | 0.203 | ||||
| Downside SD | 0.176 | ||||
| N nonnegative terms | 388.000 | ||||
| N negative terms | 1443.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1831.000 | ||||
| Mean of predictor | 0.279 | ||||
| Mean of criterion | 0.089 | ||||
| SD of predictor | 0.263 | ||||
| SD of criterion | 0.268 | ||||
| Covariance | 0.009 | ||||
| r | 0.125 | ||||
| b (slope, estimate of beta) | 0.127 | ||||
| a (intercept, estimate of alpha) | 0.054 | ||||
| Mean Square Error | 0.071 | ||||
| DF error | 1829.000 | ||||
| t(b) | 5.394 | ||||
| p(b) | 0.421 | ||||
| t(a) | 0.533 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | 0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.174 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.144 | ||||
| Upperbound of 95% confidence interval for alpha | 0.252 | ||||
| Treynor index (mean / b) | 0.701 | ||||
| Jensen alpha (a) | 0.054 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.054 | ||||
| SD | 0.266 | ||||
| Sharpe ratio (Glass type estimate) | 0.202 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.201 | ||||
| df | 1830.000 | ||||
| t | 0.533 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.540 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.943 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.540 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.943 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.296 | ||||
| Upside Potential Ratio | 5.024 | ||||
| Upside part of mean | 0.911 | ||||
| Downside part of mean | -0.858 | ||||
| Upside SD | 0.195 | ||||
| Downside SD | 0.181 | ||||
| N nonnegative terms | 388.000 | ||||
| N negative terms | 1443.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1831.000 | ||||
| Mean of predictor | 0.243 | ||||
| Mean of criterion | 0.054 | ||||
| SD of predictor | 0.265 | ||||
| SD of criterion | 0.266 | ||||
| Covariance | 0.009 | ||||
| r | 0.126 | ||||
| b (slope, estimate of beta) | 0.126 | ||||
| a (intercept, estimate of alpha) | 0.023 | ||||
| Mean Square Error | 0.070 | ||||
| DF error | 1829.000 | ||||
| t(b) | 5.421 | ||||
| p(b) | 0.420 | ||||
| t(a) | 0.229 | ||||
| p(a) | 0.497 | ||||
| Lowerbound of 95% confidence interval for beta | 0.081 | ||||
| Upperbound of 95% confidence interval for beta | 0.172 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.173 | ||||
| Upperbound of 95% confidence interval for alpha | 0.219 | ||||
| Treynor index (mean / b) | 0.425 | ||||
| Jensen alpha (a) | 0.023 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1831.000 | ||||
| Minimum | 0.876 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.181 | ||||
| Mean of quarter 1 | 0.988 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.014 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 349.000 | ||||
| Percentage of outliers low | 0.191 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 393.000 | ||||
| Percentage of outliers high | 0.215 | ||||
| Mean of outliers high | 1.017 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.324 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.124 | ||||
| VaR(95%) (regression method) | 0.012 | ||||
| Expected Shortfall (regression method) | 0.023 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 32.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.020 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.098 | ||||
| Maximum | 0.335 | ||||
| Mean of quarter 1 | 0.011 | ||||
| Mean of quarter 2 | 0.032 | ||||
| Mean of quarter 3 | 0.074 | ||||
| Mean of quarter 4 | 0.168 | ||||
| Inter Quartile Range | 0.078 | ||||
| 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 | 0.031 | ||||
| Mean of outliers high | 0.335 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.046 | ||||
| VaR(95%) (moments method) | 0.178 | ||||
| Expected Shortfall (moments method) | 0.232 | ||||
| Extreme Value Index (regression method) | 0.021 | ||||
| VaR(95%) (regression method) | 0.162 | ||||
| Expected Shortfall (regression method) | 0.200 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.140 | ||||
| Compounded annual return (geometric extrapolation) | 0.103 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.307 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.612 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.096 | ||||
| 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 | 1.069 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.332 | ||||
| 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 | 1.012 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.332 | ||||
| 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) | -8646740502666106.000 | ||||
| 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) | -213571111724105176420957999333376.000 | ||||
| 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 | ||||