Advanced Statistics: Gold Swing Survivor Futures Ptf $25K
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 | -0.027 | ||||
| SD | 0.187 | ||||
| Sharpe ratio (Glass type estimate) | -0.143 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.142 | ||||
| df | 75.000 | ||||
| t | -0.361 | ||||
| p | 0.640 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.922 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.636 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.921 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.637 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.214 | ||||
| Upside Potential Ratio | 0.898 | ||||
| Upside part of mean | 0.113 | ||||
| Downside part of mean | -0.140 | ||||
| Upside SD | 0.137 | ||||
| Downside SD | 0.125 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 76.000 | ||||
| Mean of predictor | 0.276 | ||||
| Mean of criterion | -0.027 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.187 | ||||
| Covariance | 0.002 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.020 | ||||
| a (intercept, estimate of alpha) | -0.032 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 74.000 | ||||
| t(b) | 0.288 | ||||
| p(b) | 0.387 | ||||
| t(a) | -0.420 | ||||
| p(a) | 0.662 | ||||
| Lowerbound of 95% confidence interval for beta | -0.121 | ||||
| Upperbound of 95% confidence interval for beta | 0.161 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.187 | ||||
| Upperbound of 95% confidence interval for alpha | 0.122 | ||||
| Treynor index (mean / b) | -1.316 | ||||
| Jensen alpha (a) | -0.032 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.187 | ||||
| Sharpe ratio (Glass type estimate) | -0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.232 | ||||
| df | 75.000 | ||||
| t | -0.591 | ||||
| p | 0.722 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.014 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.546 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.012 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.547 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.318 | ||||
| Upside Potential Ratio | 0.752 | ||||
| Upside part of mean | 0.104 | ||||
| Downside part of mean | -0.148 | ||||
| Upside SD | 0.125 | ||||
| Downside SD | 0.138 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 70.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 76.000 | ||||
| Mean of predictor | 0.227 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.187 | ||||
| Covariance | 0.004 | ||||
| r | 0.062 | ||||
| b (slope, estimate of beta) | 0.039 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 74.000 | ||||
| t(b) | 0.538 | ||||
| p(b) | 0.296 | ||||
| t(a) | -0.689 | ||||
| p(a) | 0.754 | ||||
| Lowerbound of 95% confidence interval for beta | -0.105 | ||||
| Upperbound of 95% confidence interval for beta | 0.182 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.205 | ||||
| Upperbound of 95% confidence interval for alpha | 0.100 | ||||
| Treynor index (mean / b) | -1.135 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.089 | ||||
| Expected Shortfall on VaR | 0.109 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.081 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 76.000 | ||||
| Minimum | 0.768 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.227 | ||||
| Mean of quarter 1 | 0.967 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.039 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.105 | ||||
| Mean of outliers low | 0.922 | ||||
| Number of outliers high | 10.000 | ||||
| Percentage of outliers high | 0.132 | ||||
| Mean of outliers high | 1.074 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -33.735 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 0.320 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.070 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.027 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.067 | ||||
| Quartile 3 | 0.170 | ||||
| Maximum | 0.362 | ||||
| Mean of quarter 1 | 0.027 | ||||
| Mean of quarter 2 | 0.028 | ||||
| Mean of quarter 3 | 0.106 | ||||
| Mean of quarter 4 | 0.362 | ||||
| Inter Quartile Range | 0.142 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.112 | ||||
| SD | 0.560 | ||||
| Sharpe ratio (Glass type estimate) | 0.200 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.200 | ||||
| df | 1676.000 | ||||
| t | 0.506 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.575 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.975 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.575 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.975 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.307 | ||||
| Upside Potential Ratio | 2.795 | ||||
| Upside part of mean | 1.021 | ||||
| Downside part of mean | -0.909 | ||||
| Upside SD | 0.425 | ||||
| Downside SD | 0.365 | ||||
| N nonnegative terms | 127.000 | ||||
| N negative terms | 1550.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1677.000 | ||||
| Mean of predictor | 0.414 | ||||
| Mean of criterion | 0.112 | ||||
| SD of predictor | 0.574 | ||||
| SD of criterion | 0.560 | ||||
| Covariance | 0.003 | ||||
| r | 0.009 | ||||
| b (slope, estimate of beta) | 0.009 | ||||
| a (intercept, estimate of alpha) | 0.108 | ||||
| Mean Square Error | 0.314 | ||||
| DF error | 1675.000 | ||||
| t(b) | 0.381 | ||||
| p(b) | 0.494 | ||||
| t(a) | 0.488 | ||||
| p(a) | 0.492 | ||||
| Lowerbound of 95% confidence interval for beta | -0.038 | ||||
| Upperbound of 95% confidence interval for beta | 0.056 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.327 | ||||
| Upperbound of 95% confidence interval for alpha | 0.543 | ||||
| Treynor index (mean / b) | 12.311 | ||||
| Jensen alpha (a) | 0.108 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.561 | ||||
| Sharpe ratio (Glass type estimate) | -0.078 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.078 | ||||
| df | 1676.000 | ||||
| t | -0.199 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.853 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.696 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.853 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.696 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.107 | ||||
| Upside Potential Ratio | 2.294 | ||||
| Upside part of mean | 0.942 | ||||
| Downside part of mean | -0.986 | ||||
| Upside SD | 0.381 | ||||
| Downside SD | 0.411 | ||||
| N nonnegative terms | 127.000 | ||||
| N negative terms | 1550.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1677.000 | ||||
| Mean of predictor | 0.251 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.570 | ||||
| SD of criterion | 0.561 | ||||
| Covariance | 0.004 | ||||
| r | 0.014 | ||||
| b (slope, estimate of beta) | 0.014 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.315 | ||||
| DF error | 1675.000 | ||||
| t(b) | 0.572 | ||||
| p(b) | 0.491 | ||||
| t(a) | -0.214 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | -0.033 | ||||
| Upperbound of 95% confidence interval for beta | 0.061 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.482 | ||||
| Upperbound of 95% confidence interval for alpha | 0.387 | ||||
| Treynor index (mean / b) | -3.202 | ||||
| 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%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.026 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1677.000 | ||||
| Minimum | 0.665 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.389 | ||||
| Mean of quarter 1 | 0.987 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 139.000 | ||||
| Percentage of outliers low | 0.083 | ||||
| Mean of outliers low | 0.960 | ||||
| Number of outliers high | 157.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.042 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.175 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| 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 | 10.000 | ||||
| Minimum | 0.009 | ||||
| Quartile 1 | 0.029 | ||||
| Median | 0.132 | ||||
| Quartile 3 | 0.229 | ||||
| Maximum | 0.364 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.047 | ||||
| Mean of quarter 3 | 0.220 | ||||
| Mean of quarter 4 | 0.317 | ||||
| Inter Quartile Range | 0.201 | ||||
| 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) | -802.074 | ||||
| VaR(95%) (moments method) | 0.333 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -4.972 | ||||
| VaR(95%) (regression method) | 0.608 | ||||
| Expected Shortfall (regression method) | 0.608 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.094 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.495 | ||||
| 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 | 0.970 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.497 | ||||
| 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) | -8736050889084595.000 | ||||
| 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) | 96908528698668187105797557190656.000 | ||||
| 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 | ||||