Advanced Statistics: Spectre Short Nikkei/S & P 500 Futures
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 | -0.029 | ||||
| SD | 0.195 | ||||
| Sharpe ratio (Glass type estimate) | -0.148 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.147 | ||||
| df | 83.000 | ||||
| t | -0.392 | ||||
| p | 0.652 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.889 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.593 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.888 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.594 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.243 | ||||
| Upside Potential Ratio | 0.646 | ||||
| Upside part of mean | 0.077 | ||||
| Downside part of mean | -0.106 | ||||
| Upside SD | 0.153 | ||||
| Downside SD | 0.119 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.211 | ||||
| Mean of criterion | -0.029 | ||||
| SD of predictor | 0.294 | ||||
| SD of criterion | 0.195 | ||||
| Covariance | -0.005 | ||||
| r | -0.079 | ||||
| b (slope, estimate of beta) | -0.052 | ||||
| a (intercept, estimate of alpha) | -0.018 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.714 | ||||
| p(b) | 0.761 | ||||
| t(a) | -0.237 | ||||
| p(a) | 0.593 | ||||
| Lowerbound of 95% confidence interval for beta | -0.198 | ||||
| Upperbound of 95% confidence interval for beta | 0.093 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.168 | ||||
| Upperbound of 95% confidence interval for alpha | 0.132 | ||||
| Treynor index (mean / b) | 0.554 | ||||
| Jensen alpha (a) | -0.018 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.047 | ||||
| SD | 0.188 | ||||
| Sharpe ratio (Glass type estimate) | -0.248 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.245 | ||||
| df | 83.000 | ||||
| t | -0.655 | ||||
| p | 0.743 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.989 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.495 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.987 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.496 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.348 | ||||
| Upside Potential Ratio | 0.501 | ||||
| Upside part of mean | 0.067 | ||||
| Downside part of mean | -0.114 | ||||
| Upside SD | 0.132 | ||||
| Downside SD | 0.134 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 77.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 84.000 | ||||
| Mean of predictor | 0.168 | ||||
| Mean of criterion | -0.047 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.188 | ||||
| Covariance | -0.004 | ||||
| r | -0.081 | ||||
| b (slope, estimate of beta) | -0.053 | ||||
| a (intercept, estimate of alpha) | -0.038 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 82.000 | ||||
| t(b) | -0.734 | ||||
| p(b) | 0.768 | ||||
| t(a) | -0.521 | ||||
| p(a) | 0.698 | ||||
| Lowerbound of 95% confidence interval for beta | -0.197 | ||||
| Upperbound of 95% confidence interval for beta | 0.091 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.182 | ||||
| Upperbound of 95% confidence interval for alpha | 0.106 | ||||
| Treynor index (mean / b) | 0.879 | ||||
| Jensen alpha (a) | -0.038 | ||||
| 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%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.063 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 84.000 | ||||
| Minimum | 0.772 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.377 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.143 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.155 | ||||
| Mean of outliers high | 1.044 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 2.060 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.275 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.208 | ||||
| Quartile 1 | 0.213 | ||||
| Median | 0.218 | ||||
| Quartile 3 | 0.223 | ||||
| Maximum | 0.228 | ||||
| Mean of quarter 1 | 0.208 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.228 | ||||
| Inter Quartile Range | 0.010 | ||||
| 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) | -0.003 | ||||
| Compounded annual return (geometric extrapolation) | -0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.012 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.012 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.024 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.337 | ||||
| SD | 1.290 | ||||
| Sharpe ratio (Glass type estimate) | 0.262 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.261 | ||||
| df | 1854.000 | ||||
| t | 0.696 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.475 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.998 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.475 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.998 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.047 | ||||
| Upside Potential Ratio | 2.337 | ||||
| Upside part of mean | 0.753 | ||||
| Downside part of mean | -0.416 | ||||
| Upside SD | 1.249 | ||||
| Downside SD | 0.322 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 1702.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1855.000 | ||||
| Mean of predictor | 0.332 | ||||
| Mean of criterion | 0.337 | ||||
| SD of predictor | 0.527 | ||||
| SD of criterion | 1.290 | ||||
| Covariance | -0.011 | ||||
| r | -0.016 | ||||
| b (slope, estimate of beta) | -0.039 | ||||
| a (intercept, estimate of alpha) | 0.350 | ||||
| Mean Square Error | 1.666 | ||||
| DF error | 1853.000 | ||||
| t(b) | -0.684 | ||||
| p(b) | 0.510 | ||||
| t(a) | 0.722 | ||||
| p(a) | 0.489 | ||||
| Lowerbound of 95% confidence interval for beta | -0.151 | ||||
| Upperbound of 95% confidence interval for beta | 0.073 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.602 | ||||
| Upperbound of 95% confidence interval for alpha | 1.302 | ||||
| Treynor index (mean / b) | -8.666 | ||||
| Jensen alpha (a) | 0.350 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.047 | ||||
| SD | 0.809 | ||||
| Sharpe ratio (Glass type estimate) | -0.058 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.058 | ||||
| df | 1854.000 | ||||
| t | -0.153 | ||||
| p | 0.502 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.794 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.679 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.794 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.679 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.082 | ||||
| Upside Potential Ratio | 0.841 | ||||
| Upside part of mean | 0.478 | ||||
| Downside part of mean | -0.524 | ||||
| Upside SD | 0.576 | ||||
| Downside SD | 0.568 | ||||
| N nonnegative terms | 153.000 | ||||
| N negative terms | 1702.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1855.000 | ||||
| Mean of predictor | 0.194 | ||||
| Mean of criterion | -0.047 | ||||
| SD of predictor | 0.527 | ||||
| SD of criterion | 0.809 | ||||
| Covariance | -0.010 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.034 | ||||
| a (intercept, estimate of alpha) | -0.040 | ||||
| Mean Square Error | 0.654 | ||||
| DF error | 1853.000 | ||||
| t(b) | -0.961 | ||||
| p(b) | 0.514 | ||||
| t(a) | -0.132 | ||||
| p(a) | 0.502 | ||||
| Lowerbound of 95% confidence interval for beta | -0.104 | ||||
| Upperbound of 95% confidence interval for beta | 0.036 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.636 | ||||
| Upperbound of 95% confidence interval for alpha | 0.556 | ||||
| Treynor index (mean / b) | 1.362 | ||||
| Jensen alpha (a) | -0.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.079 | ||||
| Expected Shortfall on VaR | 0.098 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1855.000 | ||||
| Minimum | 0.234 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 4.280 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 234.000 | ||||
| Percentage of outliers low | 0.126 | ||||
| Mean of outliers low | 0.989 | ||||
| Number of outliers high | 222.000 | ||||
| Percentage of outliers high | 0.120 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.682 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.004 | ||||
| VaR(95%) (regression method) | 0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.127 | ||||
| Median | 0.322 | ||||
| Quartile 3 | 0.549 | ||||
| Maximum | 0.767 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.168 | ||||
| Mean of quarter 3 | 0.476 | ||||
| Mean of quarter 4 | 0.767 | ||||
| Inter Quartile Range | 0.421 | ||||
| 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) | -0.003 | ||||
| Compounded annual return (geometric extrapolation) | -0.003 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.003 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.003 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.027 | ||||
| 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 | 1.099 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.491 | ||||
| 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 | 0.977 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.493 | ||||
| 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) | -8734212138974364.000 | ||||
| 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) | -588831142125270751271385965789184.000 | ||||
| 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 | ||||