Advanced Statistics: Master Mini S&P
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 | -0.051 | ||||
| SD | 0.323 | ||||
| Sharpe ratio (Glass type estimate) | -0.159 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.158 | ||||
| df | 89.000 | ||||
| t | -0.435 | ||||
| p | 0.668 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.875 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.557 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.874 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.558 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.276 | ||||
| Upside Potential Ratio | 0.694 | ||||
| Upside part of mean | 0.129 | ||||
| Downside part of mean | -0.181 | ||||
| Upside SD | 0.262 | ||||
| Downside SD | 0.186 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 88.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.200 | ||||
| Mean of criterion | -0.051 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.323 | ||||
| Covariance | 0.001 | ||||
| r | 0.017 | ||||
| b (slope, estimate of beta) | 0.020 | ||||
| a (intercept, estimate of alpha) | -0.055 | ||||
| Mean Square Error | 0.105 | ||||
| DF error | 88.000 | ||||
| t(b) | 0.158 | ||||
| p(b) | 0.437 | ||||
| t(a) | -0.457 | ||||
| p(a) | 0.675 | ||||
| Lowerbound of 95% confidence interval for beta | -0.230 | ||||
| Upperbound of 95% confidence interval for beta | 0.270 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.296 | ||||
| Upperbound of 95% confidence interval for alpha | 0.185 | ||||
| Treynor index (mean / b) | -2.571 | ||||
| Jensen alpha (a) | -0.055 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.097 | ||||
| SD | 0.300 | ||||
| Sharpe ratio (Glass type estimate) | -0.324 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.321 | ||||
| df | 89.000 | ||||
| t | -0.888 | ||||
| p | 0.811 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.040 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.394 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.039 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.396 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.449 | ||||
| Upside Potential Ratio | 0.479 | ||||
| Upside part of mean | 0.104 | ||||
| Downside part of mean | -0.201 | ||||
| Upside SD | 0.207 | ||||
| Downside SD | 0.216 | ||||
| N nonnegative terms | 2.000 | ||||
| N negative terms | 88.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.161 | ||||
| Mean of criterion | -0.097 | ||||
| SD of predictor | 0.273 | ||||
| SD of criterion | 0.300 | ||||
| Covariance | 0.003 | ||||
| r | 0.033 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | -0.103 | ||||
| Mean Square Error | 0.091 | ||||
| DF error | 88.000 | ||||
| t(b) | 0.309 | ||||
| p(b) | 0.379 | ||||
| t(a) | -0.923 | ||||
| p(a) | 0.821 | ||||
| Lowerbound of 95% confidence interval for beta | -0.196 | ||||
| Upperbound of 95% confidence interval for beta | 0.269 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.325 | ||||
| Upperbound of 95% confidence interval for alpha | 0.119 | ||||
| Treynor index (mean / b) | -2.689 | ||||
| Jensen alpha (a) | -0.103 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.140 | ||||
| Expected Shortfall on VaR | 0.170 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.052 | ||||
| Expected Shortfall on VaR | 0.110 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 90.000 | ||||
| Minimum | 0.671 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.637 | ||||
| Mean of quarter 1 | 0.955 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.042 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 6.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.828 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.022 | ||||
| Mean of outliers high | 1.488 | ||||
| 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) | -0.353 | ||||
| VaR(95%) (regression method) | 0.065 | ||||
| Expected Shortfall (regression method) | 0.167 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.540 | ||||
| Quartile 1 | 0.540 | ||||
| Median | 0.540 | ||||
| Quartile 3 | 0.540 | ||||
| Maximum | 0.540 | ||||
| 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 | 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) | -0.044 | ||||
| Compounded annual return (geometric extrapolation) | -0.052 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.096 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.305 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.010 | ||||
| SD | 0.470 | ||||
| Sharpe ratio (Glass type estimate) | 0.021 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.021 | ||||
| df | 1980.000 | ||||
| t | 0.057 | ||||
| p | 0.499 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.692 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.734 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.692 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.734 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.033 | ||||
| Upside Potential Ratio | 1.892 | ||||
| Upside part of mean | 0.558 | ||||
| Downside part of mean | -0.549 | ||||
| Upside SD | 0.366 | ||||
| Downside SD | 0.295 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 1910.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1981.000 | ||||
| Mean of predictor | 0.309 | ||||
| Mean of criterion | 0.010 | ||||
| SD of predictor | 0.509 | ||||
| SD of criterion | 0.470 | ||||
| Covariance | 0.015 | ||||
| r | 0.062 | ||||
| b (slope, estimate of beta) | 0.057 | ||||
| a (intercept, estimate of alpha) | -0.008 | ||||
| Mean Square Error | 0.220 | ||||
| DF error | 1979.000 | ||||
| t(b) | 2.757 | ||||
| p(b) | 0.461 | ||||
| t(a) | -0.046 | ||||
| p(a) | 0.501 | ||||
| Lowerbound of 95% confidence interval for beta | 0.017 | ||||
| Upperbound of 95% confidence interval for beta | 0.098 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.343 | ||||
| Upperbound of 95% confidence interval for alpha | 0.327 | ||||
| Treynor index (mean / b) | 0.171 | ||||
| Jensen alpha (a) | -0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.097 | ||||
| SD | 0.463 | ||||
| Sharpe ratio (Glass type estimate) | -0.209 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.209 | ||||
| df | 1980.000 | ||||
| t | -0.575 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.922 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.504 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.922 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.504 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.278 | ||||
| Upside Potential Ratio | 1.453 | ||||
| Upside part of mean | 0.506 | ||||
| Downside part of mean | -0.603 | ||||
| Upside SD | 0.306 | ||||
| Downside SD | 0.348 | ||||
| N nonnegative terms | 71.000 | ||||
| N negative terms | 1910.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1981.000 | ||||
| Mean of predictor | 0.179 | ||||
| Mean of criterion | -0.097 | ||||
| SD of predictor | 0.512 | ||||
| SD of criterion | 0.463 | ||||
| Covariance | 0.014 | ||||
| r | 0.058 | ||||
| b (slope, estimate of beta) | 0.052 | ||||
| a (intercept, estimate of alpha) | -0.106 | ||||
| Mean Square Error | 0.214 | ||||
| DF error | 1979.000 | ||||
| t(b) | 2.575 | ||||
| p(b) | 0.463 | ||||
| t(a) | -0.631 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.012 | ||||
| Upperbound of 95% confidence interval for beta | 0.092 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.436 | ||||
| Upperbound of 95% confidence interval for alpha | 0.224 | ||||
| Treynor index (mean / b) | -1.851 | ||||
| Jensen alpha (a) | -0.106 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.058 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1981.000 | ||||
| Minimum | 0.577 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.622 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 57.000 | ||||
| Percentage of outliers low | 0.029 | ||||
| Mean of outliers low | 0.933 | ||||
| Number of outliers high | 71.000 | ||||
| Percentage of outliers high | 0.036 | ||||
| Mean of outliers high | 1.060 | ||||
| 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 | 2.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.143 | ||||
| Median | 0.285 | ||||
| Quartile 3 | 0.427 | ||||
| Maximum | 0.569 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.569 | ||||
| Inter Quartile Range | 0.284 | ||||
| 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) | -0.044 | ||||
| Compounded annual return (geometric extrapolation) | -0.051 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.090 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.090 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.893 | ||||
| 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 | 0.981 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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 | 0.866 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.477 | ||||
| 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) | -8744511403379564.000 | ||||
| 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) | -113952167168331844466657646870528.000 | ||||
| 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 | ||||