Advanced Statistics: SMA
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 | 0.103 | ||||
| SD | 0.207 | ||||
| Sharpe ratio (Glass type estimate) | 0.499 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.494 | ||||
| df | 70.000 | ||||
| t | 1.215 | ||||
| p | 0.114 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.312 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.308 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.316 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.304 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.227 | ||||
| Upside Potential Ratio | 2.466 | ||||
| Upside part of mean | 0.207 | ||||
| Downside part of mean | -0.104 | ||||
| Upside SD | 0.189 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.277 | ||||
| Mean of criterion | 0.103 | ||||
| SD of predictor | 0.285 | ||||
| SD of criterion | 0.207 | ||||
| Covariance | 0.006 | ||||
| r | 0.094 | ||||
| b (slope, estimate of beta) | 0.068 | ||||
| a (intercept, estimate of alpha) | 0.084 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 69.000 | ||||
| t(b) | 0.787 | ||||
| p(b) | 0.217 | ||||
| t(a) | 0.952 | ||||
| p(a) | 0.172 | ||||
| Lowerbound of 95% confidence interval for beta | -0.105 | ||||
| Upperbound of 95% confidence interval for beta | 0.242 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.092 | ||||
| Upperbound of 95% confidence interval for alpha | 0.261 | ||||
| Treynor index (mean / b) | 1.507 | ||||
| Jensen alpha (a) | 0.084 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.083 | ||||
| SD | 0.194 | ||||
| Sharpe ratio (Glass type estimate) | 0.429 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.425 | ||||
| df | 70.000 | ||||
| t | 1.044 | ||||
| p | 0.150 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.381 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.237 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.384 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.233 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.928 | ||||
| Upside Potential Ratio | 2.127 | ||||
| Upside part of mean | 0.191 | ||||
| Downside part of mean | -0.108 | ||||
| Upside SD | 0.172 | ||||
| Downside SD | 0.090 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 62.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 71.000 | ||||
| Mean of predictor | 0.234 | ||||
| Mean of criterion | 0.083 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.194 | ||||
| Covariance | 0.007 | ||||
| r | 0.123 | ||||
| b (slope, estimate of beta) | 0.086 | ||||
| a (intercept, estimate of alpha) | 0.063 | ||||
| Mean Square Error | 0.038 | ||||
| DF error | 69.000 | ||||
| t(b) | 1.033 | ||||
| p(b) | 0.153 | ||||
| t(a) | 0.770 | ||||
| p(a) | 0.222 | ||||
| Lowerbound of 95% confidence interval for beta | -0.080 | ||||
| Upperbound of 95% confidence interval for beta | 0.251 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.227 | ||||
| Treynor index (mean / b) | 0.972 | ||||
| Jensen alpha (a) | 0.063 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.082 | ||||
| Expected Shortfall on VaR | 0.103 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.057 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 71.000 | ||||
| Minimum | 0.841 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.295 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.070 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 13.000 | ||||
| Percentage of outliers low | 0.183 | ||||
| Mean of outliers low | 0.970 | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.169 | ||||
| Mean of outliers high | 1.105 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -2.278 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.747 | ||||
| VaR(95%) (regression method) | 0.024 | ||||
| Expected Shortfall (regression method) | 0.155 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.077 | ||||
| Maximum | 0.159 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.039 | ||||
| Mean of quarter 4 | 0.137 | ||||
| Inter Quartile Range | 0.067 | ||||
| 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) | 0.190 | ||||
| Compounded annual return (geometric extrapolation) | 0.136 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.855 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.991 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.322 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.283 | ||||
| SD | 0.641 | ||||
| Sharpe ratio (Glass type estimate) | 0.442 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.442 | ||||
| df | 1552.000 | ||||
| t | 1.076 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.363 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.247 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.363 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.247 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.706 | ||||
| Upside Potential Ratio | 3.978 | ||||
| Upside part of mean | 1.596 | ||||
| Downside part of mean | -1.313 | ||||
| Upside SD | 0.499 | ||||
| Downside SD | 0.401 | ||||
| N nonnegative terms | 211.000 | ||||
| N negative terms | 1342.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1553.000 | ||||
| Mean of predictor | 0.380 | ||||
| Mean of criterion | 0.283 | ||||
| SD of predictor | 0.520 | ||||
| SD of criterion | 0.641 | ||||
| Covariance | -0.003 | ||||
| r | -0.009 | ||||
| b (slope, estimate of beta) | -0.011 | ||||
| a (intercept, estimate of alpha) | 0.287 | ||||
| Mean Square Error | 0.411 | ||||
| DF error | 1551.000 | ||||
| t(b) | -0.351 | ||||
| p(b) | 0.506 | ||||
| t(a) | 1.091 | ||||
| p(a) | 0.482 | ||||
| Lowerbound of 95% confidence interval for beta | -0.072 | ||||
| Upperbound of 95% confidence interval for beta | 0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.229 | ||||
| Upperbound of 95% confidence interval for alpha | 0.804 | ||||
| Treynor index (mean / b) | -25.773 | ||||
| Jensen alpha (a) | 0.287 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.083 | ||||
| SD | 0.633 | ||||
| Sharpe ratio (Glass type estimate) | 0.131 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.131 | ||||
| df | 1552.000 | ||||
| t | 0.319 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.674 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.936 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.674 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.936 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.185 | ||||
| Upside Potential Ratio | 3.317 | ||||
| Upside part of mean | 1.489 | ||||
| Downside part of mean | -1.406 | ||||
| Upside SD | 0.445 | ||||
| Downside SD | 0.449 | ||||
| N nonnegative terms | 211.000 | ||||
| N negative terms | 1342.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1553.000 | ||||
| Mean of predictor | 0.245 | ||||
| Mean of criterion | 0.083 | ||||
| SD of predictor | 0.519 | ||||
| SD of criterion | 0.633 | ||||
| Covariance | -0.002 | ||||
| r | -0.007 | ||||
| b (slope, estimate of beta) | -0.009 | ||||
| a (intercept, estimate of alpha) | 0.085 | ||||
| Mean Square Error | 0.400 | ||||
| DF error | 1551.000 | ||||
| t(b) | -0.282 | ||||
| p(b) | 0.505 | ||||
| t(a) | 0.327 | ||||
| p(a) | 0.495 | ||||
| Lowerbound of 95% confidence interval for beta | -0.069 | ||||
| Upperbound of 95% confidence interval for beta | 0.052 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.425 | ||||
| Upperbound of 95% confidence interval for alpha | 0.595 | ||||
| Treynor index (mean / b) | -9.506 | ||||
| Jensen alpha (a) | 0.085 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.062 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.036 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1553.000 | ||||
| Minimum | 0.638 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.561 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.024 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 197.000 | ||||
| Percentage of outliers low | 0.127 | ||||
| Mean of outliers low | 0.962 | ||||
| Number of outliers high | 231.000 | ||||
| Percentage of outliers high | 0.149 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.239 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.253 | ||||
| VaR(95%) (regression method) | 0.014 | ||||
| Expected Shortfall (regression method) | 0.040 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 22.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.047 | ||||
| Median | 0.125 | ||||
| Quartile 3 | 0.161 | ||||
| Maximum | 0.370 | ||||
| Mean of quarter 1 | 0.025 | ||||
| Mean of quarter 2 | 0.075 | ||||
| Mean of quarter 3 | 0.135 | ||||
| Mean of quarter 4 | 0.230 | ||||
| Inter Quartile Range | 0.114 | ||||
| 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 | 0.045 | ||||
| Mean of outliers high | 0.370 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.009 | ||||
| VaR(95%) (moments method) | 0.252 | ||||
| Expected Shortfall (moments method) | 0.311 | ||||
| Extreme Value Index (regression method) | 0.728 | ||||
| VaR(95%) (regression method) | 0.276 | ||||
| Expected Shortfall (regression method) | 0.713 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.189 | ||||
| Compounded annual return (geometric extrapolation) | 0.135 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.366 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.589 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.757 | ||||
| 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 | 1.044 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.508 | ||||
| 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 | 0.913 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.509 | ||||
| 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) | -8745747991238709.000 | ||||
| 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) | -341557401974158478833484707135488.000 | ||||
| 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 | ||||