Advanced Statistics: Q5SideWinder
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 | 0.059 | ||||
| SD | 0.297 | ||||
| Sharpe ratio (Glass type estimate) | 0.200 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.198 | ||||
| df | 89.000 | ||||
| t | 0.548 | ||||
| p | 0.293 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.517 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.916 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.518 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.915 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.297 | ||||
| Upside Potential Ratio | 1.849 | ||||
| Upside part of mean | 0.370 | ||||
| Downside part of mean | -0.310 | ||||
| Upside SD | 0.219 | ||||
| Downside SD | 0.200 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.221 | ||||
| Mean of criterion | 0.059 | ||||
| SD of predictor | 0.195 | ||||
| SD of criterion | 0.297 | ||||
| Covariance | 0.011 | ||||
| r | 0.183 | ||||
| b (slope, estimate of beta) | 0.279 | ||||
| a (intercept, estimate of alpha) | -0.002 | ||||
| Mean Square Error | 0.086 | ||||
| DF error | 88.000 | ||||
| t(b) | 1.743 | ||||
| p(b) | 0.042 | ||||
| t(a) | -0.019 | ||||
| p(a) | 0.507 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.597 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.227 | ||||
| Upperbound of 95% confidence interval for alpha | 0.223 | ||||
| Treynor index (mean / b) | 0.213 | ||||
| Jensen alpha (a) | -0.002 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.014 | ||||
| SD | 0.307 | ||||
| Sharpe ratio (Glass type estimate) | 0.046 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.045 | ||||
| df | 89.000 | ||||
| t | 0.125 | ||||
| p | 0.450 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.670 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.761 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.670 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.761 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.061 | ||||
| Upside Potential Ratio | 1.511 | ||||
| Upside part of mean | 0.347 | ||||
| Downside part of mean | -0.333 | ||||
| Upside SD | 0.201 | ||||
| Downside SD | 0.230 | ||||
| N nonnegative terms | 36.000 | ||||
| N negative terms | 54.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 90.000 | ||||
| Mean of predictor | 0.201 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.187 | ||||
| SD of criterion | 0.307 | ||||
| Covariance | 0.012 | ||||
| r | 0.202 | ||||
| b (slope, estimate of beta) | 0.331 | ||||
| a (intercept, estimate of alpha) | -0.052 | ||||
| Mean Square Error | 0.091 | ||||
| DF error | 88.000 | ||||
| t(b) | 1.932 | ||||
| p(b) | 0.028 | ||||
| t(a) | -0.452 | ||||
| p(a) | 0.674 | ||||
| Lowerbound of 95% confidence interval for beta | -0.009 | ||||
| Upperbound of 95% confidence interval for beta | 0.671 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.282 | ||||
| Upperbound of 95% confidence interval for alpha | 0.177 | ||||
| Treynor index (mean / b) | 0.042 | ||||
| Jensen alpha (a) | -0.052 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.135 | ||||
| Expected Shortfall on VaR | 0.166 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.066 | ||||
| Expected Shortfall on VaR | 0.132 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 90.000 | ||||
| Minimum | 0.627 | ||||
| Quartile 1 | 0.973 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.053 | ||||
| Maximum | 1.307 | ||||
| Mean of quarter 1 | 0.914 | ||||
| Mean of quarter 2 | 0.993 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.113 | ||||
| Inter Quartile Range | 0.080 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.011 | ||||
| Mean of outliers low | 0.627 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.022 | ||||
| Mean of outliers high | 1.262 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.163 | ||||
| VaR(95%) (moments method) | 0.076 | ||||
| Expected Shortfall (moments method) | 0.117 | ||||
| Extreme Value Index (regression method) | -0.143 | ||||
| VaR(95%) (regression method) | 0.084 | ||||
| Expected Shortfall (regression method) | 0.111 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.037 | ||||
| Quartile 1 | 0.101 | ||||
| Median | 0.162 | ||||
| Quartile 3 | 0.234 | ||||
| Maximum | 0.537 | ||||
| Mean of quarter 1 | 0.041 | ||||
| Mean of quarter 2 | 0.159 | ||||
| Mean of quarter 3 | 0.226 | ||||
| Mean of quarter 4 | 0.390 | ||||
| Inter Quartile Range | 0.133 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.537 | ||||
| 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) | 0.073 | ||||
| Compounded annual return (geometric extrapolation) | 0.060 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.111 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.153 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.361 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.056 | ||||
| SD | 0.290 | ||||
| Sharpe ratio (Glass type estimate) | 0.194 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.194 | ||||
| df | 1977.000 | ||||
| t | 0.534 | ||||
| p | 0.492 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.519 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.908 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.519 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.908 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.264 | ||||
| Upside Potential Ratio | 6.587 | ||||
| Upside part of mean | 1.408 | ||||
| Downside part of mean | -1.351 | ||||
| Upside SD | 0.196 | ||||
| Downside SD | 0.214 | ||||
| N nonnegative terms | 830.000 | ||||
| N negative terms | 1148.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1978.000 | ||||
| Mean of predictor | 0.237 | ||||
| Mean of criterion | 0.056 | ||||
| SD of predictor | 0.234 | ||||
| SD of criterion | 0.290 | ||||
| Covariance | 0.019 | ||||
| r | 0.275 | ||||
| b (slope, estimate of beta) | 0.342 | ||||
| a (intercept, estimate of alpha) | -0.025 | ||||
| Mean Square Error | 0.078 | ||||
| DF error | 1976.000 | ||||
| t(b) | 12.739 | ||||
| p(b) | 0.362 | ||||
| t(a) | -0.242 | ||||
| p(a) | 0.503 | ||||
| Lowerbound of 95% confidence interval for beta | 0.290 | ||||
| Upperbound of 95% confidence interval for beta | 0.395 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.224 | ||||
| Upperbound of 95% confidence interval for alpha | 0.175 | ||||
| Treynor index (mean / b) | 0.165 | ||||
| Jensen alpha (a) | -0.025 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.014 | ||||
| SD | 0.294 | ||||
| Sharpe ratio (Glass type estimate) | 0.046 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.046 | ||||
| df | 1977.000 | ||||
| t | 0.127 | ||||
| p | 0.498 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.667 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.760 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.667 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.760 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.061 | ||||
| Upside Potential Ratio | 6.241 | ||||
| Upside part of mean | 1.389 | ||||
| Downside part of mean | -1.375 | ||||
| Upside SD | 0.192 | ||||
| Downside SD | 0.223 | ||||
| N nonnegative terms | 830.000 | ||||
| N negative terms | 1148.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1978.000 | ||||
| Mean of predictor | 0.209 | ||||
| Mean of criterion | 0.014 | ||||
| SD of predictor | 0.235 | ||||
| SD of criterion | 0.294 | ||||
| Covariance | 0.019 | ||||
| r | 0.274 | ||||
| b (slope, estimate of beta) | 0.342 | ||||
| a (intercept, estimate of alpha) | -0.058 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 1976.000 | ||||
| t(b) | 12.657 | ||||
| p(b) | 0.363 | ||||
| t(a) | -0.562 | ||||
| p(a) | 0.506 | ||||
| Lowerbound of 95% confidence interval for beta | 0.289 | ||||
| Upperbound of 95% confidence interval for beta | 0.395 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.260 | ||||
| Upperbound of 95% confidence interval for alpha | 0.144 | ||||
| Treynor index (mean / b) | 0.040 | ||||
| Jensen alpha (a) | -0.058 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.029 | ||||
| Expected Shortfall on VaR | 0.037 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1978.000 | ||||
| Minimum | 0.773 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.110 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.012 | ||||
| Number outliers low | 134.000 | ||||
| Percentage of outliers low | 0.068 | ||||
| Mean of outliers low | 0.961 | ||||
| Number of outliers high | 108.000 | ||||
| Percentage of outliers high | 0.055 | ||||
| Mean of outliers high | 1.040 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.204 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | 0.025 | ||||
| Extreme Value Index (regression method) | 0.111 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.014 | ||||
| Median | 0.032 | ||||
| Quartile 3 | 0.098 | ||||
| Maximum | 0.565 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.021 | ||||
| Mean of quarter 3 | 0.050 | ||||
| Mean of quarter 4 | 0.254 | ||||
| Inter Quartile Range | 0.083 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.118 | ||||
| Mean of outliers high | 0.357 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.182 | ||||
| VaR(95%) (moments method) | 0.248 | ||||
| Expected Shortfall (moments method) | 0.263 | ||||
| Extreme Value Index (regression method) | -0.203 | ||||
| VaR(95%) (regression method) | 0.339 | ||||
| Expected Shortfall (regression method) | 0.439 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.072 | ||||
| Compounded annual return (geometric extrapolation) | 0.059 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.105 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.233 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.617 | ||||
| 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 | 1.163 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.331 | ||||
| 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 | 1.107 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.329 | ||||
| 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) | -8614565883052283.000 | ||||
| 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) | -60512644595014518860397863239680.000 | ||||
| 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 | ||||