Advanced Statistics: CYB
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 | -0.022 | ||||
| SD | 0.163 | ||||
| Sharpe ratio (Glass type estimate) | -0.134 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.133 | ||||
| df | 63.000 | ||||
| t | -0.310 | ||||
| p | 0.621 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.983 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.715 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.982 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.716 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.190 | ||||
| Upside Potential Ratio | 1.217 | ||||
| Upside part of mean | 0.140 | ||||
| Downside part of mean | -0.162 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.115 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.332 | ||||
| Mean of criterion | -0.022 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.163 | ||||
| Covariance | 0.005 | ||||
| r | 0.108 | ||||
| b (slope, estimate of beta) | 0.058 | ||||
| a (intercept, estimate of alpha) | -0.041 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 62.000 | ||||
| t(b) | 0.856 | ||||
| p(b) | 0.198 | ||||
| t(a) | -0.556 | ||||
| p(a) | 0.710 | ||||
| Lowerbound of 95% confidence interval for beta | -0.078 | ||||
| Upperbound of 95% confidence interval for beta | 0.194 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.189 | ||||
| Upperbound of 95% confidence interval for alpha | 0.107 | ||||
| Treynor index (mean / b) | -0.375 | ||||
| Jensen alpha (a) | -0.041 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.164 | ||||
| Sharpe ratio (Glass type estimate) | -0.213 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.210 | ||||
| df | 63.000 | ||||
| t | -0.491 | ||||
| p | 0.687 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.061 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.638 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.059 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.640 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.283 | ||||
| Upside Potential Ratio | 1.081 | ||||
| Upside part of mean | 0.133 | ||||
| Downside part of mean | -0.168 | ||||
| Upside SD | 0.107 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 13.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 64.000 | ||||
| Mean of predictor | 0.284 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.164 | ||||
| Covariance | 0.008 | ||||
| r | 0.158 | ||||
| b (slope, estimate of beta) | 0.088 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 62.000 | ||||
| t(b) | 1.258 | ||||
| p(b) | 0.107 | ||||
| t(a) | -0.814 | ||||
| p(a) | 0.791 | ||||
| Lowerbound of 95% confidence interval for beta | -0.052 | ||||
| Upperbound of 95% confidence interval for beta | 0.227 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.207 | ||||
| Upperbound of 95% confidence interval for alpha | 0.087 | ||||
| Treynor index (mean / b) | -0.398 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.078 | ||||
| Expected Shortfall on VaR | 0.096 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.041 | ||||
| Expected Shortfall on VaR | 0.082 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 64.000 | ||||
| Minimum | 0.809 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.150 | ||||
| Mean of quarter 1 | 0.958 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.050 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 14.000 | ||||
| Percentage of outliers low | 0.219 | ||||
| Mean of outliers low | 0.952 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.203 | ||||
| Mean of outliers high | 1.061 | ||||
| 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) | 0.144 | ||||
| VaR(95%) (regression method) | 0.059 | ||||
| Expected Shortfall (regression method) | 0.109 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.049 | ||||
| Quartile 1 | 0.103 | ||||
| Median | 0.140 | ||||
| Quartile 3 | 0.166 | ||||
| Maximum | 0.191 | ||||
| Mean of quarter 1 | 0.049 | ||||
| Mean of quarter 2 | 0.121 | ||||
| Mean of quarter 3 | 0.158 | ||||
| Mean of quarter 4 | 0.191 | ||||
| Inter Quartile Range | 0.063 | ||||
| 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) | 0.009 | ||||
| Compounded annual return (geometric extrapolation) | 0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.048 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.048 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.096 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.009 | ||||
| SD | 0.229 | ||||
| Sharpe ratio (Glass type estimate) | -0.037 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.037 | ||||
| df | 1416.000 | ||||
| t | -0.087 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.880 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.805 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.880 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.805 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.052 | ||||
| Upside Potential Ratio | 4.325 | ||||
| Upside part of mean | 0.705 | ||||
| Downside part of mean | -0.714 | ||||
| Upside SD | 0.160 | ||||
| Downside SD | 0.163 | ||||
| N nonnegative terms | 264.000 | ||||
| N negative terms | 1153.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1417.000 | ||||
| Mean of predictor | 0.421 | ||||
| Mean of criterion | -0.009 | ||||
| SD of predictor | 0.466 | ||||
| SD of criterion | 0.229 | ||||
| Covariance | 0.010 | ||||
| r | 0.090 | ||||
| b (slope, estimate of beta) | 0.044 | ||||
| a (intercept, estimate of alpha) | -0.027 | ||||
| Mean Square Error | 0.052 | ||||
| DF error | 1415.000 | ||||
| t(b) | 3.394 | ||||
| p(b) | 0.443 | ||||
| t(a) | -0.276 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | 0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.070 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.220 | ||||
| Upperbound of 95% confidence interval for alpha | 0.165 | ||||
| Treynor index (mean / b) | -0.194 | ||||
| Jensen alpha (a) | -0.027 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.035 | ||||
| SD | 0.231 | ||||
| Sharpe ratio (Glass type estimate) | -0.152 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.151 | ||||
| df | 1416.000 | ||||
| t | -0.352 | ||||
| p | 0.505 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.994 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.691 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.994 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.691 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.205 | ||||
| Upside Potential Ratio | 4.050 | ||||
| Upside part of mean | 0.693 | ||||
| Downside part of mean | -0.728 | ||||
| Upside SD | 0.155 | ||||
| Downside SD | 0.171 | ||||
| N nonnegative terms | 264.000 | ||||
| N negative terms | 1153.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1417.000 | ||||
| Mean of predictor | 0.313 | ||||
| Mean of criterion | -0.035 | ||||
| SD of predictor | 0.464 | ||||
| SD of criterion | 0.231 | ||||
| Covariance | 0.011 | ||||
| r | 0.104 | ||||
| b (slope, estimate of beta) | 0.052 | ||||
| a (intercept, estimate of alpha) | -0.051 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 1415.000 | ||||
| t(b) | 3.932 | ||||
| p(b) | 0.434 | ||||
| t(a) | -0.518 | ||||
| p(a) | 0.509 | ||||
| Lowerbound of 95% confidence interval for beta | 0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.078 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.245 | ||||
| Upperbound of 95% confidence interval for alpha | 0.143 | ||||
| Treynor index (mean / b) | -0.676 | ||||
| Jensen alpha (a) | -0.051 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1417.000 | ||||
| Minimum | 0.808 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.122 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 282.000 | ||||
| Percentage of outliers low | 0.199 | ||||
| Mean of outliers low | 0.987 | ||||
| Number of outliers high | 267.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.226 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.008 | ||||
| Extreme Value Index (regression method) | 0.283 | ||||
| VaR(95%) (regression method) | 0.009 | ||||
| Expected Shortfall (regression method) | 0.020 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 9.000 | ||||
| Minimum | 0.015 | ||||
| Quartile 1 | 0.059 | ||||
| Median | 0.086 | ||||
| Quartile 3 | 0.131 | ||||
| Maximum | 0.192 | ||||
| Mean of quarter 1 | 0.039 | ||||
| Mean of quarter 2 | 0.086 | ||||
| Mean of quarter 3 | 0.119 | ||||
| Mean of quarter 4 | 0.181 | ||||
| Inter Quartile Range | 0.072 | ||||
| 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) | -13.902 | ||||
| VaR(95%) (moments method) | 0.176 | ||||
| Expected Shortfall (moments method) | 0.176 | ||||
| Extreme Value Index (regression method) | -1.875 | ||||
| VaR(95%) (regression method) | 0.218 | ||||
| Expected Shortfall (regression method) | 0.220 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.009 | ||||
| Compounded annual return (geometric extrapolation) | 0.009 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.047 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.050 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.310 | ||||
| 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 | 1.039 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.474 | ||||
| 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 | 0.926 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.475 | ||||
| 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) | -8736146818425172.000 | ||||
| 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) | -139204061021597036163445915910144.000 | ||||
| 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 | ||||