Advanced Statistics: Global Investing Report-Growth Portfolio
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 | -0.084 | ||||
| SD | 0.198 | ||||
| Sharpe ratio (Glass type estimate) | -0.424 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.419 | ||||
| df | 59.000 | ||||
| t | -0.948 | ||||
| p | 0.827 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.302 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.457 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.299 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.461 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.546 | ||||
| Upside Potential Ratio | 0.885 | ||||
| Upside part of mean | 0.136 | ||||
| Downside part of mean | -0.221 | ||||
| Upside SD | 0.125 | ||||
| Downside SD | 0.154 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.360 | ||||
| Mean of criterion | -0.084 | ||||
| SD of predictor | 0.275 | ||||
| SD of criterion | 0.198 | ||||
| Covariance | 0.011 | ||||
| r | 0.193 | ||||
| b (slope, estimate of beta) | 0.139 | ||||
| a (intercept, estimate of alpha) | -0.134 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 58.000 | ||||
| t(b) | 1.501 | ||||
| p(b) | 0.069 | ||||
| t(a) | -1.430 | ||||
| p(a) | 0.921 | ||||
| Lowerbound of 95% confidence interval for beta | -0.047 | ||||
| Upperbound of 95% confidence interval for beta | 0.325 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.322 | ||||
| Upperbound of 95% confidence interval for alpha | 0.054 | ||||
| Treynor index (mean / b) | -0.604 | ||||
| Jensen alpha (a) | -0.134 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.104 | ||||
| SD | 0.202 | ||||
| Sharpe ratio (Glass type estimate) | -0.514 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.508 | ||||
| df | 59.000 | ||||
| t | -1.150 | ||||
| p | 0.873 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.394 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.369 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.389 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.373 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.626 | ||||
| Upside Potential Ratio | 0.776 | ||||
| Upside part of mean | 0.129 | ||||
| Downside part of mean | -0.233 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.166 | ||||
| N nonnegative terms | 10.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.321 | ||||
| Mean of criterion | -0.104 | ||||
| SD of predictor | 0.255 | ||||
| SD of criterion | 0.202 | ||||
| Covariance | 0.011 | ||||
| r | 0.213 | ||||
| b (slope, estimate of beta) | 0.169 | ||||
| a (intercept, estimate of alpha) | -0.158 | ||||
| Mean Square Error | 0.040 | ||||
| DF error | 58.000 | ||||
| t(b) | 1.664 | ||||
| p(b) | 0.051 | ||||
| t(a) | -1.668 | ||||
| p(a) | 0.950 | ||||
| Lowerbound of 95% confidence interval for beta | -0.034 | ||||
| Upperbound of 95% confidence interval for beta | 0.372 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.348 | ||||
| Upperbound of 95% confidence interval for alpha | 0.032 | ||||
| Treynor index (mean / b) | -0.615 | ||||
| Jensen alpha (a) | -0.158 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.099 | ||||
| Expected Shortfall on VaR | 0.121 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.057 | ||||
| Expected Shortfall on VaR | 0.114 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.808 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.206 | ||||
| Mean of quarter 1 | 0.939 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.048 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.200 | ||||
| Mean of outliers low | 0.923 | ||||
| Number of outliers high | 13.000 | ||||
| Percentage of outliers high | 0.217 | ||||
| Mean of outliers high | 1.055 | ||||
| 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) | -0.242 | ||||
| VaR(95%) (regression method) | 0.074 | ||||
| Expected Shortfall (regression method) | 0.108 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.031 | ||||
| Quartile 1 | 0.046 | ||||
| Median | 0.099 | ||||
| Quartile 3 | 0.229 | ||||
| Maximum | 0.477 | ||||
| Mean of quarter 1 | 0.031 | ||||
| Mean of quarter 2 | 0.051 | ||||
| Mean of quarter 3 | 0.147 | ||||
| Mean of quarter 4 | 0.477 | ||||
| Inter Quartile Range | 0.184 | ||||
| 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) | -0.052 | ||||
| Compounded annual return (geometric extrapolation) | -0.058 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.122 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.122 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.482 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.039 | ||||
| SD | 0.361 | ||||
| Sharpe ratio (Glass type estimate) | -0.107 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.107 | ||||
| df | 1322.000 | ||||
| t | -0.242 | ||||
| p | 0.503 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.980 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.765 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.980 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.765 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.159 | ||||
| Upside Potential Ratio | 4.496 | ||||
| Upside part of mean | 1.095 | ||||
| Downside part of mean | -1.134 | ||||
| Upside SD | 0.266 | ||||
| Downside SD | 0.244 | ||||
| N nonnegative terms | 226.000 | ||||
| N negative terms | 1097.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1323.000 | ||||
| Mean of predictor | 0.381 | ||||
| Mean of criterion | -0.039 | ||||
| SD of predictor | 0.321 | ||||
| SD of criterion | 0.361 | ||||
| Covariance | 0.030 | ||||
| r | 0.263 | ||||
| b (slope, estimate of beta) | 0.296 | ||||
| a (intercept, estimate of alpha) | -0.152 | ||||
| Mean Square Error | 0.121 | ||||
| DF error | 1321.000 | ||||
| t(b) | 9.920 | ||||
| p(b) | 0.334 | ||||
| t(a) | -0.977 | ||||
| p(a) | 0.517 | ||||
| Lowerbound of 95% confidence interval for beta | 0.238 | ||||
| Upperbound of 95% confidence interval for beta | 0.355 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.457 | ||||
| Upperbound of 95% confidence interval for alpha | 0.153 | ||||
| Treynor index (mean / b) | -0.131 | ||||
| Jensen alpha (a) | -0.152 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.103 | ||||
| SD | 0.359 | ||||
| Sharpe ratio (Glass type estimate) | -0.288 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.287 | ||||
| df | 1322.000 | ||||
| t | -0.646 | ||||
| p | 0.509 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.160 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.585 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.160 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.585 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.404 | ||||
| Upside Potential Ratio | 4.147 | ||||
| Upside part of mean | 1.062 | ||||
| Downside part of mean | -1.165 | ||||
| Upside SD | 0.252 | ||||
| Downside SD | 0.256 | ||||
| N nonnegative terms | 226.000 | ||||
| N negative terms | 1097.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1323.000 | ||||
| Mean of predictor | 0.330 | ||||
| Mean of criterion | -0.103 | ||||
| SD of predictor | 0.318 | ||||
| SD of criterion | 0.359 | ||||
| Covariance | 0.030 | ||||
| r | 0.264 | ||||
| b (slope, estimate of beta) | 0.298 | ||||
| a (intercept, estimate of alpha) | -0.202 | ||||
| Mean Square Error | 0.120 | ||||
| DF error | 1321.000 | ||||
| t(b) | 9.945 | ||||
| p(b) | 0.334 | ||||
| t(a) | -1.305 | ||||
| p(a) | 0.523 | ||||
| Lowerbound of 95% confidence interval for beta | 0.239 | ||||
| Upperbound of 95% confidence interval for beta | 0.357 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.505 | ||||
| Upperbound of 95% confidence interval for alpha | 0.102 | ||||
| Treynor index (mean / b) | -0.347 | ||||
| Jensen alpha (a) | -0.202 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.036 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1323.000 | ||||
| Minimum | 0.815 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.223 | ||||
| Mean of quarter 1 | 0.983 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 242.000 | ||||
| Percentage of outliers low | 0.183 | ||||
| Mean of outliers low | 0.977 | ||||
| Number of outliers high | 229.000 | ||||
| Percentage of outliers high | 0.173 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.037 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.066 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.033 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.030 | ||||
| Quartile 1 | 0.069 | ||||
| Median | 0.076 | ||||
| Quartile 3 | 0.249 | ||||
| Maximum | 0.505 | ||||
| Mean of quarter 1 | 0.048 | ||||
| Mean of quarter 2 | 0.074 | ||||
| Mean of quarter 3 | 0.206 | ||||
| Mean of quarter 4 | 0.398 | ||||
| Inter Quartile Range | 0.180 | ||||
| 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) | -0.051 | ||||
| Compounded annual return (geometric extrapolation) | -0.058 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.114 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.145 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.278 | ||||
| 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 | 0.955 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.461 | ||||
| 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 | 0.848 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.463 | ||||
| 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) | -8743626426854834.000 | ||||
| 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) | 518815063202801250830904188731392.000 | ||||
| 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 | ||||