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 | -0.127 | ||||
| SD | 0.423 | ||||
| Sharpe ratio (Glass type estimate) | -0.299 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.292 | ||||
| df | 30.000 | ||||
| t | -0.481 | ||||
| p | 0.683 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.518 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.925 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.513 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.930 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.454 | ||||
| Upside Potential Ratio | 1.457 | ||||
| Upside part of mean | 0.406 | ||||
| Downside part of mean | -0.532 | ||||
| Upside SD | 0.311 | ||||
| Downside SD | 0.279 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 24.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.069 | ||||
| Mean of criterion | -0.127 | ||||
| SD of predictor | 0.177 | ||||
| SD of criterion | 0.423 | ||||
| Covariance | 0.032 | ||||
| r | 0.422 | ||||
| b (slope, estimate of beta) | 1.010 | ||||
| a (intercept, estimate of alpha) | -0.196 | ||||
| Mean Square Error | 0.152 | ||||
| DF error | 29.000 | ||||
| t(b) | 2.504 | ||||
| p(b) | 0.009 | ||||
| t(a) | -0.802 | ||||
| p(a) | 0.785 | ||||
| Lowerbound of 95% confidence interval for beta | 0.185 | ||||
| Upperbound of 95% confidence interval for beta | 1.835 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.696 | ||||
| Upperbound of 95% confidence interval for alpha | 0.304 | ||||
| Treynor index (mean / b) | -0.125 | ||||
| Jensen alpha (a) | -0.196 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.212 | ||||
| SD | 0.418 | ||||
| Sharpe ratio (Glass type estimate) | -0.507 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.494 | ||||
| df | 30.000 | ||||
| t | -0.815 | ||||
| p | 0.789 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.729 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.723 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.720 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.731 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.680 | ||||
| Upside Potential Ratio | 1.168 | ||||
| Upside part of mean | 0.364 | ||||
| Downside part of mean | -0.575 | ||||
| Upside SD | 0.275 | ||||
| Downside SD | 0.311 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 24.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 31.000 | ||||
| Mean of predictor | 0.053 | ||||
| Mean of criterion | -0.212 | ||||
| SD of predictor | 0.178 | ||||
| SD of criterion | 0.418 | ||||
| Covariance | 0.029 | ||||
| r | 0.386 | ||||
| b (slope, estimate of beta) | 0.903 | ||||
| a (intercept, estimate of alpha) | -0.260 | ||||
| Mean Square Error | 0.154 | ||||
| DF error | 29.000 | ||||
| t(b) | 2.252 | ||||
| p(b) | 0.016 | ||||
| t(a) | -1.061 | ||||
| p(a) | 0.851 | ||||
| Lowerbound of 95% confidence interval for beta | 0.083 | ||||
| Upperbound of 95% confidence interval for beta | 1.723 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.760 | ||||
| Upperbound of 95% confidence interval for alpha | 0.241 | ||||
| Treynor index (mean / b) | -0.235 | ||||
| Jensen alpha (a) | -0.260 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.194 | ||||
| Expected Shortfall on VaR | 0.233 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.132 | ||||
| Expected Shortfall on VaR | 0.228 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 31.000 | ||||
| Minimum | 0.710 | ||||
| Quartile 1 | 0.924 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.309 | ||||
| Mean of quarter 1 | 0.867 | ||||
| Mean of quarter 2 | 0.972 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.134 | ||||
| Inter Quartile Range | 0.076 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.032 | ||||
| Mean of outliers low | 0.710 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.097 | ||||
| Mean of outliers high | 1.281 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.322 | ||||
| VaR(95%) (moments method) | 0.153 | ||||
| Expected Shortfall (moments method) | 0.246 | ||||
| Extreme Value Index (regression method) | 0.629 | ||||
| VaR(95%) (regression method) | 0.126 | ||||
| Expected Shortfall (regression method) | 0.255 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.131 | ||||
| Quartile 1 | 0.201 | ||||
| Median | 0.271 | ||||
| Quartile 3 | 0.385 | ||||
| Maximum | 0.499 | ||||
| Mean of quarter 1 | 0.131 | ||||
| Mean of quarter 2 | 0.271 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.499 | ||||
| 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) | -0.136 | ||||
| Compounded annual return (geometric extrapolation) | -0.154 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.310 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.310 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.663 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.162 | ||||
| SD | 0.304 | ||||
| Sharpe ratio (Glass type estimate) | -0.533 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.533 | ||||
| df | 902.000 | ||||
| t | -0.864 | ||||
| p | 0.806 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.743 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.677 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.743 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.677 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.692 | ||||
| Upside Potential Ratio | 6.196 | ||||
| Upside part of mean | 1.454 | ||||
| Downside part of mean | -1.616 | ||||
| Upside SD | 0.194 | ||||
| Downside SD | 0.235 | ||||
| N nonnegative terms | 274.000 | ||||
| N negative terms | 629.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 903.000 | ||||
| Mean of predictor | 0.117 | ||||
| Mean of criterion | -0.162 | ||||
| SD of predictor | 0.200 | ||||
| SD of criterion | 0.304 | ||||
| Covariance | 0.019 | ||||
| r | 0.316 | ||||
| b (slope, estimate of beta) | 0.480 | ||||
| a (intercept, estimate of alpha) | -0.218 | ||||
| Mean Square Error | 0.083 | ||||
| DF error | 901.000 | ||||
| t(b) | 10.002 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.224 | ||||
| p(a) | 0.889 | ||||
| Lowerbound of 95% confidence interval for beta | 0.386 | ||||
| Upperbound of 95% confidence interval for beta | 0.574 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.568 | ||||
| Upperbound of 95% confidence interval for alpha | 0.132 | ||||
| Treynor index (mean / b) | -0.338 | ||||
| Jensen alpha (a) | -0.218 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.209 | ||||
| SD | 0.307 | ||||
| Sharpe ratio (Glass type estimate) | -0.680 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.680 | ||||
| df | 902.000 | ||||
| t | -1.102 | ||||
| p | 0.865 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.890 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.530 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.890 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.530 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.866 | ||||
| Upside Potential Ratio | 5.942 | ||||
| Upside part of mean | 1.435 | ||||
| Downside part of mean | -1.644 | ||||
| Upside SD | 0.190 | ||||
| Downside SD | 0.242 | ||||
| N nonnegative terms | 274.000 | ||||
| N negative terms | 629.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 903.000 | ||||
| Mean of predictor | 0.097 | ||||
| Mean of criterion | -0.209 | ||||
| SD of predictor | 0.201 | ||||
| SD of criterion | 0.307 | ||||
| Covariance | 0.020 | ||||
| r | 0.317 | ||||
| b (slope, estimate of beta) | 0.485 | ||||
| a (intercept, estimate of alpha) | -0.256 | ||||
| Mean Square Error | 0.085 | ||||
| DF error | 901.000 | ||||
| t(b) | 10.019 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.421 | ||||
| p(a) | 0.922 | ||||
| Lowerbound of 95% confidence interval for beta | 0.390 | ||||
| Upperbound of 95% confidence interval for beta | 0.580 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.610 | ||||
| Upperbound of 95% confidence interval for alpha | 0.097 | ||||
| Treynor index (mean / b) | -0.431 | ||||
| Jensen alpha (a) | -0.256 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.034 | ||||
| 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 | 903.000 | ||||
| Minimum | 0.875 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.066 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 136.000 | ||||
| Percentage of outliers low | 0.151 | ||||
| Mean of outliers low | 0.974 | ||||
| Number of outliers high | 132.000 | ||||
| Percentage of outliers high | 0.146 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.288 | ||||
| VaR(95%) (moments method) | 0.011 | ||||
| Expected Shortfall (moments method) | 0.020 | ||||
| Extreme Value Index (regression method) | 0.134 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.028 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.028 | ||||
| Median | 0.078 | ||||
| Quartile 3 | 0.249 | ||||
| Maximum | 0.505 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.058 | ||||
| Mean of quarter 3 | 0.206 | ||||
| Mean of quarter 4 | 0.398 | ||||
| Inter Quartile Range | 0.221 | ||||
| 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) | -0.134 | ||||
| Compounded annual return (geometric extrapolation) | -0.152 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.302 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.382 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.454 | ||||
| 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) | -200.333 | ||||
| Sharpe ratio (Hedges UMVUE) | -199.453 | ||||
| df | 171.000 | ||||
| t | -141.657 | ||||
| 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) | -220.773 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -178.134 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.471 | ||||
| Upside Potential Ratio | 0.022 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 171.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.306 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.184 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.083 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 170.000 | ||||
| t(b) | 1.088 | ||||
| p(b) | 0.458 | ||||
| t(a) | -141.262 | ||||
| p(a) | 0.998 | ||||
| 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 | -0.043 | ||||
| Treynor index (mean / b) | -443.235 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -200.336 | ||||
| Sharpe ratio (Hedges UMVUE) | -199.456 | ||||
| df | 171.000 | ||||
| t | -141.659 | ||||
| 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) | -220.776 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -178.136 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.471 | ||||
| Upside Potential Ratio | 0.022 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 1.000 | ||||
| N negative terms | 171.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.289 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.183 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | 0.083 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 170.000 | ||||
| t(b) | 1.091 | ||||
| p(b) | 0.458 | ||||
| t(a) | -141.318 | ||||
| p(a) | 0.998 | ||||
| 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 | -0.043 | ||||
| Treynor index (mean / b) | -440.354 | ||||
| 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 | 172.000 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers high | 0.006 | ||||
| Mean of outliers high | 1.000 | ||||
| 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 | 2.039 | ||||
