Advanced Statistics: Corporate Investments
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 | 1.020 | ||||
| SD | 2.353 | ||||
| Sharpe ratio (Glass type estimate) | 0.434 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.429 | ||||
| df | 66.000 | ||||
| t | 1.025 | ||||
| p | 0.155 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.401 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.265 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.404 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.261 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 2.305 | ||||
| Upside Potential Ratio | 3.129 | ||||
| Upside part of mean | 1.385 | ||||
| Downside part of mean | -0.365 | ||||
| Upside SD | 2.311 | ||||
| Downside SD | 0.443 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.338 | ||||
| Mean of criterion | 1.020 | ||||
| SD of predictor | 0.378 | ||||
| SD of criterion | 2.353 | ||||
| Covariance | 0.090 | ||||
| r | 0.101 | ||||
| b (slope, estimate of beta) | 0.627 | ||||
| a (intercept, estimate of alpha) | 0.808 | ||||
| Mean Square Error | 5.563 | ||||
| DF error | 65.000 | ||||
| t(b) | 0.818 | ||||
| p(b) | 0.208 | ||||
| t(a) | 0.784 | ||||
| p(a) | 0.218 | ||||
| Lowerbound of 95% confidence interval for beta | -0.905 | ||||
| Upperbound of 95% confidence interval for beta | 2.160 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.252 | ||||
| Upperbound of 95% confidence interval for alpha | 2.868 | ||||
| Treynor index (mean / b) | 1.626 | ||||
| Jensen alpha (a) | 0.808 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 1.511 | ||||
| Sharpe ratio (Glass type estimate) | -0.029 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.029 | ||||
| df | 66.000 | ||||
| t | -0.069 | ||||
| p | 0.527 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.858 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.800 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.858 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.801 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.036 | ||||
| Upside Potential Ratio | 0.556 | ||||
| Upside part of mean | 0.687 | ||||
| Downside part of mean | -0.731 | ||||
| Upside SD | 0.852 | ||||
| Downside SD | 1.234 | ||||
| N nonnegative terms | 15.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 67.000 | ||||
| Mean of predictor | 0.272 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.344 | ||||
| SD of criterion | 1.511 | ||||
| Covariance | -0.016 | ||||
| r | -0.031 | ||||
| b (slope, estimate of beta) | -0.136 | ||||
| a (intercept, estimate of alpha) | -0.007 | ||||
| Mean Square Error | 2.316 | ||||
| DF error | 65.000 | ||||
| t(b) | -0.250 | ||||
| p(b) | 0.598 | ||||
| t(a) | -0.011 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | -1.224 | ||||
| Upperbound of 95% confidence interval for beta | 0.952 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.327 | ||||
| Upperbound of 95% confidence interval for alpha | 1.313 | ||||
| Treynor index (mean / b) | 0.323 | ||||
| Jensen alpha (a) | -0.007 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.514 | ||||
| Expected Shortfall on VaR | 0.590 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.090 | ||||
| Expected Shortfall on VaR | 0.201 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 67.000 | ||||
| Minimum | 0.057 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 6.369 | ||||
| Mean of quarter 1 | 0.891 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.458 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 9.000 | ||||
| Percentage of outliers low | 0.134 | ||||
| Mean of outliers low | 0.795 | ||||
| Number of outliers high | 16.000 | ||||
| Percentage of outliers high | 0.239 | ||||
| Mean of outliers high | 1.487 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -13.602 | ||||
| VaR(95%) (moments method) | 0.000 | ||||
| Expected Shortfall (moments method) | 0.000 | ||||
| Extreme Value Index (regression method) | 1.008 | ||||
| VaR(95%) (regression method) | 0.078 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.005 | ||||
| Quartile 1 | 0.241 | ||||
| Median | 0.476 | ||||
| Quartile 3 | 0.712 | ||||
| Maximum | 0.947 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.947 | ||||
| Inter Quartile Range | 0.471 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 5.756 | ||||
| SD | 7.331 | ||||
| Sharpe ratio (Glass type estimate) | 0.785 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.785 | ||||
| df | 1462.000 | ||||
| t | 1.855 | ||||
| p | 0.476 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.045 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.615 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.045 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.615 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 5.614 | ||||
| Upside Potential Ratio | 8.875 | ||||
| Upside part of mean | 9.099 | ||||
| Downside part of mean | -3.343 | ||||
| Upside SD | 7.266 | ||||
| Downside SD | 1.025 | ||||
| N nonnegative terms | 258.000 | ||||
| N negative terms | 1205.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1463.000 | ||||
| Mean of predictor | 0.490 | ||||
| Mean of criterion | 5.756 | ||||
| SD of predictor | 0.667 | ||||
| SD of criterion | 7.331 | ||||
| Covariance | 1.370 | ||||
| r | 0.280 | ||||
| b (slope, estimate of beta) | 3.075 | ||||
| a (intercept, estimate of alpha) | 4.250 | ||||
| Mean Square Error | 49.572 | ||||
| DF error | 1461.000 | ||||
| t(b) | 11.145 | ||||
| p(b) | 0.324 | ||||
| t(a) | 1.425 | ||||
| p(a) | 0.476 | ||||
| Lowerbound of 95% confidence interval for beta | 2.534 | ||||
| Upperbound of 95% confidence interval for beta | 3.616 | ||||
| Lowerbound of 95% confidence interval for alpha | -1.600 | ||||
| Upperbound of 95% confidence interval for alpha | 10.101 | ||||
| Treynor index (mean / b) | 1.872 | ||||
| Jensen alpha (a) | 4.250 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 2.941 | ||||
| Sharpe ratio (Glass type estimate) | -0.015 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.015 | ||||
| df | 1462.000 | ||||
| t | -0.035 | ||||
| p | 0.500 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.844 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.814 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.844 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.814 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.020 | ||||
| Upside Potential Ratio | 2.132 | ||||
| Upside part of mean | 4.626 | ||||
| Downside part of mean | -4.670 | ||||
| Upside SD | 1.984 | ||||
| Downside SD | 2.170 | ||||
| N nonnegative terms | 258.000 | ||||
| N negative terms | 1205.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1463.000 | ||||
| Mean of predictor | 0.272 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.660 | ||||
| SD of criterion | 2.941 | ||||
| Covariance | 0.354 | ||||
| r | 0.182 | ||||
| b (slope, estimate of beta) | 0.813 | ||||
| a (intercept, estimate of alpha) | -0.265 | ||||
| Mean Square Error | 8.369 | ||||
| DF error | 1461.000 | ||||
| t(b) | 7.085 | ||||
| p(b) | 0.385 | ||||
| t(a) | -0.216 | ||||
| p(a) | 0.504 | ||||
| Lowerbound of 95% confidence interval for beta | 0.588 | ||||
| Upperbound of 95% confidence interval for beta | 1.038 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.667 | ||||
| Upperbound of 95% confidence interval for alpha | 2.137 | ||||
| Treynor index (mean / b) | -0.054 | ||||
| Jensen alpha (a) | -0.265 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.258 | ||||
| Expected Shortfall on VaR | 0.311 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.039 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1463.000 | ||||
| Minimum | 0.054 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 14.339 | ||||
| Mean of quarter 1 | 0.950 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.139 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 255.000 | ||||
| Percentage of outliers low | 0.174 | ||||
| Mean of outliers low | 0.928 | ||||
| Number of outliers high | 281.000 | ||||
| Percentage of outliers high | 0.192 | ||||
| Mean of outliers high | 1.181 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.238 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.512 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.116 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.006 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.070 | ||||
| Quartile 3 | 0.722 | ||||
| Maximum | 0.947 | ||||
| Mean of quarter 1 | 0.014 | ||||
| Mean of quarter 2 | 0.056 | ||||
| Mean of quarter 3 | 0.084 | ||||
| Mean of quarter 4 | 0.941 | ||||
| Inter Quartile Range | 0.691 | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.000 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.000 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||
| 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 | 1.895 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.722 | ||||
| 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 | 1.628 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.729 | ||||
| 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) | -8716743594769799.000 | ||||
| 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) | -643641410001579000626116175069184.000 | ||||
| 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 | ||||