Advanced Statistics: 2d
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 | -0.317 | ||||
| SD | 0.648 | ||||
| Sharpe ratio (Glass type estimate) | -0.488 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.482 | ||||
| df | 59.000 | ||||
| t | -1.092 | ||||
| p | 0.860 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.367 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.395 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.363 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.399 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.510 | ||||
| Upside Potential Ratio | 0.327 | ||||
| Upside part of mean | 0.203 | ||||
| Downside part of mean | -0.520 | ||||
| Upside SD | 0.189 | ||||
| Downside SD | 0.621 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.319 | ||||
| Mean of criterion | -0.317 | ||||
| SD of predictor | 0.245 | ||||
| SD of criterion | 0.648 | ||||
| Covariance | 0.005 | ||||
| r | 0.034 | ||||
| b (slope, estimate of beta) | 0.090 | ||||
| a (intercept, estimate of alpha) | -0.345 | ||||
| Mean Square Error | 0.427 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.259 | ||||
| p(b) | 0.398 | ||||
| t(a) | -1.105 | ||||
| p(a) | 0.863 | ||||
| Lowerbound of 95% confidence interval for beta | -0.605 | ||||
| Upperbound of 95% confidence interval for beta | 0.784 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.971 | ||||
| Upperbound of 95% confidence interval for alpha | 0.280 | ||||
| Treynor index (mean / b) | -3.527 | ||||
| Jensen alpha (a) | -0.345 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.208 | ||||
| SD | 4.169 | ||||
| Sharpe ratio (Glass type estimate) | -0.530 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.523 | ||||
| df | 59.000 | ||||
| t | -1.184 | ||||
| p | 0.879 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.409 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.354 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.404 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.359 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.528 | ||||
| Upside Potential Ratio | 0.045 | ||||
| Upside part of mean | 0.188 | ||||
| Downside part of mean | -2.396 | ||||
| Upside SD | 0.162 | ||||
| Downside SD | 4.180 | ||||
| N nonnegative terms | 27.000 | ||||
| N negative terms | 33.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 60.000 | ||||
| Mean of predictor | 0.287 | ||||
| Mean of criterion | -2.208 | ||||
| SD of predictor | 0.228 | ||||
| SD of criterion | 4.169 | ||||
| Covariance | 0.079 | ||||
| r | 0.083 | ||||
| b (slope, estimate of beta) | 1.520 | ||||
| a (intercept, estimate of alpha) | -2.645 | ||||
| Mean Square Error | 17.561 | ||||
| DF error | 58.000 | ||||
| t(b) | 0.634 | ||||
| p(b) | 0.264 | ||||
| t(a) | -1.325 | ||||
| p(a) | 0.905 | ||||
| Lowerbound of 95% confidence interval for beta | -3.280 | ||||
| Upperbound of 95% confidence interval for beta | 6.320 | ||||
| Lowerbound of 95% confidence interval for alpha | -6.641 | ||||
| Upperbound of 95% confidence interval for alpha | 1.352 | ||||
| Treynor index (mean / b) | -1.452 | ||||
| Jensen alpha (a) | -2.645 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.885 | ||||
| Expected Shortfall on VaR | 0.925 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.102 | ||||
| Expected Shortfall on VaR | 0.235 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 60.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.021 | ||||
| Maximum | 1.401 | ||||
| Mean of quarter 1 | 0.835 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.064 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.067 | ||||
| Mean of outliers low | 0.396 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.067 | ||||
| Mean of outliers high | 1.143 | ||||
| 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) | 1.384 | ||||
| VaR(95%) (regression method) | 0.075 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.013 | ||||
| Quartile 1 | 0.145 | ||||
| Median | 0.278 | ||||
| Quartile 3 | 0.639 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.013 | ||||
| Mean of quarter 2 | 0.278 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 1.000 | ||||
| Inter Quartile Range | 0.493 | ||||
| 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) | -0.200 | ||||
| Compounded annual return (geometric extrapolation) | -0.885 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.885 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.885 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.957 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 782.179 | ||||
| SD | 1749.886 | ||||
| Sharpe ratio (Glass type estimate) | 0.447 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.447 | ||||
| df | 1330.000 | ||||
| t | 1.007 | ||||
| p | 0.486 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.423 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.317 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.423 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.316 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 747.122 | ||||
| Upside Potential Ratio | 749.171 | ||||
| Upside part of mean | 784.324 | ||||
| Downside part of mean | -2.146 | ||||
| Upside SD | 1749.895 | ||||
| Downside SD | 1.047 | ||||
| N nonnegative terms | 478.000 | ||||
| N negative terms | 853.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1331.000 | ||||
| Mean of predictor | 0.356 | ||||
| Mean of criterion | 782.179 | ||||
| SD of predictor | 0.276 | ||||
| SD of criterion | 1749.886 | ||||
| Covariance | -10.609 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -139.224 | ||||
| a (intercept, estimate of alpha) | 831.698 | ||||
| Mean Square Error | 3062926.536 | ||||
| DF error | 1329.000 | ||||
| t(b) | -0.801 | ||||
| p(b) | 0.514 | ||||
| t(a) | 1.068 | ||||
| p(a) | 0.481 | ||||
| Lowerbound of 95% confidence interval for beta | -480.272 | ||||
| Upperbound of 95% confidence interval for beta | 201.823 | ||||
| Lowerbound of 95% confidence interval for alpha | -696.383 | ||||
| Upperbound of 95% confidence interval for alpha | 2359.779 | ||||
| Treynor index (mean / b) | -5.618 | ||||
| Jensen alpha (a) | 831.698 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -2.174 | ||||
| SD | 6.765 | ||||
| Sharpe ratio (Glass type estimate) | -0.321 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.321 | ||||
| df | 1330.000 | ||||
| t | -0.724 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.191 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.548 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.191 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.549 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.402 | ||||
| Upside Potential Ratio | 0.693 | ||||
| Upside part of mean | 3.753 | ||||
| Downside part of mean | -5.927 | ||||
| Upside SD | 4.054 | ||||
| Downside SD | 5.414 | ||||
| N nonnegative terms | 478.000 | ||||
| N negative terms | 853.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1331.000 | ||||
| Mean of predictor | 0.318 | ||||
| Mean of criterion | -2.174 | ||||
| SD of predictor | 0.271 | ||||
| SD of criterion | 6.765 | ||||
| Covariance | -0.031 | ||||
| r | -0.017 | ||||
| b (slope, estimate of beta) | -0.420 | ||||
| a (intercept, estimate of alpha) | -2.040 | ||||
| Mean Square Error | 45.789 | ||||
| DF error | 1329.000 | ||||
| t(b) | -0.614 | ||||
| p(b) | 0.511 | ||||
| t(a) | -0.678 | ||||
| p(a) | 0.512 | ||||
| Lowerbound of 95% confidence interval for beta | -1.764 | ||||
| Upperbound of 95% confidence interval for beta | 0.923 | ||||
| Lowerbound of 95% confidence interval for alpha | -7.945 | ||||
| Upperbound of 95% confidence interval for alpha | 3.865 | ||||
| Treynor index (mean / b) | 5.172 | ||||
| Jensen alpha (a) | -2.040 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.501 | ||||
| Expected Shortfall on VaR | 0.577 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.021 | ||||
| Expected Shortfall on VaR | 0.050 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1331.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 3945.000 | ||||
| Mean of quarter 1 | 0.968 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 12.965 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 211.000 | ||||
| Percentage of outliers low | 0.159 | ||||
| Mean of outliers low | 0.950 | ||||
| Number of outliers high | 195.000 | ||||
| Percentage of outliers high | 0.147 | ||||
| Mean of outliers high | 21.432 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.606 | ||||
| VaR(95%) (moments method) | 0.012 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.034 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 101.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.011 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.007 | ||||
| Mean of quarter 4 | 0.099 | ||||
| Inter Quartile Range | 0.010 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.149 | ||||
| Mean of outliers high | 0.153 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.082 | ||||
| VaR(95%) (moments method) | 0.074 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.237 | ||||
| VaR(95%) (regression method) | 0.051 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | -0.197 | ||||
| Compounded annual return (geometric extrapolation) | -0.881 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.881 | ||||
| Compounded annual return / average of 25% largest draw downs | -8.910 | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.528 | ||||
| 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 | 1.118 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.408 | ||||
| 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 | 1.032 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.410 | ||||
| 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) | -8694316651472048.000 | ||||
| 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) | -348125781024691856059300099129344.000 | ||||
| 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 | ||||