Advanced Statistics: Cambist Fund
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 | -0.157 | ||||
| SD | 0.203 | ||||
| Sharpe ratio (Glass type estimate) | -0.772 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.756 | ||||
| df | 38.000 | ||||
| t | -1.391 | ||||
| p | 0.914 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.868 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.334 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.857 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.344 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.763 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.157 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.206 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.553 | ||||
| Mean of criterion | -0.157 | ||||
| SD of predictor | 0.301 | ||||
| SD of criterion | 0.203 | ||||
| Covariance | -0.002 | ||||
| r | -0.033 | ||||
| b (slope, estimate of beta) | -0.022 | ||||
| a (intercept, estimate of alpha) | -0.145 | ||||
| Mean Square Error | 0.042 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.200 | ||||
| p(b) | 0.579 | ||||
| t(a) | -1.115 | ||||
| p(a) | 0.864 | ||||
| Lowerbound of 95% confidence interval for beta | -0.247 | ||||
| Upperbound of 95% confidence interval for beta | 0.203 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.407 | ||||
| Upperbound of 95% confidence interval for alpha | 0.118 | ||||
| Treynor index (mean / b) | 7.073 | ||||
| Jensen alpha (a) | -0.145 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.184 | ||||
| SD | 0.253 | ||||
| Sharpe ratio (Glass type estimate) | -0.729 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.714 | ||||
| df | 38.000 | ||||
| t | -1.314 | ||||
| p | 0.902 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.823 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.375 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.813 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.385 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.722 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.184 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.255 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 39.000 | ||||
| Mean of predictor | 0.501 | ||||
| Mean of criterion | -0.184 | ||||
| SD of predictor | 0.279 | ||||
| SD of criterion | 0.253 | ||||
| Covariance | -0.003 | ||||
| r | -0.040 | ||||
| b (slope, estimate of beta) | -0.036 | ||||
| a (intercept, estimate of alpha) | -0.166 | ||||
| Mean Square Error | 0.066 | ||||
| DF error | 37.000 | ||||
| t(b) | -0.243 | ||||
| p(b) | 0.595 | ||||
| t(a) | -1.035 | ||||
| p(a) | 0.846 | ||||
| Lowerbound of 95% confidence interval for beta | -0.338 | ||||
| Upperbound of 95% confidence interval for beta | 0.266 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.491 | ||||
| Upperbound of 95% confidence interval for alpha | 0.159 | ||||
| Treynor index (mean / b) | 5.081 | ||||
| Jensen alpha (a) | -0.166 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.127 | ||||
| Expected Shortfall on VaR | 0.153 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.045 | ||||
| Expected Shortfall on VaR | 0.100 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 39.000 | ||||
| Minimum | 0.634 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 0.963 | ||||
| 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 | 1.000 | ||||
| Percentage of outliers low | 0.026 | ||||
| Mean of outliers low | 0.634 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.366 | ||||
| Quartile 1 | 0.366 | ||||
| Median | 0.366 | ||||
| Quartile 3 | 0.366 | ||||
| Maximum | 0.366 | ||||
| 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 | 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) | -0.113 | ||||
| Compounded annual return (geometric extrapolation) | -0.131 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.358 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.858 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.094 | ||||
| SD | 0.418 | ||||
| Sharpe ratio (Glass type estimate) | -0.226 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.225 | ||||
| df | 862.000 | ||||
| t | -0.410 | ||||
| p | 0.659 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.306 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.854 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.305 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.855 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.331 | ||||
| Upside Potential Ratio | 1.189 | ||||
| Upside part of mean | 0.339 | ||||
| Downside part of mean | -0.433 | ||||
| Upside SD | 0.305 | ||||
| Downside SD | 0.285 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 856.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 863.000 | ||||
| Mean of predictor | 0.574 | ||||
| Mean of criterion | -0.094 | ||||
| SD of predictor | 0.323 | ||||
| SD of criterion | 0.418 | ||||
| Covariance | -0.007 | ||||
| r | -0.051 | ||||
| b (slope, estimate of beta) | -0.066 | ||||
| a (intercept, estimate of alpha) | -0.056 | ||||
| Mean Square Error | 0.174 | ||||
| DF error | 861.000 | ||||
| t(b) | -1.500 | ||||
| p(b) | 0.933 | ||||
| t(a) | -0.244 | ||||
| p(a) | 0.596 | ||||
| Lowerbound of 95% confidence interval for beta | -0.153 | ||||
| Upperbound of 95% confidence interval for beta | 0.020 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.511 | ||||
| Upperbound of 95% confidence interval for alpha | 0.398 | ||||
| Treynor index (mean / b) | 1.427 | ||||
| Jensen alpha (a) | -0.056 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.182 | ||||
| SD | 0.425 | ||||
| Sharpe ratio (Glass type estimate) | -0.430 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.429 | ||||
| df | 862.000 | ||||
| t | -0.780 | ||||
| p | 0.782 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.510 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.651 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.509 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.651 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.551 | ||||
| Upside Potential Ratio | 0.905 | ||||
| Upside part of mean | 0.300 | ||||
| Downside part of mean | -0.482 | ||||
| Upside SD | 0.266 | ||||
| Downside SD | 0.331 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 856.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 863.000 | ||||
| Mean of predictor | 0.521 | ||||
| Mean of criterion | -0.182 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.425 | ||||
| Covariance | -0.007 | ||||
| r | -0.049 | ||||
| b (slope, estimate of beta) | -0.064 | ||||
| a (intercept, estimate of alpha) | -0.149 | ||||
| Mean Square Error | 0.180 | ||||
| DF error | 861.000 | ||||
| t(b) | -1.440 | ||||
| p(b) | 0.925 | ||||
| t(a) | -0.635 | ||||
| p(a) | 0.737 | ||||
| Lowerbound of 95% confidence interval for beta | -0.151 | ||||
| Upperbound of 95% confidence interval for beta | 0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.610 | ||||
| Upperbound of 95% confidence interval for alpha | 0.312 | ||||
| Treynor index (mean / b) | 2.854 | ||||
| Jensen alpha (a) | -0.149 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.043 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 863.000 | ||||
| Minimum | 0.653 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.384 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 10.000 | ||||
| Percentage of outliers low | 0.012 | ||||
| Mean of outliers low | 0.872 | ||||
| Number of outliers high | 7.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.159 | ||||
| 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) | -0.216 | ||||
| VaR(95%) (regression method) | -0.207 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.176 | ||||
| Quartile 1 | 0.239 | ||||
| Median | 0.302 | ||||
| Quartile 3 | 0.366 | ||||
| Maximum | 0.429 | ||||
| Mean of quarter 1 | 0.176 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.429 | ||||
| Inter Quartile Range | 0.127 | ||||
| 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) | -0.111 | ||||
| Compounded annual return (geometric extrapolation) | -0.129 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.301 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.301 | ||||
| Compounded annual return / Expected Shortfall lognormal | -2.426 | ||||
| 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 | 1.349 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.346 | ||||
| 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 | 1.286 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.344 | ||||
| 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) | -8572565287484584.000 | ||||
| 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) | -81881258614496771271272528084992.000 | ||||
| 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 | ||||