Advanced Statistics: Max hedge 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 | 0.159 | ||||
| SD | 0.167 | ||||
| Sharpe ratio (Glass type estimate) | 0.950 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.931 | ||||
| df | 37.000 | ||||
| t | 1.691 | ||||
| p | 0.050 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.178 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.066 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.191 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.052 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 13.189 | ||||
| Upside Potential Ratio | 16.350 | ||||
| Upside part of mean | 0.197 | ||||
| Downside part of mean | -0.038 | ||||
| Upside SD | 0.171 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.533 | ||||
| Mean of criterion | 0.159 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.167 | ||||
| Covariance | -0.006 | ||||
| r | -0.130 | ||||
| b (slope, estimate of beta) | -0.082 | ||||
| a (intercept, estimate of alpha) | 0.202 | ||||
| Mean Square Error | 0.028 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.785 | ||||
| p(b) | 0.781 | ||||
| t(a) | 1.847 | ||||
| p(a) | 0.036 | ||||
| Lowerbound of 95% confidence interval for beta | -0.294 | ||||
| Upperbound of 95% confidence interval for beta | 0.130 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.020 | ||||
| Upperbound of 95% confidence interval for alpha | 0.425 | ||||
| Treynor index (mean / b) | -1.934 | ||||
| Jensen alpha (a) | 0.202 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.145 | ||||
| SD | 0.154 | ||||
| Sharpe ratio (Glass type estimate) | 0.940 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.921 | ||||
| df | 37.000 | ||||
| t | 1.673 | ||||
| p | 0.051 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.188 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.056 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.200 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.042 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 12.072 | ||||
| Upside Potential Ratio | 15.233 | ||||
| Upside part of mean | 0.183 | ||||
| Downside part of mean | -0.038 | ||||
| Upside SD | 0.157 | ||||
| Downside SD | 0.012 | ||||
| N nonnegative terms | 6.000 | ||||
| N negative terms | 32.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 38.000 | ||||
| Mean of predictor | 0.489 | ||||
| Mean of criterion | 0.145 | ||||
| SD of predictor | 0.250 | ||||
| SD of criterion | 0.154 | ||||
| Covariance | -0.005 | ||||
| r | -0.123 | ||||
| b (slope, estimate of beta) | -0.076 | ||||
| a (intercept, estimate of alpha) | 0.182 | ||||
| Mean Square Error | 0.024 | ||||
| DF error | 36.000 | ||||
| t(b) | -0.742 | ||||
| p(b) | 0.769 | ||||
| t(a) | 1.812 | ||||
| p(a) | 0.039 | ||||
| Lowerbound of 95% confidence interval for beta | -0.283 | ||||
| Upperbound of 95% confidence interval for beta | 0.131 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.022 | ||||
| Upperbound of 95% confidence interval for alpha | 0.386 | ||||
| Treynor index (mean / b) | -1.913 | ||||
| Jensen alpha (a) | 0.182 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.059 | ||||
| Expected Shortfall on VaR | 0.077 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.005 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 38.000 | ||||
| Minimum | 0.998 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.202 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.065 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.079 | ||||
| Mean of outliers low | 0.999 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.158 | ||||
| Mean of outliers high | 1.108 | ||||
| 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 | 0.003 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.003 | ||||
| Quartile 3 | 0.003 | ||||
| Maximum | 0.003 | ||||
| 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) | 0.259 | ||||
| Compounded annual return (geometric extrapolation) | 0.208 | ||||
| Calmar ratio (compounded annual return / max draw down) | 73.150 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.719 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.168 | ||||
| SD | 0.224 | ||||
| Sharpe ratio (Glass type estimate) | 0.747 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.746 | ||||
| df | 838.000 | ||||
| t | 1.337 | ||||
| p | 0.091 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.349 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.843 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.349 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.842 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.244 | ||||
| Upside Potential Ratio | 4.274 | ||||
| Upside part of mean | 0.576 | ||||
| Downside part of mean | -0.408 | ||||
| Upside SD | 0.180 | ||||
| Downside SD | 0.135 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 767.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 839.000 | ||||
| Mean of predictor | 0.552 | ||||
| Mean of criterion | 0.168 | ||||
| SD of predictor | 0.326 | ||||
| SD of criterion | 0.224 | ||||
| Covariance | -0.000 | ||||
| r | -0.005 | ||||
| b (slope, estimate of beta) | -0.004 | ||||
| a (intercept, estimate of alpha) | 0.170 | ||||
| Mean Square Error | 0.050 | ||||
| DF error | 837.000 | ||||
| t(b) | -0.149 | ||||
| p(b) | 0.559 | ||||
| t(a) | 1.345 | ||||
| p(a) | 0.090 | ||||
| Lowerbound of 95% confidence interval for beta | -0.050 | ||||
| Upperbound of 95% confidence interval for beta | 0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.078 | ||||
| Upperbound of 95% confidence interval for alpha | 0.417 | ||||
| Treynor index (mean / b) | -47.255 | ||||
| Jensen alpha (a) | 0.170 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.143 | ||||
| SD | 0.221 | ||||
| Sharpe ratio (Glass type estimate) | 0.645 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.645 | ||||
| df | 838.000 | ||||
| t | 1.155 | ||||
| p | 0.124 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.451 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.741 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.451 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.740 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.025 | ||||
| Upside Potential Ratio | 4.023 | ||||
| Upside part of mean | 0.561 | ||||
| Downside part of mean | -0.418 | ||||
| Upside SD | 0.172 | ||||
| Downside SD | 0.139 | ||||
| N nonnegative terms | 72.000 | ||||
| N negative terms | 767.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 839.000 | ||||
| Mean of predictor | 0.498 | ||||
| Mean of criterion | 0.143 | ||||
| SD of predictor | 0.328 | ||||
| SD of criterion | 0.221 | ||||
| Covariance | -0.000 | ||||
| r | -0.003 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | 0.144 | ||||
| Mean Square Error | 0.049 | ||||
| DF error | 837.000 | ||||
| t(b) | -0.101 | ||||
| p(b) | 0.540 | ||||
| t(a) | 1.158 | ||||
| p(a) | 0.124 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.043 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.100 | ||||
| Upperbound of 95% confidence interval for alpha | 0.388 | ||||
| Treynor index (mean / b) | -60.612 | ||||
| Jensen alpha (a) | 0.144 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 839.000 | ||||
| Minimum | 0.906 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.136 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 48.000 | ||||
| Percentage of outliers low | 0.057 | ||||
| Mean of outliers low | 0.975 | ||||
| Number of outliers high | 74.000 | ||||
| Percentage of outliers high | 0.088 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.249 | ||||
| VaR(95%) (moments method) | 0.001 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | 0.032 | ||||
| VaR(95%) (regression method) | 0.002 | ||||
| Expected Shortfall (regression method) | 0.015 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 10.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.011 | ||||
| Median | 0.023 | ||||
| Quartile 3 | 0.134 | ||||
| Maximum | 0.216 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.013 | ||||
| Mean of quarter 3 | 0.062 | ||||
| Mean of quarter 4 | 0.178 | ||||
| Inter Quartile Range | 0.122 | ||||
| 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) | -1.801 | ||||
| VaR(95%) (moments method) | 0.203 | ||||
| Expected Shortfall (moments method) | 0.206 | ||||
| Extreme Value Index (regression method) | -0.061 | ||||
| VaR(95%) (regression method) | 0.225 | ||||
| Expected Shortfall (regression method) | 0.266 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.256 | ||||
| Compounded annual return (geometric extrapolation) | 0.206 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.953 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.157 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.533 | ||||
| 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 | 0.981 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.453 | ||||
| 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 | 0.877 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.454 | ||||
| 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) | -8737456279419168.000 | ||||
| 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) | 74896525285947382192360373878784.000 | ||||
| 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 | ||||