Advanced Statistics: LITfund
Advanced Statistics module contributed by Jules Ellis, C2 Member. Jules has written a very helpful guide for these statistics. | |||||
| |||||
| ANALYSIS BASED ON MONTHLY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.065 | ||||
| SD | 0.273 | ||||
| Sharpe ratio (Glass type estimate) | 0.238 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.235 | ||||
| df | 60.000 | ||||
| t | 0.537 | ||||
| p | 0.296 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.633 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.108 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.635 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.106 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.368 | ||||
| Upside Potential Ratio | 2.068 | ||||
| Upside part of mean | 0.366 | ||||
| Downside part of mean | -0.301 | ||||
| Upside SD | 0.206 | ||||
| Downside SD | 0.177 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.331 | ||||
| Mean of criterion | 0.065 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.273 | ||||
| Covariance | 0.013 | ||||
| r | 0.200 | ||||
| b (slope, estimate of beta) | 0.236 | ||||
| a (intercept, estimate of alpha) | -0.013 | ||||
| Mean Square Error | 0.073 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.571 | ||||
| p(b) | 0.061 | ||||
| t(a) | -0.100 | ||||
| p(a) | 0.540 | ||||
| Lowerbound of 95% confidence interval for beta | -0.065 | ||||
| Upperbound of 95% confidence interval for beta | 0.536 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.272 | ||||
| Upperbound of 95% confidence interval for alpha | 0.246 | ||||
| Treynor index (mean / b) | 0.276 | ||||
| Jensen alpha (a) | -0.013 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.273 | ||||
| Sharpe ratio (Glass type estimate) | 0.104 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.103 | ||||
| df | 60.000 | ||||
| t | 0.234 | ||||
| p | 0.408 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.766 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.973 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.767 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.972 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.148 | ||||
| Upside Potential Ratio | 1.803 | ||||
| Upside part of mean | 0.345 | ||||
| Downside part of mean | -0.317 | ||||
| Upside SD | 0.191 | ||||
| Downside SD | 0.191 | ||||
| N nonnegative terms | 26.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.300 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.227 | ||||
| SD of criterion | 0.273 | ||||
| Covariance | 0.014 | ||||
| r | 0.221 | ||||
| b (slope, estimate of beta) | 0.265 | ||||
| a (intercept, estimate of alpha) | -0.051 | ||||
| Mean Square Error | 0.072 | ||||
| DF error | 59.000 | ||||
| t(b) | 1.742 | ||||
| p(b) | 0.043 | ||||
| t(a) | -0.402 | ||||
| p(a) | 0.656 | ||||
| Lowerbound of 95% confidence interval for beta | -0.039 | ||||
| Upperbound of 95% confidence interval for beta | 0.570 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.306 | ||||
| Upperbound of 95% confidence interval for alpha | 0.204 | ||||
| Treynor index (mean / b) | 0.107 | ||||
| Jensen alpha (a) | -0.051 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.119 | ||||
| Expected Shortfall on VaR | 0.147 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.063 | ||||
| Expected Shortfall on VaR | 0.120 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.764 | ||||
| Quartile 1 | 0.967 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.054 | ||||
| Maximum | 1.228 | ||||
| Mean of quarter 1 | 0.920 | ||||
| Mean of quarter 2 | 0.991 | ||||
| Mean of quarter 3 | 1.021 | ||||
| Mean of quarter 4 | 1.109 | ||||
| Inter Quartile Range | 0.086 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.016 | ||||
| Mean of outliers low | 0.764 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.033 | ||||
| Mean of outliers high | 1.227 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.382 | ||||
| VaR(95%) (moments method) | 0.087 | ||||
| Expected Shortfall (moments method) | 0.161 | ||||
| Extreme Value Index (regression method) | 0.467 | ||||
| VaR(95%) (regression method) | 0.089 | ||||
| Expected Shortfall (regression method) | 0.180 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 7.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.031 | ||||
| Median | 0.050 | ||||
| Quartile 3 | 0.055 | ||||
| Maximum | 0.432 | ||||
| Mean of quarter 1 | 0.015 | ||||
| Mean of quarter 2 | 0.042 | ||||
| Mean of quarter 3 | 0.052 | ||||
| Mean of quarter 4 | 0.245 | ||||
| Inter Quartile Range | 0.024 | ||||
| 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 | 0.143 | ||||
| Mean of outliers high | 0.432 | ||||
| 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) | 0.087 | ||||
| Compounded annual return (geometric extrapolation) | 0.075 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.174 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.307 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.509 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.054 | ||||
| SD | 0.231 | ||||
| Sharpe ratio (Glass type estimate) | 0.235 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.235 | ||||
| df | 1343.000 | ||||
| t | 0.532 | ||||
| p | 0.491 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.631 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.100 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.631 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.100 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.349 | ||||
| Upside Potential Ratio | 7.987 | ||||
| Upside part of mean | 1.242 | ||||
| Downside part of mean | -1.188 | ||||
| Upside SD | 0.171 | ||||
| Downside SD | 0.156 | ||||
| N nonnegative terms | 539.000 | ||||
| N negative terms | 805.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1344.000 | ||||
| Mean of predictor | 0.359 | ||||
| Mean of criterion | 0.054 | ||||
| SD of predictor | 0.302 | ||||
| SD of criterion | 0.231 | ||||
| Covariance | 0.006 | ||||
| r | 0.089 | ||||
| b (slope, estimate of beta) | 0.068 | ||||
| a (intercept, estimate of alpha) | 0.030 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 1342.000 | ||||
| t(b) | 3.283 | ||||
| p(b) | 0.455 | ||||
| t(a) | 0.292 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | 0.027 | ||||
| Upperbound of 95% confidence interval for beta | 0.109 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.170 | ||||
| Upperbound of 95% confidence interval for alpha | 0.230 | ||||
| Treynor index (mean / b) | 0.796 | ||||
| Jensen alpha (a) | 0.030 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.028 | ||||
| SD | 0.231 | ||||
| Sharpe ratio (Glass type estimate) | 0.120 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.120 | ||||
| df | 1343.000 | ||||
| t | 0.272 | ||||
| p | 0.495 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.745 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.985 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.745 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.985 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.175 | ||||
| Upside Potential Ratio | 7.776 | ||||
| Upside part of mean | 1.228 | ||||
| Downside part of mean | -1.200 | ||||
| Upside SD | 0.168 | ||||
| Downside SD | 0.158 | ||||
| N nonnegative terms | 539.000 | ||||
| N negative terms | 805.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1344.000 | ||||
| Mean of predictor | 0.313 | ||||
| Mean of criterion | 0.028 | ||||
| SD of predictor | 0.305 | ||||
| SD of criterion | 0.231 | ||||
| Covariance | 0.006 | ||||
| r | 0.088 | ||||
| b (slope, estimate of beta) | 0.067 | ||||
| a (intercept, estimate of alpha) | 0.007 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 1342.000 | ||||
| t(b) | 3.247 | ||||
| p(b) | 0.456 | ||||
| t(a) | 0.066 | ||||
| p(a) | 0.499 | ||||
| Lowerbound of 95% confidence interval for beta | 0.026 | ||||
| Upperbound of 95% confidence interval for beta | 0.107 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.193 | ||||
| Upperbound of 95% confidence interval for alpha | 0.206 | ||||
| Treynor index (mean / b) | 0.414 | ||||
| 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%) | 0.023 | ||||
| Expected Shortfall on VaR | 0.029 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1344.000 | ||||
| Minimum | 0.937 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.006 | ||||
| Maximum | 1.102 | ||||
| Mean of quarter 1 | 0.984 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.018 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 73.000 | ||||
| Percentage of outliers low | 0.054 | ||||
| Mean of outliers low | 0.968 | ||||
| Number of outliers high | 84.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 1.034 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.023 | ||||
| VaR(95%) (moments method) | 0.013 | ||||
| Expected Shortfall (moments method) | 0.018 | ||||
| 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 | 32.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.010 | ||||
| Median | 0.024 | ||||
| Quartile 3 | 0.057 | ||||
| Maximum | 0.441 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.016 | ||||
| Mean of quarter 3 | 0.036 | ||||
| Mean of quarter 4 | 0.128 | ||||
| Inter Quartile Range | 0.047 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.062 | ||||
| Mean of outliers high | 0.290 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.604 | ||||
| VaR(95%) (moments method) | 0.143 | ||||
| Expected Shortfall (moments method) | 0.366 | ||||
| Extreme Value Index (regression method) | 0.999 | ||||
| VaR(95%) (regression method) | 0.108 | ||||
| Expected Shortfall (regression method) | 47.984 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.087 | ||||
| Compounded annual return (geometric extrapolation) | 0.074 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.168 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.581 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.575 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.196 | ||||
| SD | 0.262 | ||||
| Sharpe ratio (Glass type estimate) | 0.749 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.744 | ||||
| df | 130.000 | ||||
| t | 0.529 | ||||
| p | 0.477 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.026 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.521 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.029 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.518 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.212 | ||||
| Upside Potential Ratio | 9.076 | ||||
| Upside part of mean | 1.469 | ||||
| Downside part of mean | -1.273 | ||||
| Upside SD | 0.205 | ||||
| Downside SD | 0.162 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.042 | ||||
| Mean of criterion | 0.196 | ||||
| SD of predictor | 0.381 | ||||
| SD of criterion | 0.262 | ||||
| Covariance | 0.014 | ||||
| r | 0.138 | ||||
| b (slope, estimate of beta) | 0.095 | ||||
| a (intercept, estimate of alpha) | 0.097 | ||||
| Mean Square Error | 0.068 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.582 | ||||
| p(b) | 0.412 | ||||
| t(a) | 0.261 | ||||
| p(a) | 0.485 | ||||
| Lowerbound of 95% confidence interval for beta | -0.024 | ||||
| Upperbound of 95% confidence interval for beta | 0.213 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.642 | ||||
| Upperbound of 95% confidence interval for alpha | 0.837 | ||||
| Treynor index (mean / b) | 2.068 | ||||
| Jensen alpha (a) | 0.097 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.162 | ||||
| SD | 0.260 | ||||
| Sharpe ratio (Glass type estimate) | 0.623 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.620 | ||||
| df | 130.000 | ||||
| t | 0.441 | ||||
| p | 0.481 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.151 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 3.395 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.153 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 3.393 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.990 | ||||
| Upside Potential Ratio | 8.838 | ||||
| Upside part of mean | 1.448 | ||||
| Downside part of mean | -1.286 | ||||
| Upside SD | 0.201 | ||||
| Downside SD | 0.164 | ||||
| N nonnegative terms | 46.000 | ||||
| N negative terms | 85.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.966 | ||||
| Mean of criterion | 0.162 | ||||
| SD of predictor | 0.387 | ||||
| SD of criterion | 0.260 | ||||
| Covariance | 0.013 | ||||
| r | 0.128 | ||||
| b (slope, estimate of beta) | 0.086 | ||||
| a (intercept, estimate of alpha) | 0.079 | ||||
| Mean Square Error | 0.067 | ||||
| DF error | 129.000 | ||||
| t(b) | 1.464 | ||||
| p(b) | 0.419 | ||||
| t(a) | 0.214 | ||||
| p(a) | 0.488 | ||||
| Lowerbound of 95% confidence interval for beta | -0.030 | ||||
| Upperbound of 95% confidence interval for beta | 0.202 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.655 | ||||
| Upperbound of 95% confidence interval for alpha | 0.813 | ||||
| Treynor index (mean / b) | 1.888 | ||||
| Jensen alpha (a) | 0.079 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.026 | ||||
| Expected Shortfall on VaR | 0.032 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.025 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.965 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.005 | ||||
| Maximum | 1.057 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 12.000 | ||||
| Percentage of outliers low | 0.092 | ||||
| Mean of outliers low | 0.973 | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.084 | ||||
| Mean of outliers high | 1.037 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.451 | ||||
| VaR(95%) (moments method) | 0.016 | ||||
| Expected Shortfall (moments method) | 0.019 | ||||
| Extreme Value Index (regression method) | -0.363 | ||||
| VaR(95%) (regression method) | 0.016 | ||||
| Expected Shortfall (regression method) | 0.019 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.033 | ||||
| Quartile 1 | 0.038 | ||||
| Median | 0.044 | ||||
| Quartile 3 | 0.094 | ||||
| Maximum | 0.144 | ||||
| Mean of quarter 1 | 0.033 | ||||
| Mean of quarter 2 | 0.044 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.144 | ||||
| Inter Quartile Range | 0.055 | ||||
| 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) | 0.217 | ||||
| Compounded annual return (geometric extrapolation) | 0.229 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.593 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.593 | ||||
| Compounded annual return / Expected Shortfall lognormal | 7.156 | ||||