Advanced Statistics: FreeVector Capital Growth 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 | -0.002 | ||||
| SD | 0.273 | ||||
| Sharpe ratio (Glass type estimate) | -0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.008 | ||||
| df | 42.000 | ||||
| t | -0.016 | ||||
| p | 0.506 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.044 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.027 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.044 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.027 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.012 | ||||
| Upside Potential Ratio | 1.549 | ||||
| Upside part of mean | 0.306 | ||||
| Downside part of mean | -0.308 | ||||
| Upside SD | 0.184 | ||||
| Downside SD | 0.197 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.471 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.273 | ||||
| Covariance | 0.013 | ||||
| r | 0.193 | ||||
| b (slope, estimate of beta) | 0.210 | ||||
| a (intercept, estimate of alpha) | -0.101 | ||||
| Mean Square Error | 0.074 | ||||
| DF error | 41.000 | ||||
| t(b) | 1.261 | ||||
| p(b) | 0.107 | ||||
| t(a) | -0.619 | ||||
| p(a) | 0.730 | ||||
| Lowerbound of 95% confidence interval for beta | -0.126 | ||||
| Upperbound of 95% confidence interval for beta | 0.546 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.431 | ||||
| Upperbound of 95% confidence interval for alpha | 0.229 | ||||
| Treynor index (mean / b) | -0.011 | ||||
| Jensen alpha (a) | -0.101 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.040 | ||||
| SD | 0.284 | ||||
| Sharpe ratio (Glass type estimate) | -0.142 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.140 | ||||
| df | 42.000 | ||||
| t | -0.270 | ||||
| p | 0.606 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.177 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.894 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.176 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.896 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.182 | ||||
| Upside Potential Ratio | 1.301 | ||||
| Upside part of mean | 0.289 | ||||
| Downside part of mean | -0.330 | ||||
| Upside SD | 0.171 | ||||
| Downside SD | 0.222 | ||||
| N nonnegative terms | 20.000 | ||||
| N negative terms | 23.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 43.000 | ||||
| Mean of predictor | 0.432 | ||||
| Mean of criterion | -0.040 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.284 | ||||
| Covariance | 0.010 | ||||
| r | 0.150 | ||||
| b (slope, estimate of beta) | 0.178 | ||||
| a (intercept, estimate of alpha) | -0.117 | ||||
| Mean Square Error | 0.081 | ||||
| DF error | 41.000 | ||||
| t(b) | 0.972 | ||||
| p(b) | 0.168 | ||||
| t(a) | -0.691 | ||||
| p(a) | 0.753 | ||||
| Lowerbound of 95% confidence interval for beta | -0.192 | ||||
| Upperbound of 95% confidence interval for beta | 0.547 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.459 | ||||
| Upperbound of 95% confidence interval for alpha | 0.225 | ||||
| Treynor index (mean / b) | -0.227 | ||||
| Jensen alpha (a) | -0.117 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.129 | ||||
| Expected Shortfall on VaR | 0.158 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.061 | ||||
| Expected Shortfall on VaR | 0.123 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 43.000 | ||||
| Minimum | 0.713 | ||||
| Quartile 1 | 0.971 | ||||
| Median | 0.999 | ||||
| Quartile 3 | 1.036 | ||||
| Maximum | 1.203 | ||||
| Mean of quarter 1 | 0.918 | ||||
| Mean of quarter 2 | 0.989 | ||||
| Mean of quarter 3 | 1.015 | ||||
| Mean of quarter 4 | 1.093 | ||||
| Inter Quartile Range | 0.064 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.047 | ||||
| Mean of outliers low | 0.789 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.195 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.423 | ||||
| VaR(95%) (moments method) | 0.084 | ||||
| Expected Shortfall (moments method) | 0.168 | ||||
| Extreme Value Index (regression method) | 1.092 | ||||
| VaR(95%) (regression method) | 0.085 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.024 | ||||
| Median | 0.030 | ||||
| Quartile 3 | 0.030 | ||||
| Maximum | 0.333 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.030 | ||||
| Mean of quarter 3 | 0.030 | ||||
| Mean of quarter 4 | 0.333 | ||||
| Inter Quartile Range | 0.006 | ||||
| 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 | 0.200 | ||||
| Mean of outliers high | 0.333 | ||||
| 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) | 0.004 | ||||
| Compounded annual return (geometric extrapolation) | 0.004 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.011 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.011 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.023 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.020 | ||||
| SD | 0.292 | ||||
| Sharpe ratio (Glass type estimate) | 0.069 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.069 | ||||
| df | 950.000 | ||||
| t | 0.131 | ||||
| p | 0.448 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.960 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.098 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.960 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.098 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.091 | ||||
| Upside Potential Ratio | 6.534 | ||||
| Upside part of mean | 1.448 | ||||
| Downside part of mean | -1.428 | ||||
| Upside SD | 0.189 | ||||
| Downside SD | 0.222 | ||||
| N nonnegative terms | 448.000 | ||||
| N negative terms | 503.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 951.000 | ||||
| Mean of predictor | 0.486 | ||||
| Mean of criterion | 0.020 | ||||
| SD of predictor | 0.292 | ||||
| SD of criterion | 0.292 | ||||
| Covariance | 0.028 | ||||
| r | 0.334 | ||||
| b (slope, estimate of beta) | 0.333 | ||||
| a (intercept, estimate of alpha) | -0.142 | ||||
| Mean Square Error | 0.076 | ||||
| DF error | 949.000 | ||||
| t(b) | 10.901 | ||||
| p(b) | -0.000 | ||||
| t(a) | -0.978 | ||||
| p(a) | 0.836 | ||||
| Lowerbound of 95% confidence interval for beta | 0.273 | ||||
| Upperbound of 95% confidence interval for beta | 0.393 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.427 | ||||
| Upperbound of 95% confidence interval for alpha | 0.143 | ||||
| Treynor index (mean / b) | 0.060 | ||||
| Jensen alpha (a) | -0.142 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.024 | ||||
| SD | 0.300 | ||||
| Sharpe ratio (Glass type estimate) | -0.080 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.080 | ||||
| df | 950.000 | ||||
| t | -0.152 | ||||
| p | 0.561 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.109 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.949 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.109 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.949 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.102 | ||||
| Upside Potential Ratio | 6.067 | ||||
| Upside part of mean | 1.430 | ||||
| Downside part of mean | -1.454 | ||||
| Upside SD | 0.186 | ||||
| Downside SD | 0.236 | ||||
| N nonnegative terms | 448.000 | ||||
| N negative terms | 503.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 951.000 | ||||
| Mean of predictor | 0.443 | ||||
| Mean of criterion | -0.024 | ||||
| SD of predictor | 0.296 | ||||
| SD of criterion | 0.300 | ||||
| Covariance | 0.029 | ||||
| r | 0.325 | ||||
| b (slope, estimate of beta) | 0.329 | ||||
| a (intercept, estimate of alpha) | -0.170 | ||||
| Mean Square Error | 0.081 | ||||
| DF error | 949.000 | ||||
| t(b) | 10.572 | ||||
| p(b) | -0.000 | ||||
| t(a) | -1.132 | ||||
| p(a) | 0.871 | ||||
| Lowerbound of 95% confidence interval for beta | 0.268 | ||||
| Upperbound of 95% confidence interval for beta | 0.390 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.464 | ||||
| Upperbound of 95% confidence interval for alpha | 0.124 | ||||
| Treynor index (mean / b) | -0.073 | ||||
| Jensen alpha (a) | -0.170 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.030 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.013 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 951.000 | ||||
| Minimum | 0.754 | ||||
| Quartile 1 | 0.994 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.083 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.013 | ||||
| Number outliers low | 50.000 | ||||
| Percentage of outliers low | 0.053 | ||||
| Mean of outliers low | 0.957 | ||||
| Number of outliers high | 45.000 | ||||
| Percentage of outliers high | 0.047 | ||||
| Mean of outliers high | 1.041 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.277 | ||||
| VaR(95%) (moments method) | 0.017 | ||||
| Expected Shortfall (moments method) | 0.030 | ||||
| Extreme Value Index (regression method) | 0.139 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 25.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.006 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.042 | ||||
| Maximum | 0.387 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.024 | ||||
| Mean of quarter 4 | 0.154 | ||||
| Inter Quartile Range | 0.036 | ||||
| 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 | 0.080 | ||||
| Mean of outliers high | 0.334 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.790 | ||||
| VaR(95%) (moments method) | 0.166 | ||||
| Expected Shortfall (moments method) | 0.821 | ||||
| Extreme Value Index (regression method) | 1.197 | ||||
| VaR(95%) (regression method) | 0.159 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.021 | ||||
| Compounded annual return (geometric extrapolation) | 0.020 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.052 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.131 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.537 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.542 | ||||
| SD | 0.501 | ||||
| Sharpe ratio (Glass type estimate) | -1.081 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.075 | ||||
| df | 130.000 | ||||
| t | -0.764 | ||||
| p | 0.533 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.854 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.696 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.849 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.700 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.272 | ||||
| Upside Potential Ratio | 5.217 | ||||
| Upside part of mean | 2.222 | ||||
| Downside part of mean | -2.764 | ||||
| Upside SD | 0.263 | ||||
| Downside SD | 0.426 | ||||
| N nonnegative terms | 60.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.922 | ||||
| Mean of criterion | -0.542 | ||||
| SD of predictor | 0.488 | ||||
| SD of criterion | 0.501 | ||||
| Covariance | 0.086 | ||||
| r | 0.353 | ||||
| b (slope, estimate of beta) | 0.363 | ||||
| a (intercept, estimate of alpha) | -0.876 | ||||
| Mean Square Error | 0.222 | ||||
| DF error | 129.000 | ||||
| t(b) | 4.288 | ||||
| p(b) | 0.280 | ||||
| t(a) | -1.307 | ||||
| p(a) | 0.573 | ||||
| Lowerbound of 95% confidence interval for beta | 0.195 | ||||
| Upperbound of 95% confidence interval for beta | 0.530 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.202 | ||||
| Upperbound of 95% confidence interval for alpha | 0.450 | ||||
| Treynor index (mean / b) | -1.493 | ||||
| Jensen alpha (a) | -0.876 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.679 | ||||
| SD | 0.537 | ||||
| Sharpe ratio (Glass type estimate) | -1.263 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.256 | ||||
| df | 130.000 | ||||
| t | -0.893 | ||||
| p | 0.539 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.037 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.515 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.032 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.520 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.441 | ||||
| Upside Potential Ratio | 4.643 | ||||
| Upside part of mean | 2.188 | ||||
| Downside part of mean | -2.867 | ||||
| Upside SD | 0.258 | ||||
| Downside SD | 0.471 | ||||
| N nonnegative terms | 60.000 | ||||
| N negative terms | 71.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.801 | ||||
| Mean of criterion | -0.679 | ||||
| SD of predictor | 0.493 | ||||
| SD of criterion | 0.537 | ||||
| Covariance | 0.087 | ||||
| r | 0.329 | ||||
| b (slope, estimate of beta) | 0.359 | ||||
| a (intercept, estimate of alpha) | -0.966 | ||||
| Mean Square Error | 0.260 | ||||
| DF error | 129.000 | ||||
| t(b) | 3.956 | ||||
| p(b) | 0.294 | ||||
| t(a) | -1.334 | ||||
| p(a) | 0.574 | ||||
| Lowerbound of 95% confidence interval for beta | 0.179 | ||||
| Upperbound of 95% confidence interval for beta | 0.538 | ||||
| Lowerbound of 95% confidence interval for alpha | -2.399 | ||||
| Upperbound of 95% confidence interval for alpha | 0.466 | ||||
| Treynor index (mean / b) | -1.891 | ||||
| Jensen alpha (a) | -0.966 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.056 | ||||
| Expected Shortfall on VaR | 0.069 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.754 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 0.998 | ||||
| Quartile 3 | 1.014 | ||||
| Maximum | 1.062 | ||||
| Mean of quarter 1 | 0.966 | ||||
| Mean of quarter 2 | 0.992 | ||||
| Mean of quarter 3 | 1.005 | ||||
| Mean of quarter 4 | 1.029 | ||||
| Inter Quartile Range | 0.028 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.008 | ||||
| Mean of outliers low | 0.754 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.008 | ||||
| Mean of outliers high | 1.062 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.421 | ||||
| VaR(95%) (moments method) | 0.036 | ||||
| Expected Shortfall (moments method) | 0.067 | ||||
| Extreme Value Index (regression method) | 0.223 | ||||
| VaR(95%) (regression method) | 0.028 | ||||
| Expected Shortfall (regression method) | 0.041 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.181 | ||||
| Quartile 1 | 0.232 | ||||
| Median | 0.284 | ||||
| Quartile 3 | 0.335 | ||||
| Maximum | 0.387 | ||||
| Mean of quarter 1 | 0.181 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.387 | ||||
| Inter Quartile Range | 0.103 | ||||
| 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) | -0.544 | ||||
| Compounded annual return (geometric extrapolation) | -0.470 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.214 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.214 | ||||
| Compounded annual return / Expected Shortfall lognormal | -6.857 | ||||