Advanced Statistics: Isonomy
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 | 0.082 | ||||
| SD | 0.091 | ||||
| Sharpe ratio (Glass type estimate) | 0.897 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.891 | ||||
| df | 115.000 | ||||
| t | 2.788 | ||||
| p | 0.342 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.254 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.536 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.250 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.532 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.963 | ||||
| Upside Potential Ratio | 3.572 | ||||
| Upside part of mean | 0.149 | ||||
| Downside part of mean | -0.067 | ||||
| Upside SD | 0.084 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 116.000 | ||||
| Mean of predictor | 0.168 | ||||
| Mean of criterion | 0.082 | ||||
| SD of predictor | 0.202 | ||||
| SD of criterion | 0.091 | ||||
| Covariance | 0.011 | ||||
| r | 0.607 | ||||
| b (slope, estimate of beta) | 0.274 | ||||
| a (intercept, estimate of alpha) | 0.036 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 114.000 | ||||
| t(b) | 8.153 | ||||
| p(b) | 0.197 | ||||
| t(a) | 1.482 | ||||
| p(a) | 0.431 | ||||
| Lowerbound of 95% confidence interval for beta | 0.208 | ||||
| Upperbound of 95% confidence interval for beta | 0.341 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.012 | ||||
| Upperbound of 95% confidence interval for alpha | 0.083 | ||||
| Treynor index (mean / b) | 0.298 | ||||
| Jensen alpha (a) | 0.036 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.077 | ||||
| SD | 0.089 | ||||
| Sharpe ratio (Glass type estimate) | 0.868 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.863 | ||||
| df | 115.000 | ||||
| t | 2.700 | ||||
| p | 0.346 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.226 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.507 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.223 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.503 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.818 | ||||
| Upside Potential Ratio | 3.411 | ||||
| Upside part of mean | 0.145 | ||||
| Downside part of mean | -0.068 | ||||
| Upside SD | 0.081 | ||||
| Downside SD | 0.042 | ||||
| N nonnegative terms | 65.000 | ||||
| N negative terms | 51.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 116.000 | ||||
| Mean of predictor | 0.147 | ||||
| Mean of criterion | 0.077 | ||||
| SD of predictor | 0.196 | ||||
| SD of criterion | 0.089 | ||||
| Covariance | 0.010 | ||||
| r | 0.584 | ||||
| b (slope, estimate of beta) | 0.265 | ||||
| a (intercept, estimate of alpha) | 0.038 | ||||
| Mean Square Error | 0.005 | ||||
| DF error | 114.000 | ||||
| t(b) | 7.672 | ||||
| p(b) | 0.208 | ||||
| t(a) | 1.604 | ||||
| p(a) | 0.426 | ||||
| Lowerbound of 95% confidence interval for beta | 0.196 | ||||
| Upperbound of 95% confidence interval for beta | 0.333 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.009 | ||||
| Upperbound of 95% confidence interval for alpha | 0.086 | ||||
| Treynor index (mean / b) | 0.292 | ||||
| Jensen alpha (a) | 0.038 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.035 | ||||
| Expected Shortfall on VaR | 0.045 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.012 | ||||
| Expected Shortfall on VaR | 0.024 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 116.000 | ||||
| Minimum | 0.925 | ||||
| Quartile 1 | 0.996 | ||||
| Median | 1.007 | ||||
| Quartile 3 | 1.021 | ||||
| Maximum | 1.139 | ||||
| Mean of quarter 1 | 0.985 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.013 | ||||
| Mean of quarter 4 | 1.044 | ||||
| Inter Quartile Range | 0.025 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.017 | ||||
| Mean of outliers low | 0.940 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.052 | ||||
| Mean of outliers high | 1.085 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.022 | ||||
| VaR(95%) (moments method) | 0.011 | ||||
| Expected Shortfall (moments method) | 0.016 | ||||
| Extreme Value Index (regression method) | 0.084 | ||||
| VaR(95%) (regression method) | 0.017 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.002 | ||||
| Quartile 1 | 0.009 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.041 | ||||
| Maximum | 0.116 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.010 | ||||
| Mean of quarter 3 | 0.021 | ||||
| Mean of quarter 4 | 0.067 | ||||
| Inter Quartile Range | 0.032 | ||||
| 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 | 0.067 | ||||
| Mean of outliers high | 0.116 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.396 | ||||
| VaR(95%) (moments method) | 0.079 | ||||
| Expected Shortfall (moments method) | 0.129 | ||||
| Extreme Value Index (regression method) | 2.430 | ||||
| VaR(95%) (regression method) | 0.093 | ||||
| Expected Shortfall (regression method) | NA | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.230 | ||||
| Compounded annual return (geometric extrapolation) | 0.129 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.110 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.938 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.839 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.080 | ||||
| SD | 0.090 | ||||
| Sharpe ratio (Glass type estimate) | 0.884 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.884 | ||||
| df | 2537.000 | ||||
| t | 2.752 | ||||
| p | 0.003 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.254 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.514 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.254 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.514 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.321 | ||||
| Upside Potential Ratio | 7.482 | ||||
| Upside part of mean | 0.451 | ||||
| Downside part of mean | -0.371 | ||||
| Upside SD | 0.067 | ||||
| Downside SD | 0.060 | ||||
| N nonnegative terms | 1358.000 | ||||
| N negative terms | 1180.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2538.000 | ||||
| Mean of predictor | 0.181 | ||||
| Mean of criterion | 0.080 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.090 | ||||
| Covariance | 0.011 | ||||
| r | 0.497 | ||||
| b (slope, estimate of beta) | 0.177 | ||||
| a (intercept, estimate of alpha) | 0.047 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 2536.000 | ||||
| t(b) | 28.830 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.891 | ||||
| p(a) | 0.029 | ||||
| Lowerbound of 95% confidence interval for beta | 0.165 | ||||
| Upperbound of 95% confidence interval for beta | 0.189 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.002 | ||||
| Upperbound of 95% confidence interval for alpha | 0.097 | ||||
| Treynor index (mean / b) | 0.449 | ||||
| Jensen alpha (a) | 0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.075 | ||||
| SD | 0.090 | ||||
| Sharpe ratio (Glass type estimate) | 0.841 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.841 | ||||
| df | 2537.000 | ||||
| t | 2.617 | ||||
| p | 0.004 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.211 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.471 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.210 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.471 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.239 | ||||
| Upside Potential Ratio | 7.356 | ||||
| Upside part of mean | 0.448 | ||||
| Downside part of mean | -0.373 | ||||
| Upside SD | 0.066 | ||||
| Downside SD | 0.061 | ||||
| N nonnegative terms | 1358.000 | ||||
| N negative terms | 1180.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2538.000 | ||||
| Mean of predictor | 0.149 | ||||
| Mean of criterion | 0.075 | ||||
| SD of predictor | 0.252 | ||||
| SD of criterion | 0.090 | ||||
| Covariance | 0.011 | ||||
| r | 0.494 | ||||
| b (slope, estimate of beta) | 0.176 | ||||
| a (intercept, estimate of alpha) | 0.049 | ||||
| Mean Square Error | 0.006 | ||||
| DF error | 2536.000 | ||||
| t(b) | 28.586 | ||||
| p(b) | 0.000 | ||||
| t(a) | 1.962 | ||||
| p(a) | 0.025 | ||||
| Lowerbound of 95% confidence interval for beta | 0.164 | ||||
| Upperbound of 95% confidence interval for beta | 0.188 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.000 | ||||
| Upperbound of 95% confidence interval for alpha | 0.098 | ||||
| Treynor index (mean / b) | 0.429 | ||||
| Jensen alpha (a) | 0.049 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.009 | ||||
| Expected Shortfall on VaR | 0.011 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 2538.000 | ||||
| Minimum | 0.945 | ||||
| Quartile 1 | 0.999 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.078 | ||||
| Mean of quarter 1 | 0.995 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.006 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 108.000 | ||||
| Percentage of outliers low | 0.043 | ||||
| Mean of outliers low | 0.986 | ||||
| Number of outliers high | 113.000 | ||||
| Percentage of outliers high | 0.045 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.499 | ||||
| VaR(95%) (moments method) | 0.005 | ||||
| Expected Shortfall (moments method) | 0.011 | ||||
| Extreme Value Index (regression method) | 0.377 | ||||
| VaR(95%) (regression method) | 0.004 | ||||
| Expected Shortfall (regression method) | 0.008 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 117.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.145 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.039 | ||||
| Inter Quartile Range | 0.014 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 11.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 0.065 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.337 | ||||
| VaR(95%) (moments method) | 0.040 | ||||
| Expected Shortfall (moments method) | 0.071 | ||||
| Extreme Value Index (regression method) | 0.114 | ||||
| VaR(95%) (regression method) | 0.035 | ||||
| Expected Shortfall (regression method) | 0.050 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.225 | ||||
| Compounded annual return (geometric extrapolation) | 0.127 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.877 | ||||
| Compounded annual return / average of 25% largest draw downs | 3.253 | ||||
| Compounded annual return / Expected Shortfall lognormal | 11.447 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.761 | ||||
| SD | 0.182 | ||||
| Sharpe ratio (Glass type estimate) | 4.178 | ||||
| Sharpe ratio (Hedges UMVUE) | 4.154 | ||||
| df | 130.000 | ||||
| t | 2.955 | ||||
| p | 0.375 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 1.353 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 6.989 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.337 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 6.972 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6.707 | ||||
| Upside Potential Ratio | 13.268 | ||||
| Upside part of mean | 1.505 | ||||
| Downside part of mean | -0.744 | ||||
| Upside SD | 0.149 | ||||
| Downside SD | 0.113 | ||||
| N nonnegative terms | 81.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.060 | ||||
| Mean of criterion | 0.761 | ||||
| SD of predictor | 0.401 | ||||
| SD of criterion | 0.182 | ||||
| Covariance | 0.047 | ||||
| r | 0.644 | ||||
| b (slope, estimate of beta) | 0.293 | ||||
| a (intercept, estimate of alpha) | 0.450 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 129.000 | ||||
| t(b) | 9.571 | ||||
| p(b) | 0.120 | ||||
| t(a) | 2.249 | ||||
| p(a) | 0.377 | ||||
| Lowerbound of 95% confidence interval for beta | 0.232 | ||||
| Upperbound of 95% confidence interval for beta | 0.353 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.054 | ||||
| Upperbound of 95% confidence interval for alpha | 0.847 | ||||
| Treynor index (mean / b) | 2.599 | ||||
| Jensen alpha (a) | 0.450 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.743 | ||||
| SD | 0.182 | ||||
| Sharpe ratio (Glass type estimate) | 4.082 | ||||
| Sharpe ratio (Hedges UMVUE) | 4.058 | ||||
| df | 130.000 | ||||
| t | 2.886 | ||||
| p | 0.377 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 1.258 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 6.890 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.243 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 6.874 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 6.465 | ||||
| Upside Potential Ratio | 12.995 | ||||
| Upside part of mean | 1.493 | ||||
| Downside part of mean | -0.750 | ||||
| Upside SD | 0.148 | ||||
| Downside SD | 0.115 | ||||
| N nonnegative terms | 81.000 | ||||
| N negative terms | 50.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.977 | ||||
| Mean of criterion | 0.743 | ||||
| SD of predictor | 0.404 | ||||
| SD of criterion | 0.182 | ||||
| Covariance | 0.048 | ||||
| r | 0.648 | ||||
| b (slope, estimate of beta) | 0.292 | ||||
| a (intercept, estimate of alpha) | 0.458 | ||||
| Mean Square Error | 0.019 | ||||
| DF error | 129.000 | ||||
| t(b) | 9.659 | ||||
| p(b) | 0.119 | ||||
| t(a) | 2.299 | ||||
| p(a) | 0.375 | ||||
| Lowerbound of 95% confidence interval for beta | 0.232 | ||||
| Upperbound of 95% confidence interval for beta | 0.352 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.064 | ||||
| Upperbound of 95% confidence interval for alpha | 0.852 | ||||
| Treynor index (mean / b) | 2.545 | ||||
| Jensen alpha (a) | 0.458 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.016 | ||||
| Expected Shortfall on VaR | 0.020 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.012 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.959 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.004 | ||||
| Quartile 3 | 1.009 | ||||
| Maximum | 1.038 | ||||
| Mean of quarter 1 | 0.989 | ||||
| Mean of quarter 2 | 1.001 | ||||
| Mean of quarter 3 | 1.006 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.011 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.033 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.037 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.010 | ||||
| Extreme Value Index (regression method) | 0.171 | ||||
| VaR(95%) (regression method) | 0.011 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 22.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.007 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.061 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.004 | ||||
| Mean of quarter 3 | 0.012 | ||||
| Mean of quarter 4 | 0.033 | ||||
| Inter Quartile Range | 0.014 | ||||
| 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 | 0.091 | ||||
| Mean of outliers high | 0.053 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.384 | ||||
| VaR(95%) (moments method) | 0.035 | ||||
| Expected Shortfall (moments method) | 0.042 | ||||
| Extreme Value Index (regression method) | 0.050 | ||||
| VaR(95%) (regression method) | 0.046 | ||||
| Expected Shortfall (regression method) | 0.066 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.964 | ||||
| Compounded annual return (geometric extrapolation) | 1.197 | ||||
| Calmar ratio (compounded annual return / max draw down) | 19.754 | ||||
| Compounded annual return / average of 25% largest draw downs | 36.108 | ||||
| Compounded annual return / Expected Shortfall lognormal | 59.405 | ||||