Advanced Statistics: Isonomy Plus
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 | 0.088 | ||||
| SD | 0.145 | ||||
| Sharpe ratio (Glass type estimate) | 0.605 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.601 | ||||
| df | 113.000 | ||||
| t | 1.864 | ||||
| p | 0.391 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.037 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.244 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.040 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.241 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.445 | ||||
| Upside Potential Ratio | 3.133 | ||||
| Upside part of mean | 0.190 | ||||
| Downside part of mean | -0.103 | ||||
| Upside SD | 0.134 | ||||
| Downside SD | 0.061 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 114.000 | ||||
| Mean of predictor | 0.169 | ||||
| Mean of criterion | 0.088 | ||||
| SD of predictor | 0.178 | ||||
| SD of criterion | 0.145 | ||||
| Covariance | 0.007 | ||||
| r | 0.271 | ||||
| b (slope, estimate of beta) | 0.221 | ||||
| a (intercept, estimate of alpha) | 0.050 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 112.000 | ||||
| t(b) | 2.978 | ||||
| p(b) | 0.365 | ||||
| t(a) | 1.066 | ||||
| p(a) | 0.450 | ||||
| Lowerbound of 95% confidence interval for beta | 0.074 | ||||
| Upperbound of 95% confidence interval for beta | 0.368 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.043 | ||||
| Upperbound of 95% confidence interval for alpha | 0.144 | ||||
| Treynor index (mean / b) | 0.397 | ||||
| Jensen alpha (a) | 0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.078 | ||||
| SD | 0.136 | ||||
| Sharpe ratio (Glass type estimate) | 0.572 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.568 | ||||
| df | 113.000 | ||||
| t | 1.763 | ||||
| p | 0.396 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.070 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.211 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.072 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.208 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.248 | ||||
| Upside Potential Ratio | 2.921 | ||||
| Upside part of mean | 0.182 | ||||
| Downside part of mean | -0.104 | ||||
| Upside SD | 0.122 | ||||
| Downside SD | 0.062 | ||||
| N nonnegative terms | 56.000 | ||||
| N negative terms | 58.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 114.000 | ||||
| Mean of predictor | 0.152 | ||||
| Mean of criterion | 0.078 | ||||
| SD of predictor | 0.180 | ||||
| SD of criterion | 0.136 | ||||
| Covariance | 0.007 | ||||
| r | 0.268 | ||||
| b (slope, estimate of beta) | 0.203 | ||||
| a (intercept, estimate of alpha) | 0.047 | ||||
| Mean Square Error | 0.017 | ||||
| DF error | 112.000 | ||||
| t(b) | 2.948 | ||||
| p(b) | 0.366 | ||||
| t(a) | 1.067 | ||||
| p(a) | 0.450 | ||||
| Lowerbound of 95% confidence interval for beta | 0.067 | ||||
| Upperbound of 95% confidence interval for beta | 0.340 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.040 | ||||
| Upperbound of 95% confidence interval for alpha | 0.134 | ||||
| Treynor index (mean / b) | 0.383 | ||||
| Jensen alpha (a) | 0.047 | ||||
| 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 | 0.072 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.020 | ||||
| Expected Shortfall on VaR | 0.039 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 114.000 | ||||
| Minimum | 0.914 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.026 | ||||
| Maximum | 1.304 | ||||
| Mean of quarter 1 | 0.975 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.012 | ||||
| Mean of quarter 4 | 1.058 | ||||
| Inter Quartile Range | 0.033 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.018 | ||||
| Mean of outliers low | 0.924 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.053 | ||||
| Mean of outliers high | 1.129 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.502 | ||||
| VaR(95%) (moments method) | 0.025 | ||||
| Expected Shortfall (moments method) | 0.058 | ||||
| Extreme Value Index (regression method) | 0.598 | ||||
| VaR(95%) (regression method) | 0.022 | ||||
| Expected Shortfall (regression method) | 0.058 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.008 | ||||
| Median | 0.013 | ||||
| Quartile 3 | 0.049 | ||||
| Maximum | 0.187 | ||||
| Mean of quarter 1 | 0.005 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.028 | ||||
| Mean of quarter 4 | 0.104 | ||||
| Inter Quartile Range | 0.040 | ||||
| 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 | 0.187 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.896 | ||||
| VaR(95%) (moments method) | 0.114 | ||||
| Expected Shortfall (moments method) | 0.126 | ||||
| Extreme Value Index (regression method) | 0.436 | ||||
| VaR(95%) (regression method) | 0.118 | ||||
| Expected Shortfall (regression method) | 0.216 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.229 | ||||
| Compounded annual return (geometric extrapolation) | 0.129 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.694 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.241 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.807 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.078 | ||||
| SD | 0.144 | ||||
| Sharpe ratio (Glass type estimate) | 0.541 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.541 | ||||
| df | 2505.000 | ||||
| t | 1.674 | ||||
| p | 0.047 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.093 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.175 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.093 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.175 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.831 | ||||
| Upside Potential Ratio | 7.278 | ||||
| Upside part of mean | 0.682 | ||||
| Downside part of mean | -0.605 | ||||
| Upside SD | 0.109 | ||||
| Downside SD | 0.094 | ||||
| N nonnegative terms | 1310.000 | ||||
| N negative terms | 1196.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2506.000 | ||||
| Mean of predictor | 0.185 | ||||
| Mean of criterion | 0.078 | ||||
| SD of predictor | 0.231 | ||||
| SD of criterion | 0.144 | ||||
| Covariance | -0.003 | ||||
| r | -0.077 | ||||
| b (slope, estimate of beta) | -0.048 | ||||
| a (intercept, estimate of alpha) | 0.087 | ||||
| Mean Square Error | 0.021 | ||||
| DF error | 2504.000 | ||||
| t(b) | -3.855 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.867 | ||||
| p(a) | 0.031 | ||||
| Lowerbound of 95% confidence interval for beta | -0.072 | ||||
| Upperbound of 95% confidence interval for beta | -0.024 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.004 | ||||
| Upperbound of 95% confidence interval for alpha | 0.178 | ||||
| Treynor index (mean / b) | -1.628 | ||||
| Jensen alpha (a) | 0.087 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.068 | ||||
| SD | 0.143 | ||||
| Sharpe ratio (Glass type estimate) | 0.472 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.472 | ||||
| df | 2505.000 | ||||
| t | 1.459 | ||||
| p | 0.072 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.162 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.106 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.162 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.105 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.707 | ||||
| Upside Potential Ratio | 7.080 | ||||
| Upside part of mean | 0.677 | ||||
| Downside part of mean | -0.609 | ||||
| Upside SD | 0.107 | ||||
| Downside SD | 0.096 | ||||
| N nonnegative terms | 1310.000 | ||||
| N negative terms | 1196.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 2506.000 | ||||
| Mean of predictor | 0.158 | ||||
| Mean of criterion | 0.068 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.143 | ||||
| Covariance | -0.003 | ||||
| r | -0.077 | ||||
| b (slope, estimate of beta) | -0.047 | ||||
| a (intercept, estimate of alpha) | 0.075 | ||||
| Mean Square Error | 0.020 | ||||
| DF error | 2504.000 | ||||
| t(b) | -3.848 | ||||
| p(b) | 1.000 | ||||
| t(a) | 1.623 | ||||
| p(a) | 0.052 | ||||
| Lowerbound of 95% confidence interval for beta | -0.071 | ||||
| Upperbound of 95% confidence interval for beta | -0.023 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.016 | ||||
| Upperbound of 95% confidence interval for alpha | 0.166 | ||||
| Treynor index (mean / b) | -1.429 | ||||
| Jensen alpha (a) | 0.075 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.014 | ||||
| Expected Shortfall on VaR | 0.018 | ||||
| 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 | 2506.000 | ||||
| Minimum | 0.892 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.123 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.009 | ||||
| Inter Quartile Range | 0.006 | ||||
| Number outliers low | 113.000 | ||||
| Percentage of outliers low | 0.045 | ||||
| Mean of outliers low | 0.980 | ||||
| Number of outliers high | 113.000 | ||||
| Percentage of outliers high | 0.045 | ||||
| Mean of outliers high | 1.024 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.399 | ||||
| VaR(95%) (moments method) | 0.008 | ||||
| Expected Shortfall (moments method) | 0.015 | ||||
| Extreme Value Index (regression method) | 0.279 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.012 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 89.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.002 | ||||
| Median | 0.006 | ||||
| Quartile 3 | 0.022 | ||||
| Maximum | 0.284 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.005 | ||||
| Mean of quarter 3 | 0.014 | ||||
| Mean of quarter 4 | 0.071 | ||||
| Inter Quartile Range | 0.020 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 12.000 | ||||
| Percentage of outliers high | 0.135 | ||||
| Mean of outliers high | 0.105 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.374 | ||||
| VaR(95%) (moments method) | 0.067 | ||||
| Expected Shortfall (moments method) | 0.128 | ||||
| Extreme Value Index (regression method) | 0.452 | ||||
| VaR(95%) (regression method) | 0.070 | ||||
| Expected Shortfall (regression method) | 0.146 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.199 | ||||
| Compounded annual return (geometric extrapolation) | 0.118 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.416 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.654 | ||||
| Compounded annual return / Expected Shortfall lognormal | 6.620 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.917 | ||||
| SD | 0.304 | ||||
| Sharpe ratio (Glass type estimate) | 3.016 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.999 | ||||
| df | 130.000 | ||||
| t | 2.133 | ||||
| p | 0.408 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.215 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.807 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.203 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.795 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.825 | ||||
| Upside Potential Ratio | 11.879 | ||||
| Upside part of mean | 2.257 | ||||
| Downside part of mean | -1.340 | ||||
| Upside SD | 0.242 | ||||
| Downside SD | 0.190 | ||||
| N nonnegative terms | 79.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.028 | ||||
| Mean of criterion | 0.917 | ||||
| SD of predictor | 0.401 | ||||
| SD of criterion | 0.304 | ||||
| Covariance | 0.005 | ||||
| r | 0.042 | ||||
| b (slope, estimate of beta) | 0.032 | ||||
| a (intercept, estimate of alpha) | 0.884 | ||||
| Mean Square Error | 0.093 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.474 | ||||
| p(b) | 0.473 | ||||
| t(a) | 2.026 | ||||
| p(a) | 0.389 | ||||
| Lowerbound of 95% confidence interval for beta | -0.100 | ||||
| Upperbound of 95% confidence interval for beta | 0.163 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.021 | ||||
| Upperbound of 95% confidence interval for alpha | 1.748 | ||||
| Treynor index (mean / b) | 29.055 | ||||
| Jensen alpha (a) | 0.884 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.869 | ||||
| SD | 0.303 | ||||
| Sharpe ratio (Glass type estimate) | 2.866 | ||||
| Sharpe ratio (Hedges UMVUE) | 2.849 | ||||
| df | 130.000 | ||||
| t | 2.027 | ||||
| p | 0.413 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.067 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 5.654 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.056 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 5.643 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 4.484 | ||||
| Upside Potential Ratio | 11.492 | ||||
| Upside part of mean | 2.228 | ||||
| Downside part of mean | -1.359 | ||||
| Upside SD | 0.238 | ||||
| Downside SD | 0.194 | ||||
| N nonnegative terms | 79.000 | ||||
| N negative terms | 52.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.946 | ||||
| Mean of criterion | 0.869 | ||||
| SD of predictor | 0.404 | ||||
| SD of criterion | 0.303 | ||||
| Covariance | 0.005 | ||||
| r | 0.045 | ||||
| b (slope, estimate of beta) | 0.033 | ||||
| a (intercept, estimate of alpha) | 0.838 | ||||
| Mean Square Error | 0.093 | ||||
| DF error | 129.000 | ||||
| t(b) | 0.507 | ||||
| p(b) | 0.472 | ||||
| t(a) | 1.927 | ||||
| p(a) | 0.394 | ||||
| Lowerbound of 95% confidence interval for beta | -0.097 | ||||
| Upperbound of 95% confidence interval for beta | 0.164 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.022 | ||||
| Upperbound of 95% confidence interval for alpha | 1.698 | ||||
| Treynor index (mean / b) | 25.969 | ||||
| Jensen alpha (a) | 0.838 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.027 | ||||
| Expected Shortfall on VaR | 0.035 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.021 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.929 | ||||
| Quartile 1 | 0.995 | ||||
| Median | 1.003 | ||||
| Quartile 3 | 1.013 | ||||
| Maximum | 1.066 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.008 | ||||
| Mean of quarter 4 | 1.026 | ||||
| Inter Quartile Range | 0.018 | ||||
| Number outliers low | 5.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.957 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.038 | ||||
| Mean of outliers high | 1.052 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.189 | ||||
| VaR(95%) (moments method) | 0.015 | ||||
| Expected Shortfall (moments method) | 0.019 | ||||
| Extreme Value Index (regression method) | -0.125 | ||||
| VaR(95%) (regression method) | 0.019 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 16.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.004 | ||||
| Median | 0.019 | ||||
| Quartile 3 | 0.045 | ||||
| Maximum | 0.135 | ||||
| Mean of quarter 1 | 0.002 | ||||
| Mean of quarter 2 | 0.011 | ||||
| Mean of quarter 3 | 0.031 | ||||
| Mean of quarter 4 | 0.077 | ||||
| Inter Quartile Range | 0.041 | ||||
| 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 | 0.062 | ||||
| Mean of outliers high | 0.135 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.067 | ||||
| VaR(95%) (moments method) | 0.082 | ||||
| Expected Shortfall (moments method) | 0.111 | ||||
| Extreme Value Index (regression method) | 0.934 | ||||
| VaR(95%) (regression method) | 0.104 | ||||
| Expected Shortfall (regression method) | 1.142 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 1.158 | ||||
| Compounded annual return (geometric extrapolation) | 1.493 | ||||
| Calmar ratio (compounded annual return / max draw down) | 11.061 | ||||
| Compounded annual return / average of 25% largest draw downs | 19.499 | ||||
| Compounded annual return / Expected Shortfall lognormal | 43.024 | ||||