Advanced Statistics: Legend Global
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 | -0.220 | ||||
| SD | 0.305 | ||||
| Sharpe ratio (Glass type estimate) | -0.721 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.707 | ||||
| df | 40.000 | ||||
| t | -1.333 | ||||
| p | 0.905 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.789 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.355 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.779 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.364 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.844 | ||||
| Upside Potential Ratio | 0.974 | ||||
| Upside part of mean | 0.253 | ||||
| Downside part of mean | -0.473 | ||||
| Upside SD | 0.164 | ||||
| Downside SD | 0.260 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.494 | ||||
| Mean of criterion | -0.220 | ||||
| SD of predictor | 0.342 | ||||
| SD of criterion | 0.305 | ||||
| Covariance | 0.053 | ||||
| r | 0.508 | ||||
| b (slope, estimate of beta) | 0.452 | ||||
| a (intercept, estimate of alpha) | -0.443 | ||||
| Mean Square Error | 0.071 | ||||
| DF error | 39.000 | ||||
| t(b) | 3.678 | ||||
| p(b) | 0.000 | ||||
| t(a) | -2.837 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | 0.203 | ||||
| Upperbound of 95% confidence interval for beta | 0.700 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.759 | ||||
| Upperbound of 95% confidence interval for alpha | -0.127 | ||||
| Treynor index (mean / b) | -0.486 | ||||
| Jensen alpha (a) | -0.443 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.270 | ||||
| SD | 0.321 | ||||
| Sharpe ratio (Glass type estimate) | -0.839 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.823 | ||||
| df | 40.000 | ||||
| t | -1.551 | ||||
| p | 0.936 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.910 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.242 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.899 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.252 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.930 | ||||
| Upside Potential Ratio | 0.829 | ||||
| Upside part of mean | 0.241 | ||||
| Downside part of mean | -0.510 | ||||
| Upside SD | 0.150 | ||||
| Downside SD | 0.290 | ||||
| N nonnegative terms | 19.000 | ||||
| N negative terms | 22.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 41.000 | ||||
| Mean of predictor | 0.434 | ||||
| Mean of criterion | -0.270 | ||||
| SD of predictor | 0.310 | ||||
| SD of criterion | 0.321 | ||||
| Covariance | 0.045 | ||||
| r | 0.450 | ||||
| b (slope, estimate of beta) | 0.467 | ||||
| a (intercept, estimate of alpha) | -0.472 | ||||
| Mean Square Error | 0.085 | ||||
| DF error | 39.000 | ||||
| t(b) | 3.145 | ||||
| p(b) | 0.002 | ||||
| t(a) | -2.779 | ||||
| p(a) | 0.996 | ||||
| Lowerbound of 95% confidence interval for beta | 0.166 | ||||
| Upperbound of 95% confidence interval for beta | 0.767 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.816 | ||||
| Upperbound of 95% confidence interval for alpha | -0.129 | ||||
| Treynor index (mean / b) | -0.578 | ||||
| Jensen alpha (a) | -0.472 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.161 | ||||
| Expected Shortfall on VaR | 0.192 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.095 | ||||
| Expected Shortfall on VaR | 0.178 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 41.000 | ||||
| Minimum | 0.716 | ||||
| Quartile 1 | 0.952 | ||||
| Median | 0.990 | ||||
| Quartile 3 | 1.031 | ||||
| Maximum | 1.249 | ||||
| Mean of quarter 1 | 0.880 | ||||
| Mean of quarter 2 | 0.978 | ||||
| Mean of quarter 3 | 1.020 | ||||
| Mean of quarter 4 | 1.074 | ||||
| Inter Quartile Range | 0.079 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.049 | ||||
| Mean of outliers low | 0.748 | ||||
| Number of outliers high | 1.000 | ||||
| Percentage of outliers high | 0.024 | ||||
| Mean of outliers high | 1.249 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.131 | ||||
| VaR(95%) (moments method) | 0.118 | ||||
| Expected Shortfall (moments method) | 0.174 | ||||
| Extreme Value Index (regression method) | 0.388 | ||||
| VaR(95%) (regression method) | 0.129 | ||||
| Expected Shortfall (regression method) | 0.238 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.624 | ||||
| Quartile 1 | 0.624 | ||||
| Median | 0.624 | ||||
| Quartile 3 | 0.624 | ||||
| Maximum | 0.624 | ||||
| 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) | -0.157 | ||||
| Compounded annual return (geometric extrapolation) | -0.202 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.324 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.052 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.213 | ||||
| SD | 0.332 | ||||
| Sharpe ratio (Glass type estimate) | -0.642 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.641 | ||||
| df | 898.000 | ||||
| t | -1.189 | ||||
| p | 0.883 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.700 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.417 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.700 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.417 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.864 | ||||
| Upside Potential Ratio | 6.442 | ||||
| Upside part of mean | 1.590 | ||||
| Downside part of mean | -1.803 | ||||
| Upside SD | 0.222 | ||||
| Downside SD | 0.247 | ||||
| N nonnegative terms | 409.000 | ||||
| N negative terms | 490.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 899.000 | ||||
| Mean of predictor | 0.516 | ||||
| Mean of criterion | -0.213 | ||||
| SD of predictor | 0.329 | ||||
| SD of criterion | 0.332 | ||||
| Covariance | 0.044 | ||||
| r | 0.407 | ||||
| b (slope, estimate of beta) | 0.412 | ||||
| a (intercept, estimate of alpha) | -0.426 | ||||
| Mean Square Error | 0.092 | ||||
| DF error | 897.000 | ||||
| t(b) | 13.364 | ||||
| p(b) | -0.000 | ||||
| t(a) | -2.587 | ||||
| p(a) | 0.995 | ||||
| Lowerbound of 95% confidence interval for beta | 0.351 | ||||
| Upperbound of 95% confidence interval for beta | 0.472 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.749 | ||||
| Upperbound of 95% confidence interval for alpha | -0.103 | ||||
| Treynor index (mean / b) | -0.517 | ||||
| Jensen alpha (a) | -0.426 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.269 | ||||
| SD | 0.335 | ||||
| Sharpe ratio (Glass type estimate) | -0.803 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.802 | ||||
| df | 898.000 | ||||
| t | -1.487 | ||||
| p | 0.931 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.861 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.256 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.861 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.256 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.052 | ||||
| Upside Potential Ratio | 6.129 | ||||
| Upside part of mean | 1.566 | ||||
| Downside part of mean | -1.835 | ||||
| Upside SD | 0.217 | ||||
| Downside SD | 0.255 | ||||
| N nonnegative terms | 409.000 | ||||
| N negative terms | 490.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 899.000 | ||||
| Mean of predictor | 0.462 | ||||
| Mean of criterion | -0.269 | ||||
| SD of predictor | 0.331 | ||||
| SD of criterion | 0.335 | ||||
| Covariance | 0.045 | ||||
| r | 0.405 | ||||
| b (slope, estimate of beta) | 0.409 | ||||
| a (intercept, estimate of alpha) | -0.458 | ||||
| Mean Square Error | 0.094 | ||||
| DF error | 897.000 | ||||
| t(b) | 13.251 | ||||
| p(b) | -0.000 | ||||
| t(a) | -2.758 | ||||
| p(a) | 0.997 | ||||
| Lowerbound of 95% confidence interval for beta | 0.349 | ||||
| Upperbound of 95% confidence interval for beta | 0.470 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.784 | ||||
| Upperbound of 95% confidence interval for alpha | -0.132 | ||||
| Treynor index (mean / b) | -0.657 | ||||
| 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%) | 0.034 | ||||
| Expected Shortfall on VaR | 0.043 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.017 | ||||
| Expected Shortfall on VaR | 0.033 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 899.000 | ||||
| Minimum | 0.835 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.008 | ||||
| Maximum | 1.108 | ||||
| Mean of quarter 1 | 0.977 | ||||
| Mean of quarter 2 | 0.996 | ||||
| Mean of quarter 3 | 1.003 | ||||
| Mean of quarter 4 | 1.022 | ||||
| Inter Quartile Range | 0.016 | ||||
| Number outliers low | 38.000 | ||||
| Percentage of outliers low | 0.042 | ||||
| Mean of outliers low | 0.944 | ||||
| Number of outliers high | 38.000 | ||||
| Percentage of outliers high | 0.042 | ||||
| Mean of outliers high | 1.051 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.333 | ||||
| VaR(95%) (moments method) | 0.023 | ||||
| Expected Shortfall (moments method) | 0.041 | ||||
| Extreme Value Index (regression method) | 0.182 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.032 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.327 | ||||
| Maximum | 0.641 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.014 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.641 | ||||
| Inter Quartile Range | 0.320 | ||||
| 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) | -0.157 | ||||
| Compounded annual return (geometric extrapolation) | -0.201 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.314 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.314 | ||||
| Compounded annual return / Expected Shortfall lognormal | -4.713 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.024 | ||||
| SD | 0.239 | ||||
| Sharpe ratio (Glass type estimate) | 0.100 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.100 | ||||
| df | 130.000 | ||||
| t | 0.071 | ||||
| p | 0.497 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.671 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.872 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.672 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.872 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.148 | ||||
| Upside Potential Ratio | 8.410 | ||||
| Upside part of mean | 1.368 | ||||
| Downside part of mean | -1.344 | ||||
| Upside SD | 0.174 | ||||
| Downside SD | 0.163 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.099 | ||||
| Mean of criterion | 0.024 | ||||
| SD of predictor | 0.480 | ||||
| SD of criterion | 0.239 | ||||
| Covariance | 0.058 | ||||
| r | 0.508 | ||||
| b (slope, estimate of beta) | 0.253 | ||||
| a (intercept, estimate of alpha) | -0.254 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.697 | ||||
| p(b) | 0.191 | ||||
| t(a) | -0.861 | ||||
| p(a) | 0.548 | ||||
| Lowerbound of 95% confidence interval for beta | 0.179 | ||||
| Upperbound of 95% confidence interval for beta | 0.328 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.839 | ||||
| Upperbound of 95% confidence interval for alpha | 0.330 | ||||
| Treynor index (mean / b) | 0.095 | ||||
| Jensen alpha (a) | -0.254 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.004 | ||||
| SD | 0.239 | ||||
| Sharpe ratio (Glass type estimate) | -0.018 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.018 | ||||
| df | 130.000 | ||||
| t | -0.013 | ||||
| p | 0.501 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.790 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 2.754 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.790 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 2.754 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.026 | ||||
| Upside Potential Ratio | 8.213 | ||||
| Upside part of mean | 1.353 | ||||
| Downside part of mean | -1.357 | ||||
| Upside SD | 0.172 | ||||
| Downside SD | 0.165 | ||||
| N nonnegative terms | 53.000 | ||||
| N negative terms | 78.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.982 | ||||
| Mean of criterion | -0.004 | ||||
| SD of predictor | 0.481 | ||||
| SD of criterion | 0.239 | ||||
| Covariance | 0.058 | ||||
| r | 0.502 | ||||
| b (slope, estimate of beta) | 0.249 | ||||
| a (intercept, estimate of alpha) | -0.249 | ||||
| Mean Square Error | 0.043 | ||||
| DF error | 129.000 | ||||
| t(b) | 6.592 | ||||
| p(b) | 0.194 | ||||
| t(a) | -0.843 | ||||
| p(a) | 0.547 | ||||
| Lowerbound of 95% confidence interval for beta | 0.175 | ||||
| Upperbound of 95% confidence interval for beta | 0.324 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.834 | ||||
| Upperbound of 95% confidence interval for alpha | 0.336 | ||||
| Treynor index (mean / b) | -0.017 | ||||
| Jensen alpha (a) | -0.249 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.030 | ||||
| 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 | 0.963 | ||||
| Quartile 1 | 0.992 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.044 | ||||
| Mean of quarter 1 | 0.982 | ||||
| Mean of quarter 2 | 0.998 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.019 | ||||
| Inter Quartile Range | 0.015 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.965 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.046 | ||||
| Mean of outliers high | 1.037 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.008 | ||||
| VaR(95%) (moments method) | 0.017 | ||||
| Expected Shortfall (moments method) | 0.023 | ||||
| Extreme Value Index (regression method) | -0.210 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.023 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 4.000 | ||||
| Minimum | 0.027 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.059 | ||||
| Quartile 3 | 0.087 | ||||
| Maximum | 0.096 | ||||
| Mean of quarter 1 | 0.027 | ||||
| Mean of quarter 2 | 0.034 | ||||
| Mean of quarter 3 | 0.084 | ||||
| Mean of quarter 4 | 0.096 | ||||
| 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) | 0.040 | ||||
| Compounded annual return (geometric extrapolation) | 0.041 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.420 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.420 | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.351 | ||||