Advanced Statistics: WSS_Gold100oz
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 | 0.221 | ||||
| SD | 0.197 | ||||
| Sharpe ratio (Glass type estimate) | 1.123 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.111 | ||||
| df | 68.000 | ||||
| t | 2.694 | ||||
| p | 0.004 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.281 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.958 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.273 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.949 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.846 | ||||
| Upside Potential Ratio | 5.483 | ||||
| Upside part of mean | 0.315 | ||||
| Downside part of mean | -0.094 | ||||
| Upside SD | 0.197 | ||||
| Downside SD | 0.057 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.275 | ||||
| Mean of criterion | 0.221 | ||||
| SD of predictor | 0.274 | ||||
| SD of criterion | 0.197 | ||||
| Covariance | -0.005 | ||||
| r | -0.090 | ||||
| b (slope, estimate of beta) | -0.065 | ||||
| a (intercept, estimate of alpha) | 0.239 | ||||
| Mean Square Error | 0.039 | ||||
| DF error | 67.000 | ||||
| t(b) | -0.739 | ||||
| p(b) | 0.769 | ||||
| t(a) | 2.784 | ||||
| p(a) | 0.003 | ||||
| Lowerbound of 95% confidence interval for beta | -0.239 | ||||
| Upperbound of 95% confidence interval for beta | 0.110 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.068 | ||||
| Upperbound of 95% confidence interval for alpha | 0.410 | ||||
| Treynor index (mean / b) | -3.417 | ||||
| Jensen alpha (a) | 0.239 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.201 | ||||
| SD | 0.184 | ||||
| Sharpe ratio (Glass type estimate) | 1.094 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.082 | ||||
| df | 68.000 | ||||
| t | 2.624 | ||||
| p | 0.005 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.253 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.928 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.245 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.920 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 3.414 | ||||
| Upside Potential Ratio | 5.033 | ||||
| Upside part of mean | 0.296 | ||||
| Downside part of mean | -0.095 | ||||
| Upside SD | 0.182 | ||||
| Downside SD | 0.059 | ||||
| N nonnegative terms | 31.000 | ||||
| N negative terms | 38.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.238 | ||||
| Mean of criterion | 0.201 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.184 | ||||
| Covariance | -0.005 | ||||
| r | -0.096 | ||||
| b (slope, estimate of beta) | -0.068 | ||||
| a (intercept, estimate of alpha) | 0.217 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 67.000 | ||||
| t(b) | -0.786 | ||||
| p(b) | 0.783 | ||||
| t(a) | 2.731 | ||||
| p(a) | 0.004 | ||||
| Lowerbound of 95% confidence interval for beta | -0.242 | ||||
| Upperbound of 95% confidence interval for beta | 0.105 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.058 | ||||
| Upperbound of 95% confidence interval for alpha | 0.376 | ||||
| Treynor index (mean / b) | -2.940 | ||||
| Jensen alpha (a) | 0.217 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.068 | ||||
| Expected Shortfall on VaR | 0.088 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.038 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 69.000 | ||||
| Minimum | 0.916 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.031 | ||||
| Maximum | 1.249 | ||||
| Mean of quarter 1 | 0.978 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.014 | ||||
| Mean of quarter 4 | 1.100 | ||||
| Inter Quartile Range | 0.031 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.014 | ||||
| Mean of outliers low | 0.916 | ||||
| Number of outliers high | 8.000 | ||||
| Percentage of outliers high | 0.116 | ||||
| Mean of outliers high | 1.153 | ||||
| Risk estimates for a one-period unit investment (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) | -0.510 | ||||
| VaR(95%) (regression method) | 0.021 | ||||
| Expected Shortfall (regression method) | 0.027 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 5.000 | ||||
| Minimum | 0.008 | ||||
| Quartile 1 | 0.032 | ||||
| Median | 0.036 | ||||
| Quartile 3 | 0.084 | ||||
| Maximum | 0.105 | ||||
| Mean of quarter 1 | 0.020 | ||||
| Mean of quarter 2 | 0.036 | ||||
| Mean of quarter 3 | 0.084 | ||||
| Mean of quarter 4 | 0.105 | ||||
| Inter Quartile Range | 0.052 | ||||
| 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) | 0.537 | ||||
| Compounded annual return (geometric extrapolation) | 0.278 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.645 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.645 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.145 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.217 | ||||
| SD | 0.190 | ||||
| Sharpe ratio (Glass type estimate) | 1.140 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.140 | ||||
| df | 1517.000 | ||||
| t | 2.745 | ||||
| p | 0.455 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.325 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.955 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.324 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.955 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.861 | ||||
| Upside Potential Ratio | 6.802 | ||||
| Upside part of mean | 0.794 | ||||
| Downside part of mean | -0.576 | ||||
| Upside SD | 0.151 | ||||
| Downside SD | 0.117 | ||||
| N nonnegative terms | 554.000 | ||||
| N negative terms | 964.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1518.000 | ||||
| Mean of predictor | 0.291 | ||||
| Mean of criterion | 0.217 | ||||
| SD of predictor | 0.287 | ||||
| SD of criterion | 0.190 | ||||
| Covariance | -0.003 | ||||
| r | -0.056 | ||||
| b (slope, estimate of beta) | -0.037 | ||||
| a (intercept, estimate of alpha) | 0.228 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 1516.000 | ||||
| t(b) | -2.180 | ||||
| p(b) | 0.528 | ||||
| t(a) | 2.879 | ||||
| p(a) | 0.463 | ||||
| Lowerbound of 95% confidence interval for beta | -0.071 | ||||
| Upperbound of 95% confidence interval for beta | -0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.073 | ||||
| Upperbound of 95% confidence interval for alpha | 0.383 | ||||
| Treynor index (mean / b) | -5.846 | ||||
| Jensen alpha (a) | 0.228 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.199 | ||||
| SD | 0.190 | ||||
| Sharpe ratio (Glass type estimate) | 1.050 | ||||
| Sharpe ratio (Hedges UMVUE) | 1.050 | ||||
| df | 1517.000 | ||||
| t | 2.528 | ||||
| p | 0.459 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | 0.235 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.865 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.234 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.865 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 1.654 | ||||
| Upside Potential Ratio | 6.502 | ||||
| Upside part of mean | 0.783 | ||||
| Downside part of mean | -0.583 | ||||
| Upside SD | 0.147 | ||||
| Downside SD | 0.120 | ||||
| N nonnegative terms | 554.000 | ||||
| N negative terms | 964.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1518.000 | ||||
| Mean of predictor | 0.248 | ||||
| Mean of criterion | 0.199 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.190 | ||||
| Covariance | -0.003 | ||||
| r | -0.054 | ||||
| b (slope, estimate of beta) | -0.035 | ||||
| a (intercept, estimate of alpha) | 0.208 | ||||
| Mean Square Error | 0.036 | ||||
| DF error | 1516.000 | ||||
| t(b) | -2.112 | ||||
| p(b) | 0.527 | ||||
| t(a) | 2.637 | ||||
| p(a) | 0.466 | ||||
| Lowerbound of 95% confidence interval for beta | -0.067 | ||||
| Upperbound of 95% confidence interval for beta | -0.002 | ||||
| Lowerbound of 95% confidence interval for alpha | 0.053 | ||||
| Upperbound of 95% confidence interval for alpha | 0.362 | ||||
| Treynor index (mean / b) | -5.725 | ||||
| Jensen alpha (a) | 0.208 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.006 | ||||
| Expected Shortfall on VaR | 0.013 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1518.000 | ||||
| Minimum | 0.896 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.116 | ||||
| Mean of quarter 1 | 0.992 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.012 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 103.000 | ||||
| Percentage of outliers low | 0.068 | ||||
| Mean of outliers low | 0.981 | ||||
| Number of outliers high | 143.000 | ||||
| Percentage of outliers high | 0.094 | ||||
| Mean of outliers high | 1.023 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.542 | ||||
| VaR(95%) (moments method) | 0.007 | ||||
| Expected Shortfall (moments method) | 0.017 | ||||
| Extreme Value Index (regression method) | 0.358 | ||||
| VaR(95%) (regression method) | 0.007 | ||||
| Expected Shortfall (regression method) | 0.013 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 48.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.007 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.038 | ||||
| Maximum | 0.262 | ||||
| Mean of quarter 1 | 0.003 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.022 | ||||
| Mean of quarter 4 | 0.098 | ||||
| Inter Quartile Range | 0.031 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.125 | ||||
| Mean of outliers high | 0.133 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.038 | ||||
| VaR(95%) (moments method) | 0.093 | ||||
| Expected Shortfall (moments method) | 0.100 | ||||
| Extreme Value Index (regression method) | 0.163 | ||||
| VaR(95%) (regression method) | 0.098 | ||||
| Expected Shortfall (regression method) | 0.148 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.533 | ||||
| Compounded annual return (geometric extrapolation) | 0.275 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.051 | ||||
| Compounded annual return / average of 25% largest draw downs | 2.798 | ||||
| Compounded annual return / Expected Shortfall lognormal | 11.904 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | NA | ||||
| Sharpe ratio (Hedges UMVUE) | NA | ||||
| df | NA | ||||
| t | NA | ||||
| p | NA | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | NA | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.990 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.516 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | 0.000 | ||||
| r | NA | ||||
| b (slope, estimate of beta) | NA | ||||
| a (intercept, estimate of alpha) | NA | ||||
| Mean Square Error | NA | ||||
| DF error | NA | ||||
| t(b) | NA | ||||
| p(b) | NA | ||||
| t(a) | NA | ||||
| p(a) | NA | ||||
| Lowerbound of 95% confidence interval for beta | NA | ||||
| Upperbound of 95% confidence interval for beta | NA | ||||
| Lowerbound of 95% confidence interval for alpha | NA | ||||
| Upperbound of 95% confidence interval for alpha | NA | ||||
| Treynor index (mean / b) | NA | ||||
| Jensen alpha (a) | NA | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.044 | ||||
| SD | 0.000 | ||||
| Sharpe ratio (Glass type estimate) | -12492933348697024.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -12420719861132300.000 | ||||
| df | 130.000 | ||||
| t | -8833837887775228.000 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -13930479873814932.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10910959848449668.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -16.186 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.003 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 131.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.859 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.510 | ||||
| SD of criterion | 0.000 | ||||
| Covariance | -0.000 | ||||
| r | -0.000 | ||||
| b (slope, estimate of beta) | -0.000 | ||||
| a (intercept, estimate of alpha) | -0.044 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -8752114331685407.000 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.000 | ||||
| Upperbound of 95% confidence interval for beta | 0.000 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.044 | ||||
| Upperbound of 95% confidence interval for alpha | -0.044 | ||||
| Treynor index (mean / b) | 1159593673171795967890851996106752.000 | ||||
| Jensen alpha (a) | -0.044 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.000 | ||||
| Expected Shortfall on VaR | 0.000 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 1.000 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.000 | ||||
| Mean of quarter 1 | 1.000 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.000 | ||||
| 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 for a one-period unit investment (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 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 0.000 | ||||
| Minimum | NA | ||||
| Quartile 1 | NA | ||||
| Median | NA | ||||
| Quartile 3 | NA | ||||
| Maximum | NA | ||||
| 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 | NA | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 0.000 | ||||
| Percentage of outliers high | NA | ||||
| 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) | 0.000 | ||||
| Compounded annual return (geometric extrapolation) | 0.000 | ||||
| Calmar ratio (compounded annual return / max draw down) | NA | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.000 | ||||