Advanced Statistics: WSS_AustralianDollar
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 | 0.112 | ||||
| SD | 0.390 | ||||
| Sharpe ratio (Glass type estimate) | 0.287 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.282 | ||||
| df | 44.000 | ||||
| t | 0.556 | ||||
| p | 0.291 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.729 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.299 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.732 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.296 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.706 | ||||
| Upside Potential Ratio | 1.917 | ||||
| Upside part of mean | 0.304 | ||||
| Downside part of mean | -0.192 | ||||
| Upside SD | 0.353 | ||||
| Downside SD | 0.159 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.458 | ||||
| Mean of criterion | 0.112 | ||||
| SD of predictor | 0.300 | ||||
| SD of criterion | 0.390 | ||||
| Covariance | 0.013 | ||||
| r | 0.108 | ||||
| b (slope, estimate of beta) | 0.140 | ||||
| a (intercept, estimate of alpha) | 0.048 | ||||
| Mean Square Error | 0.154 | ||||
| DF error | 43.000 | ||||
| t(b) | 0.712 | ||||
| p(b) | 0.240 | ||||
| t(a) | 0.215 | ||||
| p(a) | 0.415 | ||||
| Lowerbound of 95% confidence interval for beta | -0.257 | ||||
| Upperbound of 95% confidence interval for beta | 0.538 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.400 | ||||
| Upperbound of 95% confidence interval for alpha | 0.495 | ||||
| Treynor index (mean / b) | 0.798 | ||||
| Jensen alpha (a) | 0.048 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.050 | ||||
| SD | 0.339 | ||||
| Sharpe ratio (Glass type estimate) | 0.149 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.146 | ||||
| df | 44.000 | ||||
| t | 0.289 | ||||
| p | 0.387 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.864 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.161 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.866 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.159 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.286 | ||||
| Upside Potential Ratio | 1.451 | ||||
| Upside part of mean | 0.256 | ||||
| Downside part of mean | -0.206 | ||||
| Upside SD | 0.285 | ||||
| Downside SD | 0.177 | ||||
| N nonnegative terms | 5.000 | ||||
| N negative terms | 40.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 45.000 | ||||
| Mean of predictor | 0.409 | ||||
| Mean of criterion | 0.050 | ||||
| SD of predictor | 0.282 | ||||
| SD of criterion | 0.339 | ||||
| Covariance | 0.013 | ||||
| r | 0.135 | ||||
| b (slope, estimate of beta) | 0.162 | ||||
| a (intercept, estimate of alpha) | -0.016 | ||||
| Mean Square Error | 0.115 | ||||
| DF error | 43.000 | ||||
| t(b) | 0.891 | ||||
| p(b) | 0.189 | ||||
| t(a) | -0.083 | ||||
| p(a) | 0.533 | ||||
| Lowerbound of 95% confidence interval for beta | -0.205 | ||||
| Upperbound of 95% confidence interval for beta | 0.529 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.400 | ||||
| Upperbound of 95% confidence interval for alpha | 0.368 | ||||
| Treynor index (mean / b) | 0.311 | ||||
| Jensen alpha (a) | -0.016 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.145 | ||||
| Expected Shortfall on VaR | 0.179 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.052 | ||||
| Expected Shortfall on VaR | 0.107 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 45.000 | ||||
| Minimum | 0.759 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.616 | ||||
| Mean of quarter 1 | 0.952 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.105 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 8.000 | ||||
| Percentage of outliers low | 0.178 | ||||
| Mean of outliers low | 0.928 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.111 | ||||
| Mean of outliers high | 1.232 | ||||
| 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) | 0.662 | ||||
| VaR(95%) (regression method) | 0.077 | ||||
| Expected Shortfall (regression method) | 0.332 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.147 | ||||
| Quartile 1 | 0.160 | ||||
| Median | 0.174 | ||||
| Quartile 3 | 0.207 | ||||
| Maximum | 0.241 | ||||
| Mean of quarter 1 | 0.147 | ||||
| Mean of quarter 2 | 0.174 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.241 | ||||
| Inter Quartile Range | 0.047 | ||||
| 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) | 0.113 | ||||
| Compounded annual return (geometric extrapolation) | 0.099 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.412 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.412 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.555 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.074 | ||||
| SD | 0.216 | ||||
| Sharpe ratio (Glass type estimate) | 0.341 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.341 | ||||
| df | 983.000 | ||||
| t | 0.661 | ||||
| p | 0.255 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.671 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.352 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.671 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.352 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.503 | ||||
| Upside Potential Ratio | 4.790 | ||||
| Upside part of mean | 0.703 | ||||
| Downside part of mean | -0.629 | ||||
| Upside SD | 0.159 | ||||
| Downside SD | 0.147 | ||||
| N nonnegative terms | 145.000 | ||||
| N negative terms | 839.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 984.000 | ||||
| Mean of predictor | 0.461 | ||||
| Mean of criterion | 0.074 | ||||
| SD of predictor | 0.305 | ||||
| SD of criterion | 0.216 | ||||
| Covariance | 0.003 | ||||
| r | 0.052 | ||||
| b (slope, estimate of beta) | 0.037 | ||||
| a (intercept, estimate of alpha) | 0.057 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 982.000 | ||||
| t(b) | 1.636 | ||||
| p(b) | 0.051 | ||||
| t(a) | 0.506 | ||||
| p(a) | 0.306 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.081 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.163 | ||||
| Upperbound of 95% confidence interval for alpha | 0.276 | ||||
| Treynor index (mean / b) | 1.996 | ||||
| Jensen alpha (a) | 0.057 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.050 | ||||
| SD | 0.216 | ||||
| Sharpe ratio (Glass type estimate) | 0.232 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.232 | ||||
| df | 983.000 | ||||
| t | 0.451 | ||||
| p | 0.326 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.779 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.244 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.779 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.244 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.333 | ||||
| Upside Potential Ratio | 4.569 | ||||
| Upside part of mean | 0.690 | ||||
| Downside part of mean | -0.640 | ||||
| Upside SD | 0.155 | ||||
| Downside SD | 0.151 | ||||
| N nonnegative terms | 145.000 | ||||
| N negative terms | 839.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 984.000 | ||||
| Mean of predictor | 0.413 | ||||
| Mean of criterion | 0.050 | ||||
| SD of predictor | 0.307 | ||||
| SD of criterion | 0.216 | ||||
| Covariance | 0.004 | ||||
| r | 0.053 | ||||
| b (slope, estimate of beta) | 0.038 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.047 | ||||
| DF error | 982.000 | ||||
| t(b) | 1.676 | ||||
| p(b) | 0.047 | ||||
| t(a) | 0.310 | ||||
| p(a) | 0.378 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.082 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.185 | ||||
| Upperbound of 95% confidence interval for alpha | 0.254 | ||||
| Treynor index (mean / b) | 1.337 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.022 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.008 | ||||
| Expected Shortfall on VaR | 0.016 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 984.000 | ||||
| Minimum | 0.899 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.106 | ||||
| Mean of quarter 1 | 0.991 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 136.000 | ||||
| Percentage of outliers low | 0.138 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 147.000 | ||||
| Percentage of outliers high | 0.149 | ||||
| Mean of outliers high | 1.018 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.079 | ||||
| VaR(95%) (moments method) | 0.003 | ||||
| Expected Shortfall (moments method) | 0.005 | ||||
| Extreme Value Index (regression method) | 0.097 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.018 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 16.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.017 | ||||
| Median | 0.040 | ||||
| Quartile 3 | 0.091 | ||||
| Maximum | 0.324 | ||||
| Mean of quarter 1 | 0.006 | ||||
| Mean of quarter 2 | 0.025 | ||||
| Mean of quarter 3 | 0.058 | ||||
| Mean of quarter 4 | 0.216 | ||||
| Inter Quartile Range | 0.074 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.188 | ||||
| Mean of outliers high | 0.254 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -10.502 | ||||
| VaR(95%) (moments method) | 0.201 | ||||
| Expected Shortfall (moments method) | 0.201 | ||||
| Extreme Value Index (regression method) | -0.693 | ||||
| VaR(95%) (regression method) | 0.233 | ||||
| Expected Shortfall (regression method) | 0.261 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.113 | ||||
| Compounded annual return (geometric extrapolation) | 0.099 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.305 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.459 | ||||
| Compounded annual return / Expected Shortfall lognormal | 3.663 | ||||
| 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 | 1.020 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.430 | ||||
| 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 | 0.926 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.432 | ||||
| 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) | -8723124155893386.000 | ||||
| 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) | 225799164291428976545007260401664.000 | ||||
| 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 | ||||