Advanced Statistics: Kingda Forex
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 | 0.039 | ||||
| SD | 0.165 | ||||
| Sharpe ratio (Glass type estimate) | 0.237 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.234 | ||||
| df | 68.000 | ||||
| t | 0.568 | ||||
| p | 0.286 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.582 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.055 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.584 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.053 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.288 | ||||
| Upside Potential Ratio | 1.184 | ||||
| Upside part of mean | 0.160 | ||||
| Downside part of mean | -0.121 | ||||
| Upside SD | 0.092 | ||||
| Downside SD | 0.135 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.293 | ||||
| Mean of criterion | 0.039 | ||||
| SD of predictor | 0.264 | ||||
| SD of criterion | 0.165 | ||||
| Covariance | 0.000 | ||||
| r | 0.000 | ||||
| b (slope, estimate of beta) | 0.000 | ||||
| a (intercept, estimate of alpha) | 0.039 | ||||
| Mean Square Error | 0.027 | ||||
| DF error | 67.000 | ||||
| t(b) | 0.003 | ||||
| p(b) | 0.499 | ||||
| t(a) | 0.536 | ||||
| p(a) | 0.297 | ||||
| Lowerbound of 95% confidence interval for beta | -0.152 | ||||
| Upperbound of 95% confidence interval for beta | 0.152 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.106 | ||||
| Upperbound of 95% confidence interval for alpha | 0.184 | ||||
| Treynor index (mean / b) | 186.797 | ||||
| Jensen alpha (a) | 0.039 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.024 | ||||
| SD | 0.183 | ||||
| Sharpe ratio (Glass type estimate) | 0.129 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.128 | ||||
| df | 68.000 | ||||
| t | 0.310 | ||||
| p | 0.379 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.689 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.946 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.690 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.945 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.149 | ||||
| Upside Potential Ratio | 0.984 | ||||
| Upside part of mean | 0.156 | ||||
| Downside part of mean | -0.132 | ||||
| Upside SD | 0.089 | ||||
| Downside SD | 0.158 | ||||
| N nonnegative terms | 30.000 | ||||
| N negative terms | 39.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 69.000 | ||||
| Mean of predictor | 0.257 | ||||
| Mean of criterion | 0.024 | ||||
| SD of predictor | 0.251 | ||||
| SD of criterion | 0.183 | ||||
| Covariance | 0.001 | ||||
| r | 0.013 | ||||
| b (slope, estimate of beta) | 0.010 | ||||
| a (intercept, estimate of alpha) | 0.021 | ||||
| Mean Square Error | 0.034 | ||||
| DF error | 67.000 | ||||
| t(b) | 0.109 | ||||
| p(b) | 0.457 | ||||
| t(a) | 0.264 | ||||
| p(a) | 0.396 | ||||
| Lowerbound of 95% confidence interval for beta | -0.168 | ||||
| Upperbound of 95% confidence interval for beta | 0.187 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.139 | ||||
| Upperbound of 95% confidence interval for alpha | 0.181 | ||||
| Treynor index (mean / b) | 2.430 | ||||
| Jensen alpha (a) | 0.021 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.081 | ||||
| Expected Shortfall on VaR | 0.101 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.024 | ||||
| Expected Shortfall on VaR | 0.055 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 69.000 | ||||
| Minimum | 0.699 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.002 | ||||
| Quartile 3 | 1.022 | ||||
| Maximum | 1.104 | ||||
| Mean of quarter 1 | 0.969 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.011 | ||||
| Mean of quarter 4 | 1.050 | ||||
| Inter Quartile Range | 0.024 | ||||
| Number outliers low | 3.000 | ||||
| Percentage of outliers low | 0.043 | ||||
| Mean of outliers low | 0.860 | ||||
| Number of outliers high | 4.000 | ||||
| Percentage of outliers high | 0.058 | ||||
| Mean of outliers high | 1.088 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 1.264 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 1.362 | ||||
| VaR(95%) (regression method) | 0.025 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 8.000 | ||||
| Minimum | 0.003 | ||||
| Quartile 1 | 0.005 | ||||
| Median | 0.014 | ||||
| Quartile 3 | 0.041 | ||||
| Maximum | 0.338 | ||||
| Mean of quarter 1 | 0.004 | ||||
| Mean of quarter 2 | 0.009 | ||||
| Mean of quarter 3 | 0.028 | ||||
| Mean of quarter 4 | 0.190 | ||||
| Inter Quartile Range | 0.036 | ||||
| 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 | 0.125 | ||||
| Mean of outliers high | 0.338 | ||||
| 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) | 0.083 | ||||
| Compounded annual return (geometric extrapolation) | 0.070 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.207 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.369 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.692 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.040 | ||||
| SD | 0.183 | ||||
| Sharpe ratio (Glass type estimate) | 0.220 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.220 | ||||
| df | 1512.000 | ||||
| t | 0.529 | ||||
| p | 0.493 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.596 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.036 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.596 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.036 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.285 | ||||
| Upside Potential Ratio | 3.945 | ||||
| Upside part of mean | 0.557 | ||||
| Downside part of mean | -0.517 | ||||
| Upside SD | 0.116 | ||||
| Downside SD | 0.141 | ||||
| N nonnegative terms | 613.000 | ||||
| N negative terms | 900.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1513.000 | ||||
| Mean of predictor | 0.315 | ||||
| Mean of criterion | 0.040 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.183 | ||||
| Covariance | 0.001 | ||||
| r | 0.027 | ||||
| b (slope, estimate of beta) | 0.017 | ||||
| a (intercept, estimate of alpha) | 0.035 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 1511.000 | ||||
| t(b) | 1.059 | ||||
| p(b) | 0.483 | ||||
| t(a) | 0.458 | ||||
| p(a) | 0.493 | ||||
| Lowerbound of 95% confidence interval for beta | -0.014 | ||||
| Upperbound of 95% confidence interval for beta | 0.048 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.114 | ||||
| Upperbound of 95% confidence interval for alpha | 0.184 | ||||
| Treynor index (mean / b) | 2.387 | ||||
| Jensen alpha (a) | 0.035 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | 0.023 | ||||
| SD | 0.186 | ||||
| Sharpe ratio (Glass type estimate) | 0.124 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.124 | ||||
| df | 1512.000 | ||||
| t | 0.298 | ||||
| p | 0.496 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.692 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.940 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.692 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.940 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.156 | ||||
| Upside Potential Ratio | 3.720 | ||||
| Upside part of mean | 0.550 | ||||
| Downside part of mean | -0.527 | ||||
| Upside SD | 0.113 | ||||
| Downside SD | 0.148 | ||||
| N nonnegative terms | 613.000 | ||||
| N negative terms | 900.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1513.000 | ||||
| Mean of predictor | 0.269 | ||||
| Mean of criterion | 0.023 | ||||
| SD of predictor | 0.308 | ||||
| SD of criterion | 0.186 | ||||
| Covariance | 0.002 | ||||
| r | 0.026 | ||||
| b (slope, estimate of beta) | 0.016 | ||||
| a (intercept, estimate of alpha) | 0.019 | ||||
| Mean Square Error | 0.035 | ||||
| DF error | 1511.000 | ||||
| t(b) | 1.022 | ||||
| p(b) | 0.483 | ||||
| t(a) | 0.243 | ||||
| p(a) | 0.496 | ||||
| Lowerbound of 95% confidence interval for beta | -0.015 | ||||
| Upperbound of 95% confidence interval for beta | 0.046 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.133 | ||||
| Upperbound of 95% confidence interval for alpha | 0.171 | ||||
| Treynor index (mean / b) | 1.455 | ||||
| Jensen alpha (a) | 0.019 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.019 | ||||
| Expected Shortfall on VaR | 0.023 | ||||
| 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 | 1513.000 | ||||
| Minimum | 0.854 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.001 | ||||
| Maximum | 1.109 | ||||
| Mean of quarter 1 | 0.993 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.008 | ||||
| Inter Quartile Range | 0.002 | ||||
| Number outliers low | 169.000 | ||||
| Percentage of outliers low | 0.112 | ||||
| Mean of outliers low | 0.984 | ||||
| Number of outliers high | 197.000 | ||||
| Percentage of outliers high | 0.130 | ||||
| Mean of outliers high | 1.014 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.861 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.038 | ||||
| Extreme Value Index (regression method) | 0.431 | ||||
| VaR(95%) (regression method) | 0.006 | ||||
| Expected Shortfall (regression method) | 0.015 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 63.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.011 | ||||
| Quartile 3 | 0.037 | ||||
| Maximum | 0.341 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.024 | ||||
| Mean of quarter 4 | 0.087 | ||||
| Inter Quartile Range | 0.034 | ||||
| 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 | 0.095 | ||||
| Mean of outliers high | 0.143 | ||||
| Risk estimates based on draw downs (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.329 | ||||
| VaR(95%) (moments method) | 0.091 | ||||
| Expected Shortfall (moments method) | 0.156 | ||||
| Extreme Value Index (regression method) | 0.586 | ||||
| VaR(95%) (regression method) | 0.081 | ||||
| Expected Shortfall (regression method) | 0.181 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.082 | ||||
| Compounded annual return (geometric extrapolation) | 0.069 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.204 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.799 | ||||
| Compounded annual return / Expected Shortfall lognormal | 2.973 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.008 | ||||
| Sharpe ratio (Glass type estimate) | -7.384 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.341 | ||||
| df | 130.000 | ||||
| t | -5.221 | ||||
| p | 0.708 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -10.284 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.458 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10.253 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.429 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -7.526 | ||||
| Upside Potential Ratio | 3.520 | ||||
| Upside part of mean | 0.027 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.008 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 92.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.049 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.499 | ||||
| SD of criterion | 0.008 | ||||
| Covariance | -0.001 | ||||
| r | -0.335 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.038 | ||||
| p(b) | 0.709 | ||||
| t(a) | -4.951 | ||||
| p(a) | 0.747 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | -0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.073 | ||||
| Upperbound of 95% confidence interval for alpha | -0.032 | ||||
| Treynor index (mean / b) | 10.988 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.058 | ||||
| SD | 0.008 | ||||
| Sharpe ratio (Glass type estimate) | -7.386 | ||||
| Sharpe ratio (Hedges UMVUE) | -7.344 | ||||
| df | 130.000 | ||||
| t | -5.223 | ||||
| p | 0.708 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -10.287 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.460 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -10.256 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.432 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -7.527 | ||||
| Upside Potential Ratio | 3.517 | ||||
| Upside part of mean | 0.027 | ||||
| Downside part of mean | -0.085 | ||||
| Upside SD | 0.004 | ||||
| Downside SD | 0.008 | ||||
| N nonnegative terms | 39.000 | ||||
| N negative terms | 92.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 0.924 | ||||
| Mean of criterion | -0.058 | ||||
| SD of predictor | 0.496 | ||||
| SD of criterion | 0.008 | ||||
| Covariance | -0.001 | ||||
| r | -0.335 | ||||
| b (slope, estimate of beta) | -0.005 | ||||
| a (intercept, estimate of alpha) | -0.053 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 129.000 | ||||
| t(b) | -4.033 | ||||
| p(b) | 0.709 | ||||
| t(a) | -5.021 | ||||
| p(a) | 0.750 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | -0.003 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.074 | ||||
| Upperbound of 95% confidence interval for alpha | -0.032 | ||||
| Treynor index (mean / b) | 10.948 | ||||
| Jensen alpha (a) | -0.053 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.001 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.998 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.001 | ||||
| Mean of quarter 1 | 0.999 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.001 | ||||
| Inter Quartile Range | 0.001 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.015 | ||||
| Mean of outliers high | 1.001 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.004 | ||||
| VaR(95%) (moments method) | -0.002 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | 0.573 | ||||
| VaR(95%) (regression method) | 0.001 | ||||
| Expected Shortfall (regression method) | 0.001 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.000 | ||||
| Quartile 1 | 0.000 | ||||
| Median | 0.000 | ||||
| Quartile 3 | 0.004 | ||||
| Maximum | 0.008 | ||||
| Mean of quarter 1 | 0.000 | ||||
| Mean of quarter 2 | 0.000 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.008 | ||||
| Inter Quartile Range | 0.004 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.014 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.689 | ||||
| Compounded annual return / average of 25% largest draw downs | -1.689 | ||||
| Compounded annual return / Expected Shortfall lognormal | -11.415 | ||||