Advanced Statistics: Ninja 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 | -0.118 | ||||
| SD | 0.100 | ||||
| Sharpe ratio (Glass type estimate) | -1.183 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.138 | ||||
| df | 20.000 | ||||
| t | -1.565 | ||||
| p | 0.665 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.695 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.357 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.661 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.385 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.350 | ||||
| Upside Potential Ratio | 0.779 | ||||
| Upside part of mean | 0.068 | ||||
| Downside part of mean | -0.186 | ||||
| Upside SD | 0.055 | ||||
| Downside SD | 0.088 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 21.000 | ||||
| Mean of predictor | 0.118 | ||||
| Mean of criterion | -0.118 | ||||
| SD of predictor | 0.198 | ||||
| SD of criterion | 0.100 | ||||
| Covariance | 0.001 | ||||
| r | 0.046 | ||||
| b (slope, estimate of beta) | 0.023 | ||||
| a (intercept, estimate of alpha) | -0.121 | ||||
| Mean Square Error | 0.010 | ||||
| DF error | 19.000 | ||||
| t(b) | 0.199 | ||||
| p(b) | 0.471 | ||||
| t(a) | -1.538 | ||||
| p(a) | 0.708 | ||||
| Lowerbound of 95% confidence interval for beta | -0.219 | ||||
| Upperbound of 95% confidence interval for beta | 0.266 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.285 | ||||
| Upperbound of 95% confidence interval for alpha | 0.044 | ||||
| Treynor index (mean / b) | -5.114 | ||||
| Jensen alpha (a) | -0.121 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.123 | ||||
| SD | 0.100 | ||||
| Sharpe ratio (Glass type estimate) | -1.228 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.181 | ||||
| df | 20.000 | ||||
| t | -1.624 | ||||
| p | 0.671 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.742 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.316 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.707 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.345 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.376 | ||||
| Upside Potential Ratio | 0.743 | ||||
| Upside part of mean | 0.066 | ||||
| Downside part of mean | -0.190 | ||||
| Upside SD | 0.053 | ||||
| Downside SD | 0.089 | ||||
| N nonnegative terms | 4.000 | ||||
| N negative terms | 17.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 21.000 | ||||
| Mean of predictor | 0.099 | ||||
| Mean of criterion | -0.123 | ||||
| SD of predictor | 0.194 | ||||
| SD of criterion | 0.100 | ||||
| Covariance | 0.001 | ||||
| r | 0.046 | ||||
| b (slope, estimate of beta) | 0.024 | ||||
| a (intercept, estimate of alpha) | -0.125 | ||||
| Mean Square Error | 0.011 | ||||
| DF error | 19.000 | ||||
| t(b) | 0.201 | ||||
| p(b) | 0.471 | ||||
| t(a) | -1.597 | ||||
| p(a) | 0.715 | ||||
| Lowerbound of 95% confidence interval for beta | -0.224 | ||||
| Upperbound of 95% confidence interval for beta | 0.271 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.290 | ||||
| Upperbound of 95% confidence interval for alpha | 0.039 | ||||
| Treynor index (mean / b) | -5.191 | ||||
| Jensen alpha (a) | -0.125 | ||||
| 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 | 0.068 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.046 | ||||
| Expected Shortfall on VaR | 0.073 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 21.000 | ||||
| Minimum | 0.942 | ||||
| Quartile 1 | 0.979 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.065 | ||||
| Mean of quarter 1 | 0.960 | ||||
| Mean of quarter 2 | 0.995 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.027 | ||||
| Inter Quartile Range | 0.021 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.095 | ||||
| Mean of outliers low | 0.942 | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 1.051 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -1.488 | ||||
| VaR(95%) (moments method) | 0.043 | ||||
| Expected Shortfall (moments method) | 0.044 | ||||
| Extreme Value Index (regression method) | -1.735 | ||||
| VaR(95%) (regression method) | 0.058 | ||||
| Expected Shortfall (regression method) | 0.059 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.139 | ||||
| Quartile 1 | 0.139 | ||||
| Median | 0.139 | ||||
| Quartile 3 | 0.139 | ||||
| Maximum | 0.139 | ||||
| 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) | -0.074 | ||||
| Compounded annual return (geometric extrapolation) | -0.076 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.545 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -1.126 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.114 | ||||
| SD | 0.121 | ||||
| Sharpe ratio (Glass type estimate) | -0.938 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.936 | ||||
| df | 618.000 | ||||
| t | -1.258 | ||||
| p | 0.896 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.399 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.525 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.398 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.526 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.373 | ||||
| Upside Potential Ratio | 5.060 | ||||
| Upside part of mean | 0.419 | ||||
| Downside part of mean | -0.532 | ||||
| Upside SD | 0.089 | ||||
| Downside SD | 0.083 | ||||
| N nonnegative terms | 118.000 | ||||
| N negative terms | 501.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 619.000 | ||||
| Mean of predictor | 0.208 | ||||
| Mean of criterion | -0.114 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.121 | ||||
| Covariance | -0.004 | ||||
| r | -0.140 | ||||
| b (slope, estimate of beta) | -0.072 | ||||
| a (intercept, estimate of alpha) | -0.099 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 617.000 | ||||
| t(b) | -3.509 | ||||
| p(b) | 1.000 | ||||
| t(a) | -1.101 | ||||
| p(a) | 0.864 | ||||
| Lowerbound of 95% confidence interval for beta | -0.112 | ||||
| Upperbound of 95% confidence interval for beta | -0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.275 | ||||
| Upperbound of 95% confidence interval for alpha | 0.077 | ||||
| Treynor index (mean / b) | 1.585 | ||||
| Jensen alpha (a) | -0.099 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.121 | ||||
| SD | 0.121 | ||||
| Sharpe ratio (Glass type estimate) | -1.002 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.000 | ||||
| df | 618.000 | ||||
| t | -1.344 | ||||
| p | 0.910 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -2.463 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.461 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -2.463 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.462 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -1.447 | ||||
| Upside Potential Ratio | 4.963 | ||||
| Upside part of mean | 0.415 | ||||
| Downside part of mean | -0.536 | ||||
| Upside SD | 0.087 | ||||
| Downside SD | 0.084 | ||||
| N nonnegative terms | 118.000 | ||||
| N negative terms | 501.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 619.000 | ||||
| Mean of predictor | 0.180 | ||||
| Mean of criterion | -0.121 | ||||
| SD of predictor | 0.236 | ||||
| SD of criterion | 0.121 | ||||
| Covariance | -0.004 | ||||
| r | -0.140 | ||||
| b (slope, estimate of beta) | -0.072 | ||||
| a (intercept, estimate of alpha) | -0.108 | ||||
| Mean Square Error | 0.014 | ||||
| DF error | 617.000 | ||||
| t(b) | -3.512 | ||||
| p(b) | 1.000 | ||||
| t(a) | -1.210 | ||||
| p(a) | 0.887 | ||||
| Lowerbound of 95% confidence interval for beta | -0.112 | ||||
| Upperbound of 95% confidence interval for beta | -0.032 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.283 | ||||
| Upperbound of 95% confidence interval for alpha | 0.067 | ||||
| Treynor index (mean / b) | 1.689 | ||||
| Jensen alpha (a) | -0.108 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.011 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.005 | ||||
| Expected Shortfall on VaR | 0.010 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 619.000 | ||||
| Minimum | 0.960 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.053 | ||||
| Mean of quarter 1 | 0.994 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.005 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 144.000 | ||||
| Percentage of outliers low | 0.233 | ||||
| Mean of outliers low | 0.994 | ||||
| Number of outliers high | 128.000 | ||||
| Percentage of outliers high | 0.207 | ||||
| Mean of outliers high | 1.006 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.299 | ||||
| VaR(95%) (moments method) | 0.004 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| Extreme Value Index (regression method) | 0.033 | ||||
| VaR(95%) (regression method) | 0.005 | ||||
| Expected Shortfall (regression method) | 0.009 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 3.000 | ||||
| Minimum | 0.034 | ||||
| Quartile 1 | 0.055 | ||||
| Median | 0.077 | ||||
| Quartile 3 | 0.130 | ||||
| Maximum | 0.183 | ||||
| Mean of quarter 1 | 0.034 | ||||
| Mean of quarter 2 | 0.077 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.183 | ||||
| Inter Quartile Range | 0.075 | ||||
| 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) | -0.072 | ||||
| Compounded annual return (geometric extrapolation) | -0.074 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.405 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.405 | ||||
| Compounded annual return / Expected Shortfall lognormal | -5.410 | ||||
| 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 | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.716 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.293 | ||||
| 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) | -7936535306446244.000 | ||||
| Sharpe ratio (Hedges UMVUE) | -7901674975671223.000 | ||||
| df | 171.000 | ||||
| t | -5611977934314593.000 | ||||
| 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) | -8739115425704417.000 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7064234525638030.000 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -18.547 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.044 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.002 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 172.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 172.000 | ||||
| Mean of predictor | 0.673 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.291 | ||||
| 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 | 170.000 | ||||
| t(b) | -0.000 | ||||
| p(b) | 0.500 | ||||
| t(a) | -5552233134898999.000 | ||||
| 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) | 163752174123358314840886578511872.000 | ||||
| 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 | 172.000 | ||||
| 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 | ||||


