Advanced Statistics: MFT
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 | -0.046 | ||||
| SD | 0.007 | ||||
| Sharpe ratio (Glass type estimate) | -6.191 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.113 | ||||
| df | 60.000 | ||||
| t | -13.958 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.774 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7.510 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.716 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.029 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.420 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.240 | ||||
| SD of criterion | 0.007 | ||||
| Covariance | 0.000 | ||||
| r | 0.054 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.419 | ||||
| p(b) | 0.338 | ||||
| t(a) | -12.541 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.006 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.055 | ||||
| Upperbound of 95% confidence interval for alpha | -0.040 | ||||
| Treynor index (mean / b) | -27.260 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.008 | ||||
| Sharpe ratio (Glass type estimate) | -6.136 | ||||
| Sharpe ratio (Hedges UMVUE) | -6.059 | ||||
| df | 60.000 | ||||
| t | -13.833 | ||||
| p | 1.000 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | NA | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -4.727 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -7.448 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.669 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.023 | ||||
| Upside Potential Ratio | 0.000 | ||||
| Upside part of mean | 0.000 | ||||
| Downside part of mean | -0.046 | ||||
| Upside SD | 0.000 | ||||
| Downside SD | 0.015 | ||||
| N nonnegative terms | 0.000 | ||||
| N negative terms | 61.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 61.000 | ||||
| Mean of predictor | 0.385 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.232 | ||||
| SD of criterion | 0.008 | ||||
| Covariance | 0.000 | ||||
| r | 0.052 | ||||
| b (slope, estimate of beta) | 0.002 | ||||
| a (intercept, estimate of alpha) | -0.047 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 59.000 | ||||
| t(b) | 0.401 | ||||
| p(b) | 0.345 | ||||
| t(a) | -12.543 | ||||
| p(a) | 1.000 | ||||
| Lowerbound of 95% confidence interval for beta | -0.007 | ||||
| Upperbound of 95% confidence interval for beta | 0.010 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.054 | ||||
| Upperbound of 95% confidence interval for alpha | -0.039 | ||||
| Treynor index (mean / b) | -27.273 | ||||
| Jensen alpha (a) | -0.047 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.008 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.007 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 61.000 | ||||
| Minimum | 0.984 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.002 | ||||
| Mean of quarter 1 | 0.999 | ||||
| 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 | 4.000 | ||||
| Percentage of outliers low | 0.066 | ||||
| Mean of outliers low | 0.996 | ||||
| Number of outliers high | 6.000 | ||||
| Percentage of outliers high | 0.098 | ||||
| Mean of outliers high | 1.001 | ||||
| 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 | 1.000 | ||||
| Minimum | 0.016 | ||||
| Quartile 1 | 0.016 | ||||
| Median | 0.016 | ||||
| Quartile 3 | 0.016 | ||||
| Maximum | 0.016 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.137 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.271 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.018 | ||||
| Sharpe ratio (Glass type estimate) | -2.555 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.554 | ||||
| df | 1333.000 | ||||
| t | -5.765 | ||||
| p | 0.599 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.429 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.681 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.428 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.680 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.326 | ||||
| Upside Potential Ratio | 0.785 | ||||
| Upside part of mean | 0.011 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.012 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 1320.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1334.000 | ||||
| Mean of predictor | 0.470 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.402 | ||||
| SD of criterion | 0.018 | ||||
| Covariance | 0.001 | ||||
| r | 0.118 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.049 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 1332.000 | ||||
| t(b) | 4.354 | ||||
| p(b) | 0.441 | ||||
| t(a) | -6.103 | ||||
| p(a) | 0.582 | ||||
| Lowerbound of 95% confidence interval for beta | 0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -8.666 | ||||
| Jensen alpha (a) | -0.049 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.046 | ||||
| SD | 0.018 | ||||
| Sharpe ratio (Glass type estimate) | -2.561 | ||||
| Sharpe ratio (Hedges UMVUE) | -2.559 | ||||
| df | 1333.000 | ||||
| t | -5.778 | ||||
| p | 0.599 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -3.434 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | -1.686 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -3.433 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.685 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -3.307 | ||||
| Upside Potential Ratio | 0.773 | ||||
| Upside part of mean | 0.011 | ||||
| Downside part of mean | -0.057 | ||||
| Upside SD | 0.012 | ||||
| Downside SD | 0.014 | ||||
| N nonnegative terms | 14.000 | ||||
| N negative terms | 1320.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1334.000 | ||||
| Mean of predictor | 0.389 | ||||
| Mean of criterion | -0.046 | ||||
| SD of predictor | 0.401 | ||||
| SD of criterion | 0.018 | ||||
| Covariance | 0.001 | ||||
| r | 0.118 | ||||
| b (slope, estimate of beta) | 0.005 | ||||
| a (intercept, estimate of alpha) | -0.048 | ||||
| Mean Square Error | 0.000 | ||||
| DF error | 1332.000 | ||||
| t(b) | 4.324 | ||||
| p(b) | 0.441 | ||||
| t(a) | -6.064 | ||||
| p(a) | 0.582 | ||||
| Lowerbound of 95% confidence interval for beta | 0.003 | ||||
| Upperbound of 95% confidence interval for beta | 0.008 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.064 | ||||
| Upperbound of 95% confidence interval for alpha | -0.033 | ||||
| Treynor index (mean / b) | -8.738 | ||||
| Jensen alpha (a) | -0.048 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.002 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.001 | ||||
| Expected Shortfall on VaR | 0.002 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 1334.000 | ||||
| Minimum | 0.980 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.021 | ||||
| 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 | 42.000 | ||||
| Percentage of outliers low | 0.031 | ||||
| Mean of outliers low | 0.998 | ||||
| Number of outliers high | 43.000 | ||||
| Percentage of outliers high | 0.032 | ||||
| Mean of outliers high | 1.001 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -4.136 | ||||
| VaR(95%) (moments method) | -0.539 | ||||
| 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 | 8.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.001 | ||||
| Median | 0.002 | ||||
| Quartile 3 | 0.007 | ||||
| Maximum | 0.020 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.002 | ||||
| Mean of quarter 3 | 0.002 | ||||
| Mean of quarter 4 | 0.020 | ||||
| Inter Quartile Range | 0.005 | ||||
| Number outliers low | 0.000 | ||||
| Percentage of outliers low | 0.000 | ||||
| Mean of outliers low | NA | ||||
| Number of outliers high | 2.000 | ||||
| Percentage of outliers high | 0.250 | ||||
| Mean of outliers high | 0.020 | ||||
| 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) | -0.002 | ||||
| Compounded annual return (geometric extrapolation) | -0.002 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.111 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.111 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.908 | ||||
| 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 | 1.451 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.378 | ||||
| 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 | 1.377 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.378 | ||||
| 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) | -8583867201492958.000 | ||||
| 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) | 173042659574603462371211531517952.000 | ||||
| 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 | ||||