Advanced Statistics: LottaBits NASD-1
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 | -0.055 | ||||
| SD | 0.084 | ||||
| Sharpe ratio (Glass type estimate) | -0.660 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.654 | ||||
| df | 88.000 | ||||
| t | -1.798 | ||||
| p | 0.962 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.385 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.068 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.381 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.072 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.830 | ||||
| Upside Potential Ratio | 0.701 | ||||
| Upside part of mean | 0.047 | ||||
| Downside part of mean | -0.102 | ||||
| Upside SD | 0.052 | ||||
| Downside SD | 0.067 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 80.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.140 | ||||
| Mean of criterion | -0.055 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.084 | ||||
| Covariance | 0.001 | ||||
| r | 0.040 | ||||
| b (slope, estimate of beta) | 0.011 | ||||
| a (intercept, estimate of alpha) | -0.057 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 87.000 | ||||
| t(b) | 0.372 | ||||
| p(b) | 0.355 | ||||
| t(a) | -1.823 | ||||
| p(a) | 0.964 | ||||
| Lowerbound of 95% confidence interval for beta | -0.049 | ||||
| Upperbound of 95% confidence interval for beta | 0.072 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.119 | ||||
| Upperbound of 95% confidence interval for alpha | 0.005 | ||||
| Treynor index (mean / b) | -4.885 | ||||
| Jensen alpha (a) | -0.057 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.059 | ||||
| SD | 0.084 | ||||
| Sharpe ratio (Glass type estimate) | -0.697 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.691 | ||||
| df | 88.000 | ||||
| t | -1.898 | ||||
| p | 0.970 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.422 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.032 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.418 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.036 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.852 | ||||
| Upside Potential Ratio | 0.656 | ||||
| Upside part of mean | 0.045 | ||||
| Downside part of mean | -0.104 | ||||
| Upside SD | 0.051 | ||||
| Downside SD | 0.069 | ||||
| N nonnegative terms | 9.000 | ||||
| N negative terms | 80.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 89.000 | ||||
| Mean of predictor | 0.096 | ||||
| Mean of criterion | -0.059 | ||||
| SD of predictor | 0.295 | ||||
| SD of criterion | 0.084 | ||||
| Covariance | 0.001 | ||||
| r | 0.046 | ||||
| b (slope, estimate of beta) | 0.013 | ||||
| a (intercept, estimate of alpha) | -0.060 | ||||
| Mean Square Error | 0.007 | ||||
| DF error | 87.000 | ||||
| t(b) | 0.431 | ||||
| p(b) | 0.334 | ||||
| t(a) | -1.921 | ||||
| p(a) | 0.971 | ||||
| Lowerbound of 95% confidence interval for beta | -0.048 | ||||
| Upperbound of 95% confidence interval for beta | 0.074 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.122 | ||||
| Upperbound of 95% confidence interval for alpha | 0.002 | ||||
| Treynor index (mean / b) | -4.452 | ||||
| Jensen alpha (a) | -0.060 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.044 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.028 | ||||
| Expected Shortfall on VaR | 0.053 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 89.000 | ||||
| Minimum | 0.899 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.090 | ||||
| Mean of quarter 1 | 0.980 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.017 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 15.000 | ||||
| Percentage of outliers low | 0.169 | ||||
| Mean of outliers low | 0.969 | ||||
| Number of outliers high | 15.000 | ||||
| Percentage of outliers high | 0.169 | ||||
| Mean of outliers high | 1.025 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -23.735 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.002 | ||||
| Extreme Value Index (regression method) | -0.949 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.049 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.169 | ||||
| Quartile 1 | 0.169 | ||||
| Median | 0.169 | ||||
| Quartile 3 | 0.169 | ||||
| Maximum | 0.169 | ||||
| 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) | -0.014 | ||||
| Compounded annual return (geometric extrapolation) | -0.015 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.086 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.272 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.042 | ||||
| SD | 0.182 | ||||
| Sharpe ratio (Glass type estimate) | -0.230 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.230 | ||||
| df | 1944.000 | ||||
| t | -0.627 | ||||
| p | 0.507 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -0.950 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.489 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -0.950 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.489 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.337 | ||||
| Upside Potential Ratio | 2.819 | ||||
| Upside part of mean | 0.352 | ||||
| Downside part of mean | -0.394 | ||||
| Upside SD | 0.133 | ||||
| Downside SD | 0.125 | ||||
| N nonnegative terms | 197.000 | ||||
| N negative terms | 1748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1945.000 | ||||
| Mean of predictor | 0.231 | ||||
| Mean of criterion | -0.042 | ||||
| SD of predictor | 0.532 | ||||
| SD of criterion | 0.182 | ||||
| Covariance | 0.010 | ||||
| r | 0.101 | ||||
| b (slope, estimate of beta) | 0.035 | ||||
| a (intercept, estimate of alpha) | -0.050 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 1943.000 | ||||
| t(b) | 4.462 | ||||
| p(b) | 0.436 | ||||
| t(a) | -0.750 | ||||
| p(a) | 0.511 | ||||
| Lowerbound of 95% confidence interval for beta | 0.019 | ||||
| Upperbound of 95% confidence interval for beta | 0.050 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.181 | ||||
| Upperbound of 95% confidence interval for alpha | 0.081 | ||||
| Treynor index (mean / b) | -1.216 | ||||
| Jensen alpha (a) | -0.050 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.059 | ||||
| SD | 0.182 | ||||
| Sharpe ratio (Glass type estimate) | -0.321 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.321 | ||||
| df | 1944.000 | ||||
| t | -0.876 | ||||
| p | 0.510 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.041 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.398 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.041 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.398 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.447 | ||||
| Upside Potential Ratio | 2.619 | ||||
| Upside part of mean | 0.343 | ||||
| Downside part of mean | -0.402 | ||||
| Upside SD | 0.127 | ||||
| Downside SD | 0.131 | ||||
| N nonnegative terms | 197.000 | ||||
| N negative terms | 1748.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 1945.000 | ||||
| Mean of predictor | 0.091 | ||||
| Mean of criterion | -0.059 | ||||
| SD of predictor | 0.528 | ||||
| SD of criterion | 0.182 | ||||
| Covariance | 0.010 | ||||
| r | 0.104 | ||||
| b (slope, estimate of beta) | 0.036 | ||||
| a (intercept, estimate of alpha) | -0.062 | ||||
| Mean Square Error | 0.033 | ||||
| DF error | 1943.000 | ||||
| t(b) | 4.607 | ||||
| p(b) | 0.434 | ||||
| t(a) | -0.929 | ||||
| p(a) | 0.513 | ||||
| Lowerbound of 95% confidence interval for beta | 0.021 | ||||
| Upperbound of 95% confidence interval for beta | 0.051 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.193 | ||||
| Upperbound of 95% confidence interval for alpha | 0.069 | ||||
| Treynor index (mean / b) | -1.631 | ||||
| Jensen alpha (a) | -0.062 | ||||
| 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 | 1945.000 | ||||
| Minimum | 0.833 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.181 | ||||
| Mean of quarter 1 | 0.995 | ||||
| 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 | 224.000 | ||||
| Percentage of outliers low | 0.115 | ||||
| Mean of outliers low | 0.988 | ||||
| Number of outliers high | 239.000 | ||||
| Percentage of outliers high | 0.123 | ||||
| Mean of outliers high | 1.011 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.384 | ||||
| VaR(95%) (moments method) | 0.002 | ||||
| Expected Shortfall (moments method) | 0.007 | ||||
| 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 | 3.000 | ||||
| Minimum | 0.105 | ||||
| Quartile 1 | 0.116 | ||||
| Median | 0.127 | ||||
| Quartile 3 | 0.155 | ||||
| Maximum | 0.184 | ||||
| Mean of quarter 1 | 0.105 | ||||
| Mean of quarter 2 | 0.127 | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.184 | ||||
| Inter Quartile Range | 0.039 | ||||
| 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) | -0.015 | ||||
| Calmar ratio (compounded annual return / max draw down) | -0.079 | ||||
| Compounded annual return / average of 25% largest draw downs | -0.079 | ||||
| Compounded annual return / Expected Shortfall lognormal | -0.626 | ||||
| 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 | 0.910 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.675 | ||||
| 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 | 0.693 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.655 | ||||
| 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) | -8780919041950223.000 | ||||
| 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) | 460821902997223243832512642809856.000 | ||||
| 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 | ||||