Advanced Statistics: Sharktrades
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 | -0.001 | ||||
| SD | 0.038 | ||||
| Sharpe ratio (Glass type estimate) | -0.028 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.027 | ||||
| df | 41.000 | ||||
| t | -0.052 | ||||
| p | 0.520 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.075 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.020 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.075 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.021 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.060 | ||||
| Upside Potential Ratio | 2.393 | ||||
| Upside part of mean | 0.042 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.033 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.449 | ||||
| Mean of criterion | -0.001 | ||||
| SD of predictor | 0.257 | ||||
| SD of criterion | 0.038 | ||||
| Covariance | -0.001 | ||||
| r | -0.132 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.008 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 40.000 | ||||
| t(b) | -0.845 | ||||
| p(b) | 0.798 | ||||
| t(a) | 0.338 | ||||
| p(a) | 0.368 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.027 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.038 | ||||
| Upperbound of 95% confidence interval for alpha | 0.054 | ||||
| Treynor index (mean / b) | 0.054 | ||||
| Jensen alpha (a) | 0.008 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.037 | ||||
| Sharpe ratio (Glass type estimate) | -0.046 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.045 | ||||
| df | 41.000 | ||||
| t | -0.086 | ||||
| p | 0.534 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.094 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.002 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.093 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.002 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.099 | ||||
| Upside Potential Ratio | 2.344 | ||||
| Upside part of mean | 0.041 | ||||
| Downside part of mean | -0.043 | ||||
| Upside SD | 0.032 | ||||
| Downside SD | 0.017 | ||||
| N nonnegative terms | 7.000 | ||||
| N negative terms | 35.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 42.000 | ||||
| Mean of predictor | 0.409 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.247 | ||||
| SD of criterion | 0.037 | ||||
| Covariance | -0.001 | ||||
| r | -0.123 | ||||
| b (slope, estimate of beta) | -0.019 | ||||
| a (intercept, estimate of alpha) | 0.006 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 40.000 | ||||
| t(b) | -0.787 | ||||
| p(b) | 0.782 | ||||
| t(a) | 0.265 | ||||
| p(a) | 0.396 | ||||
| Lowerbound of 95% confidence interval for beta | -0.066 | ||||
| Upperbound of 95% confidence interval for beta | 0.029 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.039 | ||||
| Upperbound of 95% confidence interval for alpha | 0.051 | ||||
| Treynor index (mean / b) | 0.092 | ||||
| Jensen alpha (a) | 0.006 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.018 | ||||
| Expected Shortfall on VaR | 0.022 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.010 | ||||
| Expected Shortfall on VaR | 0.014 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 42.000 | ||||
| Minimum | 0.979 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.039 | ||||
| Mean of quarter 1 | 0.998 | ||||
| Mean of quarter 2 | 1.000 | ||||
| Mean of quarter 3 | 1.000 | ||||
| Mean of quarter 4 | 1.016 | ||||
| Inter Quartile Range | 0.000 | ||||
| Number outliers low | 1.000 | ||||
| Percentage of outliers low | 0.024 | ||||
| Mean of outliers low | 0.979 | ||||
| Number of outliers high | 9.000 | ||||
| Percentage of outliers high | 0.214 | ||||
| Mean of outliers high | 1.019 | ||||
| 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 | 0.021 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.021 | ||||
| Quartile 3 | 0.021 | ||||
| Maximum | 0.021 | ||||
| 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) | 0.046 | ||||
| Compounded annual return (geometric extrapolation) | 0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | 2.076 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | 1.957 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -0.054 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.054 | ||||
| df | 927.000 | ||||
| t | -0.101 | ||||
| p | 0.540 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.095 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.988 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.095 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.988 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.080 | ||||
| Upside Potential Ratio | 4.053 | ||||
| Upside part of mean | 0.086 | ||||
| Downside part of mean | -0.088 | ||||
| Upside SD | 0.024 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 106.000 | ||||
| N negative terms | 822.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 928.000 | ||||
| Mean of predictor | 0.493 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.339 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.000 | ||||
| r | -0.024 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 926.000 | ||||
| t(b) | -0.735 | ||||
| p(b) | 0.769 | ||||
| t(a) | -0.035 | ||||
| p(a) | 0.514 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.034 | ||||
| Upperbound of 95% confidence interval for alpha | 0.033 | ||||
| Treynor index (mean / b) | 0.752 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.002 | ||||
| SD | 0.032 | ||||
| Sharpe ratio (Glass type estimate) | -0.070 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.070 | ||||
| df | 927.000 | ||||
| t | -0.131 | ||||
| p | 0.552 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.111 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.972 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.111 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.972 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.104 | ||||
| Upside Potential Ratio | 4.017 | ||||
| Upside part of mean | 0.086 | ||||
| Downside part of mean | -0.088 | ||||
| Upside SD | 0.024 | ||||
| Downside SD | 0.021 | ||||
| N nonnegative terms | 106.000 | ||||
| N negative terms | 822.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 928.000 | ||||
| Mean of predictor | 0.432 | ||||
| Mean of criterion | -0.002 | ||||
| SD of predictor | 0.352 | ||||
| SD of criterion | 0.032 | ||||
| Covariance | -0.000 | ||||
| r | -0.022 | ||||
| b (slope, estimate of beta) | -0.002 | ||||
| a (intercept, estimate of alpha) | -0.001 | ||||
| Mean Square Error | 0.001 | ||||
| DF error | 926.000 | ||||
| t(b) | -0.684 | ||||
| p(b) | 0.753 | ||||
| t(a) | -0.079 | ||||
| p(a) | 0.531 | ||||
| Lowerbound of 95% confidence interval for beta | -0.008 | ||||
| Upperbound of 95% confidence interval for beta | 0.004 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.035 | ||||
| Upperbound of 95% confidence interval for alpha | 0.032 | ||||
| Treynor index (mean / b) | 1.091 | ||||
| Jensen alpha (a) | -0.001 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.003 | ||||
| Expected Shortfall on VaR | 0.004 | ||||
| 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 | 928.000 | ||||
| Minimum | 0.983 | ||||
| Quartile 1 | 1.000 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.000 | ||||
| Maximum | 1.022 | ||||
| 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 | 0.000 | ||||
| Number outliers low | 35.000 | ||||
| Percentage of outliers low | 0.038 | ||||
| Mean of outliers low | 0.995 | ||||
| Number of outliers high | 109.000 | ||||
| Percentage of outliers high | 0.117 | ||||
| Mean of outliers high | 1.003 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | -0.312 | ||||
| VaR(95%) (moments method) | -0.000 | ||||
| Expected Shortfall (moments method) | NA | ||||
| Extreme Value Index (regression method) | -0.030 | ||||
| VaR(95%) (regression method) | -0.000 | ||||
| Expected Shortfall (regression method) | NA | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 15.000 | ||||
| Minimum | 0.001 | ||||
| Quartile 1 | 0.003 | ||||
| Median | 0.008 | ||||
| Quartile 3 | 0.015 | ||||
| Maximum | 0.034 | ||||
| Mean of quarter 1 | 0.001 | ||||
| Mean of quarter 2 | 0.006 | ||||
| Mean of quarter 3 | 0.011 | ||||
| Mean of quarter 4 | 0.027 | ||||
| Inter Quartile Range | 0.013 | ||||
| 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) | -3.284 | ||||
| VaR(95%) (moments method) | 0.029 | ||||
| Expected Shortfall (moments method) | 0.029 | ||||
| Extreme Value Index (regression method) | -1.283 | ||||
| VaR(95%) (regression method) | 0.036 | ||||
| Expected Shortfall (regression method) | 0.038 | ||||
| COMBINED STATISTICS | |||||
| Annualized return (arithmetic extrapolation) | 0.045 | ||||
| Compounded annual return (geometric extrapolation) | 0.043 | ||||
| Calmar ratio (compounded annual return / max draw down) | 1.239 | ||||
| Compounded annual return / average of 25% largest draw downs | 1.607 | ||||
| Compounded annual return / Expected Shortfall lognormal | 10.499 | ||||
| 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 | 1.120 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.505 | ||||
| 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 | 0.990 | ||||
| Mean of criterion | -0.044 | ||||
| SD of predictor | 0.508 | ||||
| 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) | -8736170439944940.000 | ||||
| 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) | 688579905791114063844524372787200.000 | ||||
| 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 | ||||