Advanced Statistics: Stock trade
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 | 0.002 | ||||
| SD | 0.287 | ||||
| Sharpe ratio (Glass type estimate) | 0.009 | ||||
| Sharpe ratio (Hedges UMVUE) | 0.008 | ||||
| df | 33.000 | ||||
| t | 0.014 | ||||
| p | 0.494 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.156 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.173 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.156 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.173 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | 0.021 | ||||
| Upside Potential Ratio | 1.913 | ||||
| Upside part of mean | 0.219 | ||||
| Downside part of mean | -0.217 | ||||
| Upside SD | 0.259 | ||||
| Downside SD | 0.115 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 26.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.530 | ||||
| Mean of criterion | 0.002 | ||||
| SD of predictor | 0.249 | ||||
| SD of criterion | 0.287 | ||||
| Covariance | -0.018 | ||||
| r | -0.245 | ||||
| b (slope, estimate of beta) | -0.283 | ||||
| a (intercept, estimate of alpha) | 0.152 | ||||
| Mean Square Error | 0.080 | ||||
| DF error | 32.000 | ||||
| t(b) | -1.432 | ||||
| p(b) | 0.919 | ||||
| t(a) | 0.770 | ||||
| p(a) | 0.223 | ||||
| Lowerbound of 95% confidence interval for beta | -0.685 | ||||
| Upperbound of 95% confidence interval for beta | 0.120 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.251 | ||||
| Upperbound of 95% confidence interval for alpha | 0.556 | ||||
| Treynor index (mean / b) | -0.009 | ||||
| Jensen alpha (a) | 0.152 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.031 | ||||
| SD | 0.251 | ||||
| Sharpe ratio (Glass type estimate) | -0.123 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.120 | ||||
| df | 33.000 | ||||
| t | -0.207 | ||||
| p | 0.581 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.287 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.043 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.285 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.045 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.258 | ||||
| Upside Potential Ratio | 1.606 | ||||
| Upside part of mean | 0.192 | ||||
| Downside part of mean | -0.223 | ||||
| Upside SD | 0.217 | ||||
| Downside SD | 0.120 | ||||
| N nonnegative terms | 8.000 | ||||
| N negative terms | 26.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 34.000 | ||||
| Mean of predictor | 0.491 | ||||
| Mean of criterion | -0.031 | ||||
| SD of predictor | 0.233 | ||||
| SD of criterion | 0.251 | ||||
| Covariance | -0.016 | ||||
| r | -0.278 | ||||
| b (slope, estimate of beta) | -0.300 | ||||
| a (intercept, estimate of alpha) | 0.116 | ||||
| Mean Square Error | 0.060 | ||||
| DF error | 32.000 | ||||
| t(b) | -1.635 | ||||
| p(b) | 0.944 | ||||
| t(a) | 0.679 | ||||
| p(a) | 0.251 | ||||
| Lowerbound of 95% confidence interval for beta | -0.674 | ||||
| Upperbound of 95% confidence interval for beta | 0.074 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.233 | ||||
| Upperbound of 95% confidence interval for alpha | 0.465 | ||||
| Treynor index (mean / b) | 0.103 | ||||
| Jensen alpha (a) | 0.116 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.115 | ||||
| Expected Shortfall on VaR | 0.141 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.053 | ||||
| Expected Shortfall on VaR | 0.093 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 34.000 | ||||
| Minimum | 0.885 | ||||
| Quartile 1 | 0.985 | ||||
| Median | 0.996 | ||||
| Quartile 3 | 1.003 | ||||
| Maximum | 1.428 | ||||
| Mean of quarter 1 | 0.951 | ||||
| Mean of quarter 2 | 0.991 | ||||
| Mean of quarter 3 | 0.999 | ||||
| Mean of quarter 4 | 1.073 | ||||
| Inter Quartile Range | 0.018 | ||||
| Number outliers low | 4.000 | ||||
| Percentage of outliers low | 0.118 | ||||
| Mean of outliers low | 0.918 | ||||
| Number of outliers high | 5.000 | ||||
| Percentage of outliers high | 0.147 | ||||
| Mean of outliers high | 1.125 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.336 | ||||
| VaR(95%) (moments method) | 0.047 | ||||
| Expected Shortfall (moments method) | 0.087 | ||||
| Extreme Value Index (regression method) | -0.138 | ||||
| VaR(95%) (regression method) | 0.054 | ||||
| Expected Shortfall (regression method) | 0.072 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 2.000 | ||||
| Minimum | 0.086 | ||||
| Quartile 1 | 0.131 | ||||
| Median | 0.177 | ||||
| Quartile 3 | 0.222 | ||||
| Maximum | 0.267 | ||||
| Mean of quarter 1 | 0.086 | ||||
| Mean of quarter 2 | NA | ||||
| Mean of quarter 3 | NA | ||||
| Mean of quarter 4 | 0.267 | ||||
| Inter Quartile Range | 0.091 | ||||
| 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) | 0.013 | ||||
| Compounded annual return (geometric extrapolation) | 0.013 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.049 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.049 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.094 | ||||
| ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.008 | ||||
| SD | 0.260 | ||||
| Sharpe ratio (Glass type estimate) | -0.031 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.031 | ||||
| df | 755.000 | ||||
| t | -0.053 | ||||
| p | 0.521 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.185 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.122 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.185 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.122 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.066 | ||||
| Upside Potential Ratio | 5.957 | ||||
| Upside part of mean | 0.732 | ||||
| Downside part of mean | -0.740 | ||||
| Upside SD | 0.228 | ||||
| Downside SD | 0.123 | ||||
| N nonnegative terms | 315.000 | ||||
| N negative terms | 441.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 756.000 | ||||
| Mean of predictor | 0.616 | ||||
| Mean of criterion | -0.008 | ||||
| SD of predictor | 0.385 | ||||
| SD of criterion | 0.260 | ||||
| Covariance | -0.032 | ||||
| r | -0.320 | ||||
| b (slope, estimate of beta) | -0.216 | ||||
| a (intercept, estimate of alpha) | 0.125 | ||||
| Mean Square Error | 0.061 | ||||
| DF error | 754.000 | ||||
| t(b) | -9.279 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.858 | ||||
| p(a) | 0.196 | ||||
| Lowerbound of 95% confidence interval for beta | -0.261 | ||||
| Upperbound of 95% confidence interval for beta | -0.170 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.161 | ||||
| Upperbound of 95% confidence interval for alpha | 0.411 | ||||
| Treynor index (mean / b) | 0.038 | ||||
| Jensen alpha (a) | 0.125 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.039 | ||||
| SD | 0.244 | ||||
| Sharpe ratio (Glass type estimate) | -0.160 | ||||
| Sharpe ratio (Hedges UMVUE) | -0.160 | ||||
| df | 755.000 | ||||
| t | -0.272 | ||||
| p | 0.607 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -1.314 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 0.994 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.314 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.994 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -0.309 | ||||
| Upside Potential Ratio | 5.614 | ||||
| Upside part of mean | 0.709 | ||||
| Downside part of mean | -0.748 | ||||
| Upside SD | 0.208 | ||||
| Downside SD | 0.126 | ||||
| N nonnegative terms | 315.000 | ||||
| N negative terms | 441.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 756.000 | ||||
| Mean of predictor | 0.539 | ||||
| Mean of criterion | -0.039 | ||||
| SD of predictor | 0.396 | ||||
| SD of criterion | 0.244 | ||||
| Covariance | -0.033 | ||||
| r | -0.341 | ||||
| b (slope, estimate of beta) | -0.210 | ||||
| a (intercept, estimate of alpha) | 0.074 | ||||
| Mean Square Error | 0.053 | ||||
| DF error | 754.000 | ||||
| t(b) | -9.946 | ||||
| p(b) | 1.000 | ||||
| t(a) | 0.546 | ||||
| p(a) | 0.293 | ||||
| Lowerbound of 95% confidence interval for beta | -0.251 | ||||
| Upperbound of 95% confidence interval for beta | -0.168 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.192 | ||||
| Upperbound of 95% confidence interval for alpha | 0.340 | ||||
| Treynor index (mean / b) | 0.186 | ||||
| Jensen alpha (a) | 0.074 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.007 | ||||
| Expected Shortfall on VaR | 0.015 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 756.000 | ||||
| Minimum | 0.886 | ||||
| Quartile 1 | 0.998 | ||||
| Median | 1.000 | ||||
| Quartile 3 | 1.002 | ||||
| Maximum | 1.258 | ||||
| Mean of quarter 1 | 0.990 | ||||
| Mean of quarter 2 | 0.999 | ||||
| Mean of quarter 3 | 1.001 | ||||
| Mean of quarter 4 | 1.011 | ||||
| Inter Quartile Range | 0.004 | ||||
| Number outliers low | 82.000 | ||||
| Percentage of outliers low | 0.108 | ||||
| Mean of outliers low | 0.982 | ||||
| Number of outliers high | 72.000 | ||||
| Percentage of outliers high | 0.095 | ||||
| Mean of outliers high | 1.023 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.651 | ||||
| VaR(95%) (moments method) | 0.009 | ||||
| Expected Shortfall (moments method) | 0.030 | ||||
| Extreme Value Index (regression method) | 0.356 | ||||
| VaR(95%) (regression method) | 0.008 | ||||
| Expected Shortfall (regression method) | 0.015 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 6.000 | ||||
| Minimum | 0.004 | ||||
| Quartile 1 | 0.021 | ||||
| Median | 0.045 | ||||
| Quartile 3 | 0.155 | ||||
| Maximum | 0.303 | ||||
| Mean of quarter 1 | 0.009 | ||||
| Mean of quarter 2 | 0.042 | ||||
| Mean of quarter 3 | 0.048 | ||||
| Mean of quarter 4 | 0.247 | ||||
| Inter Quartile Range | 0.134 | ||||
| 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) | 0.005 | ||||
| Compounded annual return (geometric extrapolation) | 0.005 | ||||
| Calmar ratio (compounded annual return / max draw down) | 0.016 | ||||
| Compounded annual return / average of 25% largest draw downs | 0.020 | ||||
| Compounded annual return / Expected Shortfall lognormal | 0.162 | ||||
| ANALYSIS BASED ON DAILY VALUES, LAST 6 MONTHS (Back) | |||||
| RATIO STATISTICS | |||||
| Ratio statistics of excess return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.356 | ||||
| SD | 0.238 | ||||
| Sharpe ratio (Glass type estimate) | -1.491 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.483 | ||||
| df | 130.000 | ||||
| t | -1.055 | ||||
| p | 0.546 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.266 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.289 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.260 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.295 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.016 | ||||
| Upside Potential Ratio | 7.225 | ||||
| Upside part of mean | 1.275 | ||||
| Downside part of mean | -1.630 | ||||
| Upside SD | 0.161 | ||||
| Downside SD | 0.176 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.564 | ||||
| Mean of criterion | -0.356 | ||||
| SD of predictor | 0.553 | ||||
| SD of criterion | 0.238 | ||||
| Covariance | -0.078 | ||||
| r | -0.593 | ||||
| b (slope, estimate of beta) | -0.256 | ||||
| a (intercept, estimate of alpha) | 0.044 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 129.000 | ||||
| t(b) | -8.363 | ||||
| p(b) | 0.854 | ||||
| t(a) | 0.160 | ||||
| p(a) | 0.491 | ||||
| Lowerbound of 95% confidence interval for beta | -0.316 | ||||
| Upperbound of 95% confidence interval for beta | -0.195 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.503 | ||||
| Upperbound of 95% confidence interval for alpha | 0.592 | ||||
| Treynor index (mean / b) | 1.392 | ||||
| Jensen alpha (a) | 0.044 | ||||
| Ratio statistics of excess log return rates | |||||
| Statistics related to Sharpe ratio | |||||
| Mean | -0.384 | ||||
| SD | 0.239 | ||||
| Sharpe ratio (Glass type estimate) | -1.610 | ||||
| Sharpe ratio (Hedges UMVUE) | -1.600 | ||||
| df | 130.000 | ||||
| t | -1.138 | ||||
| p | 0.550 | ||||
| Lowerbound of 95% confidence interval for Sharpe Ratio | -4.385 | ||||
| Upperbound of 95% confidence interval for Sharpe Ratio | 1.172 | ||||
| Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -4.379 | ||||
| Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 1.178 | ||||
| Statistics related to Sortino ratio | |||||
| Sortino ratio | -2.149 | ||||
| Upside Potential Ratio | 7.060 | ||||
| Upside part of mean | 1.262 | ||||
| Downside part of mean | -1.646 | ||||
| Upside SD | 0.158 | ||||
| Downside SD | 0.179 | ||||
| N nonnegative terms | 58.000 | ||||
| N negative terms | 73.000 | ||||
| Statistics related to linear regression on benchmark | |||||
| N of observations | 131.000 | ||||
| Mean of predictor | 1.409 | ||||
| Mean of criterion | -0.384 | ||||
| SD of predictor | 0.552 | ||||
| SD of criterion | 0.239 | ||||
| Covariance | -0.078 | ||||
| r | -0.593 | ||||
| b (slope, estimate of beta) | -0.256 | ||||
| a (intercept, estimate of alpha) | -0.023 | ||||
| Mean Square Error | 0.037 | ||||
| DF error | 129.000 | ||||
| t(b) | -8.371 | ||||
| p(b) | 0.854 | ||||
| t(a) | -0.083 | ||||
| p(a) | 0.505 | ||||
| Lowerbound of 95% confidence interval for beta | -0.317 | ||||
| Upperbound of 95% confidence interval for beta | -0.196 | ||||
| Lowerbound of 95% confidence interval for alpha | -0.569 | ||||
| Upperbound of 95% confidence interval for alpha | 0.523 | ||||
| Treynor index (mean / b) | 1.498 | ||||
| Jensen alpha (a) | -0.023 | ||||
| Risk estimates for a one-period unit investment (parametric) | |||||
| assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||
| VaR(95%) | 0.025 | ||||
| Expected Shortfall on VaR | 0.031 | ||||
| assuming Pareto losses only (using partial moments from Sortino statistics) | |||||
| VaR(95%) | 0.015 | ||||
| Expected Shortfall on VaR | 0.027 | ||||
| ORDER STATISTICS | |||||
| Quartiles of return rates | |||||
| Number of observations | 131.000 | ||||
| Minimum | 0.955 | ||||
| Quartile 1 | 0.989 | ||||
| Median | 0.999 | ||||
| Quartile 3 | 1.007 | ||||
| Maximum | 1.040 | ||||
| Mean of quarter 1 | 0.981 | ||||
| Mean of quarter 2 | 0.994 | ||||
| Mean of quarter 3 | 1.002 | ||||
| Mean of quarter 4 | 1.018 | ||||
| Inter Quartile Range | 0.017 | ||||
| Number outliers low | 2.000 | ||||
| Percentage of outliers low | 0.015 | ||||
| Mean of outliers low | 0.958 | ||||
| Number of outliers high | 3.000 | ||||
| Percentage of outliers high | 0.023 | ||||
| Mean of outliers high | 1.036 | ||||
| Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||
| Extreme Value Index (moments method) | 0.287 | ||||
| VaR(95%) (moments method) | 0.021 | ||||
| Expected Shortfall (moments method) | 0.032 | ||||
| Extreme Value Index (regression method) | 0.309 | ||||
| VaR(95%) (regression method) | 0.018 | ||||
| Expected Shortfall (regression method) | 0.026 | ||||
| DRAW DOWN STATISTICS | |||||
| Quartiles of draw downs | |||||
| Number of observations | 1.000 | ||||
| Minimum | 0.159 | ||||
| Quartile 1 | 0.159 | ||||
| Median | 0.159 | ||||
| Quartile 3 | 0.159 | ||||
| Maximum | 0.159 | ||||
| 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) | -0.313 | ||||
| Compounded annual return (geometric extrapolation) | -0.288 | ||||
| Calmar ratio (compounded annual return / max draw down) | -1.815 | ||||
| Compounded annual return / average of 25% largest draw downs | NA | ||||
| Compounded annual return / Expected Shortfall lognormal | -9.193 | ||||