### Advanced Statistics: ETF OPTION TIMER

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 | -0.014 | ||||

SD | 0.083 | ||||

Sharpe ratio (Glass type estimate) | -0.168 | ||||

Sharpe ratio (Hedges UMVUE) | -0.165 | ||||

df | 37.000 | ||||

t | -0.299 | ||||

p | 0.617 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -1.269 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 0.935 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.267 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.937 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | -0.252 | ||||

Upside Potential Ratio | 1.276 | ||||

Upside part of mean | 0.070 | ||||

Downside part of mean | -0.084 | ||||

Upside SD | 0.060 | ||||

Downside SD | 0.055 | ||||

N nonnegative terms | 5.000 | ||||

N negative terms | 33.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 38.000 | ||||

Mean of predictor | 0.136 | ||||

Mean of criterion | -0.014 | ||||

SD of predictor | 0.100 | ||||

SD of criterion | 0.083 | ||||

Covariance | 0.001 | ||||

r | 0.138 | ||||

b (slope, estimate of beta) | 0.114 | ||||

a (intercept, estimate of alpha) | -0.029 | ||||

Mean Square Error | 0.007 | ||||

DF error | 36.000 | ||||

t(b) | 0.837 | ||||

p(b) | 0.204 | ||||

t(a) | -0.585 | ||||

p(a) | 0.719 | ||||

Lowerbound of 95% confidence interval for beta | -0.162 | ||||

Upperbound of 95% confidence interval for beta | 0.390 | ||||

Lowerbound of 95% confidence interval for alpha | -0.131 | ||||

Upperbound of 95% confidence interval for alpha | 0.072 | ||||

Treynor index (mean / b) | -0.122 | ||||

Jensen alpha (a) | -0.029 | ||||

Ratio statistics of excess log return rates | |||||

Statistics related to Sharpe ratio | |||||

Mean | -0.017 | ||||

SD | 0.082 | ||||

Sharpe ratio (Glass type estimate) | -0.208 | ||||

Sharpe ratio (Hedges UMVUE) | -0.204 | ||||

df | 37.000 | ||||

t | -0.371 | ||||

p | 0.644 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -1.310 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 0.895 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.307 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.898 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | -0.303 | ||||

Upside Potential Ratio | 1.206 | ||||

Upside part of mean | 0.068 | ||||

Downside part of mean | -0.086 | ||||

Upside SD | 0.059 | ||||

Downside SD | 0.057 | ||||

N nonnegative terms | 5.000 | ||||

N negative terms | 33.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 38.000 | ||||

Mean of predictor | 0.130 | ||||

Mean of criterion | -0.017 | ||||

SD of predictor | 0.099 | ||||

SD of criterion | 0.082 | ||||

Covariance | 0.001 | ||||

r | 0.145 | ||||

b (slope, estimate of beta) | 0.121 | ||||

a (intercept, estimate of alpha) | -0.033 | ||||

Mean Square Error | 0.007 | ||||

DF error | 36.000 | ||||

t(b) | 0.880 | ||||

p(b) | 0.192 | ||||

t(a) | -0.660 | ||||

p(a) | 0.743 | ||||

Lowerbound of 95% confidence interval for beta | -0.157 | ||||

Upperbound of 95% confidence interval for beta | 0.398 | ||||

Lowerbound of 95% confidence interval for alpha | -0.134 | ||||

Upperbound of 95% confidence interval for alpha | 0.068 | ||||

Treynor index (mean / b) | -0.143 | ||||

Jensen alpha (a) | -0.033 | ||||

Risk estimates for a one-period unit investment (parametric) | |||||

assuming log normal returns and losses (using central moments from Sharpe statistics) | |||||

VaR(95%) | 0.040 | ||||

Expected Shortfall on VaR | 0.049 | ||||

assuming Pareto losses only (using partial moments from Sortino statistics) | |||||

VaR(95%) | 0.022 | ||||

Expected Shortfall on VaR | 0.043 | ||||

ORDER STATISTICS | |||||

Quartiles of return rates | |||||

Number of observations | 38.000 | ||||

Minimum | 0.930 | ||||

Quartile 1 | 1.000 | ||||

Median | 1.000 | ||||

Quartile 3 | 1.000 | ||||

Maximum | 1.074 | ||||

Mean of quarter 1 | 0.985 | ||||

Mean of quarter 2 | 1.000 | ||||

Mean of quarter 3 | 1.000 | ||||

Mean of quarter 4 | 1.024 | ||||

Inter Quartile Range | 0.000 | ||||

Number outliers low | 3.000 | ||||

Percentage of outliers low | 0.079 | ||||

Mean of outliers low | 0.951 | ||||

Number of outliers high | 6.000 | ||||

Percentage of outliers high | 0.158 | ||||

Mean of outliers high | 1.040 | ||||

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) | -1.319 | ||||

VaR(95%) (regression method) | 0.055 | ||||

Expected Shortfall (regression method) | 0.075 | ||||

DRAW DOWN STATISTICS | |||||

Quartiles of draw downs | |||||

Number of observations | 2.000 | ||||

Minimum | 0.027 | ||||

Quartile 1 | 0.037 | ||||

Median | 0.048 | ||||

Quartile 3 | 0.059 | ||||

Maximum | 0.070 | ||||

Mean of quarter 1 | 0.027 | ||||

Mean of quarter 2 | NA | ||||

Mean of quarter 3 | NA | ||||

Mean of quarter 4 | 0.070 | ||||

Inter Quartile Range | 0.021 | ||||

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) | 0.028 | ||||

Compounded annual return (geometric extrapolation) | 0.027 | ||||

Calmar ratio (compounded annual return / max draw down) | 0.391 | ||||

Compounded annual return / average of 25% largest draw downs | 0.391 | ||||

Compounded annual return / Expected Shortfall lognormal | 0.553 | ||||

ANALYSIS BASED ON DAILY VALUES, FULL HISTORY (Back) | |||||

RATIO STATISTICS | |||||

Ratio statistics of excess return rates | |||||

Statistics related to Sharpe ratio | |||||

Mean | -0.014 | ||||

SD | 0.082 | ||||

Sharpe ratio (Glass type estimate) | -0.171 | ||||

Sharpe ratio (Hedges UMVUE) | -0.171 | ||||

df | 1096.000 | ||||

t | -0.306 | ||||

p | 0.505 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -1.269 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 0.926 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.269 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.926 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | -0.239 | ||||

Upside Potential Ratio | 3.659 | ||||

Upside part of mean | 0.214 | ||||

Downside part of mean | -0.228 | ||||

Upside SD | 0.057 | ||||

Downside SD | 0.059 | ||||

N nonnegative terms | 110.000 | ||||

N negative terms | 987.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 1097.000 | ||||

Mean of predictor | 0.129 | ||||

Mean of criterion | -0.014 | ||||

SD of predictor | 0.121 | ||||

SD of criterion | 0.082 | ||||

Covariance | 0.001 | ||||

r | 0.091 | ||||

b (slope, estimate of beta) | 0.061 | ||||

a (intercept, estimate of alpha) | -0.022 | ||||

Mean Square Error | 0.007 | ||||

DF error | 1095.000 | ||||

t(b) | 3.021 | ||||

p(b) | 0.442 | ||||

t(a) | -0.480 | ||||

p(a) | 0.509 | ||||

Lowerbound of 95% confidence interval for beta | 0.022 | ||||

Upperbound of 95% confidence interval for beta | 0.101 | ||||

Lowerbound of 95% confidence interval for alpha | -0.112 | ||||

Upperbound of 95% confidence interval for alpha | 0.068 | ||||

Treynor index (mean / b) | -0.228 | ||||

Jensen alpha (a) | -0.022 | ||||

Ratio statistics of excess log return rates | |||||

Statistics related to Sharpe ratio | |||||

Mean | -0.017 | ||||

SD | 0.082 | ||||

Sharpe ratio (Glass type estimate) | -0.212 | ||||

Sharpe ratio (Hedges UMVUE) | -0.212 | ||||

df | 1096.000 | ||||

t | -0.379 | ||||

p | 0.506 | ||||

Lowerbound of 95% confidence interval for Sharpe Ratio | -1.310 | ||||

Upperbound of 95% confidence interval for Sharpe Ratio | 0.886 | ||||

Lowerbound of 95% CI (Gibbons, Hedeker & Davis approximation) | -1.310 | ||||

Upperbound of 95% CI (Gibbons, Hedeker & Davis approximation) | 0.886 | ||||

Statistics related to Sortino ratio | |||||

Sortino ratio | -0.293 | ||||

Upside Potential Ratio | 3.587 | ||||

Upside part of mean | 0.213 | ||||

Downside part of mean | -0.230 | ||||

Upside SD | 0.056 | ||||

Downside SD | 0.059 | ||||

N nonnegative terms | 110.000 | ||||

N negative terms | 987.000 | ||||

Statistics related to linear regression on benchmark | |||||

N of observations | 1097.000 | ||||

Mean of predictor | 0.121 | ||||

Mean of criterion | -0.017 | ||||

SD of predictor | 0.121 | ||||

SD of criterion | 0.082 | ||||

Covariance | 0.001 | ||||

r | 0.091 | ||||

b (slope, estimate of beta) | 0.062 | ||||

a (intercept, estimate of alpha) | -0.025 | ||||

Mean Square Error | 0.007 | ||||

DF error | 1095.000 | ||||

t(b) | 3.018 | ||||

p(b) | 0.442 | ||||

t(a) | -0.543 | ||||

p(a) | 0.510 | ||||

Lowerbound of 95% confidence interval for beta | 0.022 | ||||

Upperbound of 95% confidence interval for beta | 0.102 | ||||

Lowerbound of 95% confidence interval for alpha | -0.115 | ||||

Upperbound of 95% confidence interval for alpha | 0.065 | ||||

Treynor index (mean / b) | -0.282 | ||||

Jensen alpha (a) | -0.025 | ||||

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 | 0.009 | ||||

assuming Pareto losses only (using partial moments from Sortino statistics) | |||||

VaR(95%) | 0.002 | ||||

Expected Shortfall on VaR | 0.005 | ||||

ORDER STATISTICS | |||||

Quartiles of return rates | |||||

Number of observations | 1097.000 | ||||

Minimum | 0.963 | ||||

Quartile 1 | 1.000 | ||||

Median | 1.000 | ||||

Quartile 3 | 1.000 | ||||

Maximum | 1.037 | ||||

Mean of quarter 1 | 0.998 | ||||

Mean of quarter 2 | 1.000 | ||||

Mean of quarter 3 | 1.000 | ||||

Mean of quarter 4 | 1.003 | ||||

Inter Quartile Range | 0.000 | ||||

Number outliers low | 70.000 | ||||

Percentage of outliers low | 0.064 | ||||

Mean of outliers low | 0.991 | ||||

Number of outliers high | 111.000 | ||||

Percentage of outliers high | 0.101 | ||||

Mean of outliers high | 1.006 | ||||

Risk estimates for a one-period unit investment (based on Extreme Value Theory) | |||||

Extreme Value Index (moments method) | 0.169 | ||||

VaR(95%) (moments method) | 0.001 | ||||

Expected Shortfall (moments method) | 0.003 | ||||

Extreme Value Index (regression method) | 0.070 | ||||

VaR(95%) (regression method) | 0.001 | ||||

Expected Shortfall (regression method) | 0.007 | ||||

DRAW DOWN STATISTICS | |||||

Quartiles of draw downs | |||||

Number of observations | 9.000 | ||||

Minimum | 0.000 | ||||

Quartile 1 | 0.002 | ||||

Median | 0.004 | ||||

Quartile 3 | 0.083 | ||||

Maximum | 0.132 | ||||

Mean of quarter 1 | 0.001 | ||||

Mean of quarter 2 | 0.004 | ||||

Mean of quarter 3 | 0.046 | ||||

Mean of quarter 4 | 0.116 | ||||

Inter Quartile Range | 0.081 | ||||

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) | -2.125 | ||||

VaR(95%) (moments method) | 0.121 | ||||

Expected Shortfall (moments method) | 0.122 | ||||

Extreme Value Index (regression method) | -0.179 | ||||

VaR(95%) (regression method) | 0.141 | ||||

Expected Shortfall (regression method) | 0.165 | ||||

COMBINED STATISTICS | |||||

Annualized return (arithmetic extrapolation) | 0.028 | ||||

Compounded annual return (geometric extrapolation) | 0.027 | ||||

Calmar ratio (compounded annual return / max draw down) | 0.205 | ||||

Compounded annual return / average of 25% largest draw downs | 0.232 | ||||

Compounded annual return / Expected Shortfall lognormal | 2.963 | ||||

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 | 0.016 | ||||

Mean of criterion | -0.044 | ||||

SD of predictor | 0.115 | ||||

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 | 0.009 | ||||

Mean of criterion | -0.044 | ||||

SD of predictor | 0.115 | ||||

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) | -5595490259468162.000 | ||||

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) | 382608600236975855708360696397824.000 | ||||

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 |