## 4 Empirical Results and Analyses
### Results for Exits following BBTS Viewed by a Heatmap Matrix  
Following our new design, investors enter the market in reaction to buying signals given by the BBTS and subsequently measure the performance of leaving the market in response to selling signals generated by the BBTS. Table 3 (Table 4) exhibits the AHR results of a 12 by 10 heatmap matrix generated by employing numerous BBTSs whose parameters for MA lengths range from 5 days to 60 days with a 5-day interval and for SDs ranging from 0.25 SD to 2.5 SDs with a 2.5 SD interval for trading Bitcoin spot (ETH spot). Moreover, several AHRs in red in Table 3 (Table 4) are larger than the 52.12% (77.03%) return of the conventional design for trading Bitcoin spot (ETH spot) in Panel A (Panel B) of Table 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **(1)** & **(2)** & **(3)** & **(4)** & **(5)** \\ \hline
**BBTS** & **CHR (\%)** & **No. of Trades** & **AHR (\%)** & \
\begin{tabular}{c} **Average** \\ **Duration Day** \\ \end{tabular} &
\begin{tabular}{c} **Maximum** \\ **Duration Day** \\ \end{tabular} \\ \hline \multicolumn{5}{c}{Panel A Bitcoin spot} \\ \multicolumn{5}{c}{(20, 2)} & 959.17\% & 48 & 19.98\% & 52 & 231 \\ \multicolumn{5}{c}{(20, 1)} & 129.50\% & 14 & 9.25\% & 32 & 108 \\ \multicolumn{5}{c}{(60, 2)} & 1322.86\% & 24 & **55.12\%** & 96 & 426 \\ \multicolumn{5}{c}{(60, 1)} & 771.10\% & 30 & 25.70\% & 52 & 205 \\ \multicolumn{5}{c}{(10, 2)} & 824.26\% & 61 & 13.51\% & 42 & 170 \\ \multicolumn{5}{c}{(10, 1)} & 489.91\% & 207 & 2.37\% & 13 & 80 \\ \multicolumn{5}{c}{Panel B ETH spot} \\ \multicolumn{5}{c}{(20, 2)} & 3031.25\% & 60 & 50.52\% & 41 & 217 \\ \multicolumn{5}{c}{(20, 1)} & 0.49\% & 14 & 0.03\% & 20 & 54 \\ \multicolumn{5}{c}{(60, 2)} & 3.61\% & 6 & 0.60\% & 26 & 88 \\ \multicolumn{5}{c}{(60, 1)} & 1463.59\% & 19 & **77.03\%** & 56 & 263 \\ \multicolumn{5}{c}{(10, 2)} & 1523.52\% & 60 & 25.39\% & 39 & 174 \\ \multicolumn{5}{c}{(10, 1)} & 1154.74\% & 197 & 5.86\% & 13 & 76 \\ \hline \hline \multicolumn{5}{c}{Note: CHR Cumulative Holding Return; AHR: Average Holding Return; BBTS (20, 2): The BBTS uses 20-day MA and 2 SDs. The AHRs in blue indicate the highest AHP for Bitcoin and ETH, respectively.} \\ \end{tabular}
\end{table} 
Table 2: CHR and AHR of trading Bitcoin and ETH spots from 2016 to 2022. The CHRs, number of trades, AHRs, average duration days, and maximum duration days are calculated for six different BBTS combinations involving two different SDs and three different MA periods. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**60** & 12.67\% & 11.25\% & 18.06\% & 25.70\% & 21.69\% & 25.59\% & 49.80\% & **55.12\%** & **125.94\%** & **156.78\%** \\ \hline
**55** & 12.83\% & \(-\)0.27\% & 11.30\% & 16.84\% & 17.92\% & 25.11\% & 38.31\% & 52.36\% & **74.62\%** & **92.49\%** \\ \hline
**50** & 13.05\% & 10.74\% & 0.07\% & \(-\)14.07\% & 15.00\% & 29.98\% & 33.25\% & 50.30\% & **80.48\%** & **101.03\%** \\ \hline
**45** & 13.18\% & 1.72\% & \(-\)9.51\% & \(-\)0.19\% & 2.65\% & 19.00\% & 33.69\% & 38.50\% & **58.82\%** & **63.12\%** \\ \hline
**40** & 9.73\% & 13.32\% & 16.45\% & 12.77\% & \(-\)6.96\% & 2.46\% & 23.47\% & 32.86\% & 11.41\% & 53.56\% \\ \hline
**35** & 8.26\% & 13.86\% & 13.82\% & 26.33\% & 12.49\% & 13.69\% & 16.21\% & 1.21\% & 29.87\% & 47.17\% \\ \hline
**30** & 7.60\% & 8.74\% & 9.17\% & 15.11\% & 11.21\% & 14.23\% & 16.92\% & 20.09\% & 25.04\% & 36.02\% \\ \hline
**25** & 6.45\% & 0.78\% & 6.17\% & 7.73\% & 14.28\% & 18.39\% & 16.92\% & 17.13\% & 26.23\% & 33.80\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Heatmap Matrix results of trading Bitcoin spots based on the BBTS. This table shows the AHR results using BBTS (n1, n2), where n1 (moving average lengths) ranges from 5 to 60 days with a 5-day interval and n2 (standard deviations) ranges from 0.25 SD to 2.5 SDs with a 0.25 SD interval. Additionally, each cell in the heatmap matrix presents AHR derived using one of the BBTS (n1, n2). The red cells display AHRs greater than 55.12%, the highest AHR in the conventional design.