*5.4. Experimental Results*

Tables 1–3 reports the overall performance measures of RM-WCVaR Portfolio, our proposed portfolio, and the 11 compared portfolios introduced in the Experimental Settings section for FF25, FF48, and FF100 dataset. The out-of-sample period is from January 2005 to June 2020. Among the comparisons of the various portfolios, the best performance is highlighted in **bold**.

Table 1 shows that the RM-WCVaR Portfolio outperformed all the compared portfolios in all performance measures. It achieved the highest AR and R/R and the lowest RISK, MaxDD and TO.

**Table 1.** The out-of-sample performance of each portfolio for FF25 dataset.


Performance measures are the annualized return (AR), annualized risk (RISK), annualized return–risk ratio (R/R), maximum drawdown (MaxDD) and turnover rate (TO). The out-of-sample period is from January 2005 to June 2020. Among the comparisons of the various portfolios, the best performance is highlighted in **bold**.

In Table 2, we can see the RM-WCVaR Portfolio had the best AR, R/R, MaxDD and TO. Only the RISK was the best for the DRP portfolio.


**Table 2.** The out-of-sample performance of each portfolio for FF48 dataset.

Performance measures are the annualized return (AR), annualized risk (RISK), annualized return–risk ratio (R/R),maximum drawdown (MaxDD) and turnover rate (TO). The out-of-sample period is from January 2005 to June 2020. Among the comparisons of the various portfolios, the best performance is highlighted in **bold**.

In Table 3, the RM-WCVaR Portfolio had the best AR, R/R, and MaxDD. The TO for the RM-WCVaR portfolio was the second lowest after the EW portfolio.


**Table 3.** The out-of-sample performance of each portfolio for FF100 dataset.

Performance measures are the annualized return (AR), annualized risk (RISK), annualized return–risk ratio (R/R), maximum drawdown (MaxDD) and turnover rate (TO). The out-of-sample period is from January 2005 to June 2020. Among the comparisons of the various portfolios, the best performance is highlighted in **bold**.

In all datasets, the proposed RM-WCVaR Portfolio achieved the highest AR and R/R, and the lowest MaxDD.

Unsurprisingly, the RM-WCVaR Portfolio was different from ACVaR, which is the simple average of five probability levels' WCVaR portfolios. RM-WCVaR Portfolio also exceeded the individual *β* levels of WCVaR portfolios in terms of AR, R/R, MaxDD and TO. This is because the RM procedure implies a minimization of the maximum margin among multiple WCVaR levels, which enables more efficient portfolio construction. Analyzing the

relationship between the margin level and performance of RM-WCVaR is an important future task.

Therefore, we can confirm that the RM-WCVaR Portfolio has high R/R and avoids a large drawdown despite the lower turnover rate. Since the TO is the lowest of all compared portfolios, the results do not change when transaction costs are taken into account. We consider the RM-WCVaR portfolio to have had a good R/R because it reduced tail risk, resulting in lower drawdowns and higher returns.
