*3.5. Transaction Operations*

In the real market, the utilization of the moving average timing strategy would induce more transaction operations, resulting in higher transaction costs. In this section, we examine the effect of trading costs on the earlier results. Table 4 reports the statistics that address this issue.

The average holding days is the average number of days that we hold the portfolio. Longer average holding days sugges<sup>t</sup> that the trading portfolio is more stable. From Table 4, we can tell that the average holding days becomes longer as the moving average lag length increases. The average holding days of the 5-day MAP is around 4 days, while that of the 20-day MAP is around 10 days. Moreover, the average holding days for 200-day MAP ranges from 130.99 days to 183.08 days. We do not report those of the two zero-cost trading strategies because it is difficult to define the holding period while investors hold two portfolios simultaneously.


**Table 4.** Transaction operations.

157

enhanced BM strategy and the traditional buy-and-hold BM strategy.

number of days in the whole sample period. Break-even transaction cost (BETC) is the fee which is required in each round-trip transaction for the portfolios if the final profit is zero. Transactions Cost for TLS consists commission, transfer fee, stamp tax, and interest fee for stock borrow. MAP for TLS is the return difference between the proposed technical analysis

*Economies* **2019**, *7*, 92

Next, we calculate the trading frequency of the MAP and TLS portfolios, which is the fraction of the number of trading days of the number of days in the whole period. A shorter (longer) lag length strategy implies that the portfolios will be traded more (less) and that the trading frequency should be higher (smaller). For the 20-day lag length, the trading frequency ranges from 0.11 to 0.13 for the 10 deciles and is 0.22 for the High–Low and TLS strategies. The trading frequency for all of the deciles with lag lengths longer than 20 days is lower than 0.10. Apparently, the MA timing strategies incur higher transaction fees if a shorter lag length is chosen for the MA indicator.

According to the China Securities Regulatory Commission, the Securities Association of China and notices of securities companies, the cost for trading A-shares consists of a commission, transfer fee, and stamp tax. The commission fee should be lower than 30 basis points of the transaction amount and is determined by securities companies in the allowable interval. Because securities companies in China use low price strategies to attract customers, according to the Eastmoney Choice Database, the average commission fee for trading stocks in 2015 is just 5.1 basis points. The amounts of the other two kinds of fees are fixed. The transfer fee for A-shares is 0.2 basis points of the transaction amount, and the stamp tax is 10 basis points only on the sell side. To sum up, we need to pay 20.6 ((5.1 + 0.2)\*2 + 10) basis points on average for a round trip of transactions. Following Balduzzi and Lynch (1999), we assume that we pay the transaction fee when we trade BM portfolios but not when we trade the risk-free asset.

Following Han et al. (2013) and Ko et al. (2014), we use break-even transaction costs (BETCs) to evaluate the profit versus cost for the MAP returns. BETC here is the fee that we can a fford in each round-trip transaction for the deciles if the final profit is zero. We report the results in Table 4, where we label BETCs with n.a. when the MAP return is negative, as BETCs are meaningless in such a situation. Overall, the BETCs are mostly higher than 20.6 basis points. The MAP(5) and MAP(10) strategies in general have lower BETCs because transaction operations are too frequent, thus incurring higher transaction fees. The BETCs of MAP(20) are higher than 20.6 for all deciles, indicating positive after-cost profitability. The BETCs start to decline after the MAP(20) strategy. This pattern is similar to the results in Figure 1.

In our new proposed zero-cost trading strategy, TLS, we need to borrow stocks when receiving short signals and pay interest for stock borrowing. In China, most interest rates for short-selling are lower than 9% annually, which is 2.4658 points daily (9%/365). To compute the after-cost returns of TLS, in addition to the normal transaction fee, we need to subtract the interest fee. We calculate the interest fee by multiplying the short-selling interest rate by the number of days that we borrow stocks. From Table 4, we can see that transaction costs for TLS decrease monotonically from 7.09 to 2.58 points as the lag length increases. We obtain a positive final return for all of the portfolios except for the MAP(200) strategy. Again, the MAP(20) strategy generates the highest after-transaction-cost TLS returns, which is consistent with the findings in Figure 1. Therefore, MA timing strategy with 20-day lag seems to be the best choice both before and after transaction costs.<sup>2</sup>
