*4.2. Business Cycles*

We now come to the question of whether there is any relation between the moving average signals and business cycles. Here, we use two methods to test the influence of business cycles. First, Liew and Vassalou (2000) construct the following model, which uses the GDP growth rate as a proxy for good and bad business states

$$\begin{aligned} \text{MAP}\_{\text{j},\text{f},\text{L}} \quad &= a\_{\text{j},\text{L}} + \beta\_{\text{j},\text{L},\text{MKT}} R\_{\text{MKT},\text{f}} + \beta\_{\text{j},\text{L},\text{SMB}} R\_{\text{SMB},\text{f}} + \beta\_{\text{j},\text{L},\text{HML}} R\_{\text{HML},\text{f}} + \beta\_{\text{j},\text{L},\text{G}\text{and}} D\_{\text{G}\text{and},\text{f}}^{\text{GLP}} + \\ & \quad \beta\_{\text{j},\text{L},\text{Bal}} D\_{\text{Bal},\text{f}}^{\text{GDP}} + \varepsilon\_{\text{j},\text{f},\text{L}}, \ j = 1,\ldots,10, \end{aligned} \tag{10}$$

$$\text{TLS}\_{\text{l},\text{L}} = \left. a\_{\text{L}} + \beta\_{\text{L},\text{MKT}} R\_{\text{MKT},\text{t}} + \beta\_{\text{L},\text{SMB}} R\_{\text{SMB},\text{t}} + \beta\_{\text{L},\text{HML}} R\_{\text{HML},\text{t}} + \beta\_{\text{L},\text{Good}} D\_{\text{Good},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{Rall}} D\_{\text{Rat},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{S},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{S},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{H},\text{S}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{S},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{S},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{S},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{S},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{S},\text{t}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{H},\text{S}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{H},\text{S}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{H},\text{S}}^{\text{GDP}} + \beta\_{\text{L},\text{S}} D\_{\text{H},\text{S}}^{\text{GDP}} + \beta\_{\text{L},\text{$$

In the model, *DGDP Good*,*t* and *DGDP Bad*,*t* are the dummy variables for good and bad business states. When the GDP growth rate in the quarter is in the top 25% of the whole sample period, *DGDP Good*,*t* will be one, which indicates that business cycles are in a good period. *DGDP Bad*,*t* indicates the bad state when the quarterly GDP growth rate is in the bottom 25% of the overall sample. We can determine the contribution of both expansionary (good business state) and recessionary (bad business state) periods from their coefficients. If they are significantly positive, the predictability is strong, and the strategy works in the state.

The other model from Cooper et al. (2004) uses a dummy variable for bad market performance. We follow them and perform the following regression using market return data:

$$\begin{aligned} \text{MAP}\_{\text{j},\text{L}} \quad &= a\_{\text{j},\text{L}} + \beta\_{\text{j},\text{L},\text{MKT}} \text{R}\_{\text{MKT},\text{f}} + \beta\_{\text{j},\text{L},\text{SMB}} \text{R}\_{\text{SMB},\text{f}} + \beta\_{\text{j},\text{L},\text{HML}} \text{R}\_{\text{HML},\text{f}} + \beta\_{\text{j},\text{L},\text{Bal}} D\_{\text{Bal},\text{f}}^{\text{Mbarl}\text{ct}} + \varepsilon\_{\text{j},\text{L},\text{r}} \\ &\quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad$$

$$\text{TLS}\_{\text{l.}L} = a\underline{\text{L}} + \beta \underline{\text{L}}\_{\text{r.}M\text{KT}} \text{R}\_{\text{MKT},\text{f}} + \beta \underline{\text{L}}\_{\text{r.}\text{SMB}} \underline{\text{R}}\_{\text{SMB},\text{f}} + \beta \underline{\text{L}}\_{\text{r.}\text{HML}} \text{R}\_{\text{HML},\text{f}} + \beta \underline{\text{L}}\_{\text{r.}\text{Bad}} \text{D}^{\text{Mtau}}\_{\text{Bad},\text{f}} + \varepsilon\_{\text{l.}\text{L}} \tag{13}$$

*DMarket Bad*,*t* is the dummy variable that denotes the bad state of the business cycle. We calculate the market return of the past three years before every yearly holding period. If the result is negative, *DMarket Bad*,*t* will be one, and zero otherwise. We can determine the effect of a bad market environment on our excess return from its coefficients. If the coefficients on *DMarket Bad*,*t* are significantly positive, our strategy works in the bad market state.

Panels A and B of Table 6 show the results of these two regressions. We find that the pattern of the alphas in the two models changes only slightly from before. However, the coefficients on most of the dummy variables are insignificant. For the first model, 9 of the 10 portfolio coefficients are insignificant at the 10% level. For the second model, only two of the coefficients of the dummy variable *DMarket Bad*,*t* are significant at either the 5% or 10% level. These results clearly show that business cycles have a very weak influence on the average returns of MA strategy.<sup>3</sup>

<sup>3</sup> From unablated robustness test results, we find that other famous cycle effects like the January effect and the Lunar cycle (Wong and McAleer 2009) also have weak influence over the MA and TLS strategies.



presented in the parentheses.

## *4.3. Market Timing Ability*

To find out more about how the moving average and TLS strategies can outperform the buy-and-hold strategy, we also investigate their timing ability, which may drive the performance. We take use approaches proposed by Treynor and Mazuy (1966) and Henriksson and Merton (1981) to test the market timing ability of the two strategies in our paper.

Treynor and Mazuy (1966)'s model is

$$MAP\_{j,t,L} = a\_{j,L} + \beta\_{j,L,\text{MKT}} R\_{\text{MKT},t} + \beta\_{j,L,\text{MKT}^2} R\_{\text{MKT},t}^2 + \varepsilon\_{j,t,L,\text{ }j} \ = 1, \dots, 10,\tag{14}$$

$$TLS\_{\rm l,L} = \alpha\_{\rm L} + \beta\_{\rm L,MKT} R\_{MKT,t} + \beta\_{\rm L,MKT} R\_{MKT,t}^2 + \varepsilon\_{\rm t,L} \tag{15}$$

These is a quadratic model where *<sup>R</sup>*2*MKT*,*<sup>t</sup>* is the squared market excess return. If the coe fficients are significantly positive, it indicates that the strategies may have some market timing ability.

Henriksson and Merton (1981) propose the following model to test market timing ability:

$$\text{MAP}\_{\text{j},\text{l},\text{l}} = \alpha\_{\text{j},\text{l}} + \beta\_{\text{j},\text{l},\text{MKT}} R\_{\text{MKT},\text{l}} + \gamma\_{\text{j},\text{l},\text{MKT}} R\_{\text{MKT},\text{l}}\\\text{I}\_{\text{r}\_{\text{MKT},\text{j}}>0} + \varepsilon\_{\text{j},\text{l},\text{L}} \quad j = 1,\ldots,10,\tag{16}$$

$$TLS\_{t,L} = \alpha\_L + \beta\_{L,MKT}R\_{MKT,t} + \gamma\_{L,MKT}R\_{MKT,t}I\_{TMT,t>0} + \varepsilon\_{t,L} \tag{17}$$

In these regressions, the value of the indicator function, *IrMKT* , will be one if the market excess return is positive and zero otherwise. If the parameter γ*L*,*MKT* is significantly positive, it suggests that there is market timing ability.

The regression results of these two tests are shown in Table 7. Di fferent from the results of Han et al. (2013) and Ko et al. (2014), most of the coe fficients on β*j*,*L*,*MKT*<sup>2</sup> and γ*j*,*L*,*MKT* in our regressions are insignificant. In particular, both of the market timing coe fficients for the TLS strategy are insignificant. In addition, the alpha values do not change substantially from our main findings. The overall results sugges<sup>t</sup> that the profits generated by our strategy are not due to market timing ability.


**Table 7.** Market timing ability.

Two methods are used to test the market timing ability. One is *MAPj*,*t*,*<sup>L</sup>* = <sup>α</sup>*j*.*<sup>L</sup>* + β*j*,*L*,*MKTRMKT*,*<sup>t</sup>* + <sup>β</sup>*j*,*L*,*MKT*<sup>2</sup>*R*2*MKT*,*<sup>t</sup>* + <sup>ε</sup>*j*,*t*,*L*. These are quadratic models, where *<sup>R</sup>*2*MKT*,*<sup>t</sup>* the squared market excess return. The other model is *MAPj*,*t*,*<sup>L</sup>* = <sup>α</sup>*j*.*<sup>L</sup>* + β*j*,*L*,*MKTRMKT*,*<sup>t</sup>* + <sup>γ</sup>*j*,*L*,*MKTRMKT*,*<sup>t</sup>IrMKT*,*t*><sup>0</sup> + <sup>ε</sup>*j*,*t*,*L*. In these regressions, we have *IrMKT*,*t*>0. The value of this indicator function will be one if the market excess return is positive and will be zero otherwise. *t*-test statistics are presented in the parentheses.

## *4.4. Subsample of Short-Selling*

As China's stock market is very young, the governmen<sup>t</sup> and stock exchanges have implemented a number of regulations to stabilize investors' trading behaviors and control risks. On 31 March 2010, China lifted the restriction on short-selling and allowed certain large cap stocks to be short-sold by qualified investors. The list quickly expanded in the following years, and short-selling activities in China developed rapidly.

Because short-selling was not allowed before 2010, it may not be possible to implement the MA and TLS strategies for our whole sample period. To check whether the profits generated from our strategies are realistic, we re-ran our tests in the period after 2010, when short-selling was flexible. Because not all stocks can be short-sold, when we conduct the TLS strategy, some stocks in the low BM portfolio cannot be shorted in the real market. We exclude those stocks and perform a subsample test from 31 March 2010 to 30 June 2015. We repeat the method used in Section 4.1 to obtain the summary statistics of the average returns of BM deciles, MA(20), and MAP(20) strategy.

From the summary statistics in Table 8, we find that the moving average strategy still outperforms the tradition buy-and-hold strategy, with higher returns on all portfolios. Almost all of the MAPs are positive. The result of the zero-cost trading strategy (TLS) for MA(20) is 10.50 points (t = 3.25), which is much bigger than the result from the high-minus-low with buy-and-hold strategy. Obviously, the moving average indicator is useful, and the TLS strategy is profitable.



Stocks that cannot be shorted are excluded from the lowest BM portfolio and a subsample test is performed for the period from 31 March 2010 to 30 June 2015. Summary statistics of average return of BM decile portfolios, MA(20) strategy and MAP returns. *t*-test statistics are presented in the parentheses.

In conclusion, excluding stocks that cannot be shorted in the lowest BM portfolio, the moving average technical analysis indicator and proposed TLS strategy work well and still contribute impressive and significant excess returns. This subsample test provides further evidence for the validity and usefulness of our two trading strategies.
