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R. and Ricardo P.C. Leal (1999) used ten Variable Length Moving Average (VMA) technical trading rules in ten emerging equity markets in Latin America and Asia from January 1982 through April 1995. They used inflation adjusted returns instead of normal returns and apply a trading band that accounts for differences in volatility be-tween markets. They compared these trading rules to a buy and hold strategy and fined that Taiwan, Thailand and Mexico where technical trading strategies may be profitable.
At the same time, there are several studies add “volumes” to make trading rules to see if it can have better predictive power than only using prices. Blume, Easley and O’Hara (1994) present a model in which both past price and volume provide valuable information. Volume contains information regarding the quality of information in past price movements, which perhaps should be more useful for smaller, less widely fol-lowed firms. Ramazan G. and Thanasis S. (1998) used the daily Dow Jones Industri-als Average Index from 1963 to 1988 to examine the linear and non-linear predictabil-ity of stock market returns with some simple technical trading rules. They found that past information on volume improves the forecast accuracy of current returns.
3. Data and Methodology 3.1 Data
The database used in this research are the daily closing prices and trading volumes of the constituent stocks of FTSE TWSE Mid-Cap Taiwan 100 Index from TEJ2 for the period from the first trading day of 2005 to the last trading day of April 2011. The constituents are those published by TWSE at the end of April 2011. FTSE TWSE Taiwan Mid-Cap 100 Index consists of the next 100 companies ranked by full market
2 Taiwan Economic Journal (TEJ) is a database providing accurate and reliable data on companies throughout Asia.
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value, outside the FTSE TWSE Taiwan 50 Index, and it represents over 20% of the Taiwanese market. This index is reviewed quarterly in January, April, July and Octo-ber every year, and constituent changes are implemented on the next trading day fol-lowing the third Friday of the same month. The industries of the constituents of this index are classified by Industry Classification Benchmark (ICB)3 which was created by FTSE Group and Dow Jones Indexes in 2005 to provide a standardized base for analysis, stock selection and performance measurement. The constituents of FTSE TWSE Mid-Cap Taiwan 100 Index are listed at Appendix A.
3.2 Trading Rules
One of the most popular technical trading rules is the MA rule. According to this rule, buy (sell) signals are emitted when the short-term moving average exceeds (is less than) the long-term average. The simple MA is computed as any other mathemat-ical average. The usual method is to take the closing price over a certain period, add them together and then divide them by the selected number of days. The next day’s closing price will be added into the total and the initial day price will be dropped.
In this study, I use three kinds of MA rules. The first one named “Price Strategy”
is the commonest MA rule which only consider price and the formula can be written as:
𝑀𝐴𝑡𝑝(n) =∑𝑛−1𝑖=0 𝑃𝑡−𝑖
𝑛 (1)
where 𝑀𝐴𝑝𝑡(𝑛) is n-day moving average for price at time t, 𝑃𝑡 is the closing price at
3 ICB contains four classification levels: Industries(10), Supersectors(19), Sectors(41), and Subsec-tors(114). This classification system covers over 60,000 companies and 65,000 securities worldwide from Dow Jones and FTSE Universes. Industry classifications: Oil & Gas,0001; Basic Materials, 1000;
Industrials, 2000; Consumer Goods, 3000; Health Care, 4000; Consumer Services, 5000; Telecommu-nications, 6000; Utilities,7000; Financials, 8000; Technology, 9000.
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time t, and 𝑛 is the total number of selected period.
The other two will add volume into the consideration to come out trading rules.
“Price and Volume Strategy” will generate price and volume MA rules individually first and then consider both rules to have a trading action, which means investors will buy (sell) the stock only when both of price and volume MA rules show buy (sell) signals. Thus Strategy 2 rule becomes like Equation (2).
𝑀𝐴𝑡𝑝(n) = ∑𝑛−1𝑖=0 𝑃𝑡−𝑖
𝑛 𝑀𝐴𝑡𝑣(n) =∑𝑛−1𝑖=0 𝑉𝑡−𝑖
𝑛 (2)
where 𝑀𝐴𝑣𝑡(𝑛) is n-day moving average for volume at time t, 𝑉𝑡 is the trading volume at time t, and 𝑛 is the total number of selected period. For Strategy 2, not only the moving average for prices but also the moving average for volumes will be taken into account to issue a buy or a sell signal.
“PV Strategy” takes volume as a weight for price and uses the weighted price to make a MA rule. The formula is like Equation (3).
𝑀𝐴𝑡𝑝𝑣(n) =
∑ [ 𝑉𝑡−𝑖
∑𝑛−1𝑖=0 𝑉𝑡−𝑖× 𝑃𝑡−𝑖]
𝑛−1𝑖=0
𝑛 (3)
where 𝑀𝐴𝑝𝑣𝑡 (n) is n-day moving average for weighted price at time t, ∑ 𝑉𝑡−𝑖𝑉
𝑛−1 𝑡−𝑖
𝑖=0 is a percentage of the trading volume at time t-i to total trading volumes for n days. This strategy can be taken as a transformed MA rules for prices. The prices with higher trading volumes may contain more information and should be paid more attention on, so this strategy can give higher weights to those prices which have higher trading volumes.
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Each strategy will use 5-day MA as the short-term moving average (SMA) and 10, 50, 100, 150, 200 days as the long-term moving average (LMA), so total will be fif-teen MA rules. When the short-term moving average breaks the long one from below (above), a buy (sell) signal comes out and investors will buy (sell). Once the follow-ing short-term movfollow-ing average breaks the long one from above (below), investors will close the buy (sell) trade and start to sell (buy) the stock, like Figure 3.2.1:
Figure 3.2.1 Trading rule
From this trading rule, each stock will have several buy times (buy the stock when there are buy signals) and sell times (sell the stock when there are sell signals) during the period from 2005 to April 2011. In order to examine the profitability of these MA rules, I will calculate “Hit Ratio” for each of buy and sell times to see the proportion of positive returns by these MA rules, like Equation (4),
𝐻𝑖𝑡𝑏 = 𝐵𝑝
𝐵𝑎𝑙𝑙 ; 𝐻𝑖𝑡𝑠 = 𝑆𝑝
𝑆𝑎𝑙𝑙 (4)
where 𝐻𝑖𝑡𝑏 (𝐻𝑖𝑡𝑠) is the “Hit Ratio” of buy (sell) times, 𝐵𝑝 (𝑆𝑝) is the buy (sell) times with positive returns, and 𝐵𝑎𝑙𝑙 (𝑆𝑎𝑙𝑙) is total buy (sell) times. The result may
Day t
Day t+n
Buy signal:
Buy the stock at the closing price on day t and keep holding it until there’s no buy signals.
Sell signal:
Close buy trading and sell the stock at the closing price on day t+n.
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show what kind of trading rules have more opportunities to earn positive returns. I will also compute average return and average holding days per trading times for every trading rule. Hit ratios, average returns and average holding days will be generated not only for all constituents without considering industries but also for specific indus-tries. All of these trading rules are generated under the hypotheses of no transaction costs.