APPLYING A COMBINED MAX-MIN SIMPLE MOVING AVERAGE TRADING STRATEGY TO MARKET INDEXES.

• Date: 01 June 2018
• Author: Ren, Louie

1. Introduction

   The weak form of the Efficient Market Hypothesis (EMH) asserts that all information contained in past price movements is fully reflected in current market price. If this were true, then information about recent trends in stock prices would be of no use in selecting stocks. In contrast, technical analysts believe that past trends or patterns in stock price can be used to predict future stock prices (Brigham and Daves, 2016: 69-70).

   Yen and Lee (2008) made an extensive review of EMH. Some of the influential studies about EMH are Bachelier (1900), Kendall (1953), Fama (1965), Samuelson (1965), Fama and Blume (1966), Mandelbrot (1966), Fama et al. (1969), Fama (1970), Fama (1991), Nichols (1993), Thaler (1993), Conrad (1995), Shanken and Smith (1996), Fama (1998), Malkiel (2003, 2005), and Jiang and Tian (2012).

   On the other hand, increasing skepticism about the EMH led to support for trading rules. Examples of trend include Osborne (1959, 1962), Levy (1967), Jensen and Henington (1970), Rozeff and Kinney (1976), Basu (1977), Jensen (1978), Schneeweis and Woolridge (1979), Taylor (1982), Mishkin (1983), Renshaw (1984), Keane (1986), Sweeney (1988), Balvers et al. (1990), Campbell et al. (1993), Jegadeesh and Titman (1993), Blume et al. (1994), Lo and MacKinlay (1997), Haugen (1999), Schleifer (2000), Beckmann (2002), Shiller (2003), Avramov et al. (2006), Daniel and Sheridan (2006), Al-Khazali et al. (2007), Cooper et al. (2008), Cohen et al. (2009), Lakshmi and Roy (2012), Brown (2013), Almudhaf (2014), Malhotra et al. (2015), and Ross (2015).

   One aspect of technical analysis involves analyzing historical market data to identify potentially profitable trades. According to Lento (2007), technical analysis is one of the earliest forms of investment analysis, because stock prices are publicly made available before other types of financial information. In Brock et al. (1992: 1735), one of the simplest and most widely used technical rules is the trading rule based on moving average-oscillators.

   Under the moving average trading rule, buy and sell signals are generated by two moving averages of the returns: a long-period average return and a short-period average return. The moving average strategy is to buy or sell when the short-period moving average rises above (or falls below) the long-period moving average. That is, buy if MA(S) > MA(L); otherwise, sell, where MA(S) and MA(L) is the short-period and long-period moving average, respectively. The rationale behind computing moving averages is to smooth out an otherwise volatile series. When the short-period moving average penetrates the long-period moving average, a trend is considered to be initiated. We denote the moving average trading rule with a short moving period of S, and a long moving period as MA(S, L).

   In this paper, the popular moving average rules with the short moving period of S = 1 and 5 and the long moving period of L = 50, 100, 150, and 200 are evaluated as replicate studies for their ability to forecast market returns, where the returns are defined to be ln(pt)-ln(pt-1) as in Fama (1965: 45).

   In Arnold and Rahfeldt (2008, AR hereafter), a trading rule is created by combining information from two simple moving averages (MA). That is, buy when the actual price crosses above both moving averages and exit the market when the price crosses below either moving average. Namely, it means

   [Buy: if [p.sub.t] > MA(S) [and.bar] [p.sub.t] > MA(L); [Sell: if [p.sub.t] < MA(S) [or.bar] [p.sub.t] < MA(L),

   where [p.sub.t] is the closing price at time t, MA(S) and MA(L) are short and long moving averages up to closing price at time t-1. Short MA period of S = 5 and 10 days, and long MA period of L = 50, 100, 150, and 200 days are examined in Chang et al. (2006). Let us denote those decision rules as AR-MA(S, L), where S and L are short and long moving average periods, respectively. Chang et al. (2006) found that AR-MA(S, L) rules provide more useful information for investor to identify profitable opportunities compared to MA(S, L) in the Taiwan stock markets.

   In this study, we examine MA(S, L) and AR-MA(S, L) rules, along with other two suggested variation forms of AR-MA(S, L) rules, to compare their profitability on the Dow Jones Industry Averages (DJIA), the National Association of Securities Dealers Automated Quotations (NASDAQ), and the Standard and Poor 500 (S&P). We propose a new combined trading rule based on simple MA(S, L) methods. The new trading rule improves the Buy and Sell-day returns by a factor of 10 to 20 when applied to the DJIA, the NASDAQ, and the S&P.

2. Data and Trading Rules

   As a replicate comparison study, 5,780 observations each from the DJIA, the NASDAQ, and the S&P in Yahoo Finance are examined. We use data from 1/29/1985 to 12/27/2007 in comparison to the study of MA(S, L) trading rules on the DJIA (Brock et al., 1992), the NASDAQ (Metghalchi et al., 2011), and the S&P (Metghalchi et al., 2005), where S = 1, 5, and L = 50, 100, 150, 200.

   From Chang et al. (2006), AR-MA(S, L) trading rules outperform regular moving average trading rules in the Taiwan Stock market. In this study, we examine if AR-MA(S, L) will outperform under a more efficient market in the United States. The three market indices that we will consider are the DJIA, the NASDAQ, and the S&P.

   In addition to the AR-MA(S, L) decision rule studied in Chang et al. (2006), mathematically, we can come up with three other similar versions of AR-MA(S, L) trading rules as follows. The differences among those rules are underlined.

   [Buy: if [p.sub.t] > MA(S) [and.bar] [p.sub.t] > MA(L); [Sell: if [p.sub.t] < MA(S) [and.bar] [p.sub.t] < MA(L),

   [Buy: if [p.sub.t] > MA(S) [and.bar] [p.sub.t] > MA(L); [Sell: if [p.sub.t] < MA(S) [or.bar] [p.sub.t] < MA(L),

   [Buy: if [p.sub.t] > MA(S) [or.bar] [p.sub.t] > MA(L); [Sell: if [p.sub.t] < MA(S) [or.bar] [p.sub.t] < MA(L),

   [Buy: if [p.sub.t] > MA(S) [or.bar] [p.sub.t] > MA(L); [Sell: if [p.sub.t] < MA(S) [and.bar] [p.sub.t] < MA(L).

   We can rewrite the above four trading rules as follows where MA(S) and MA(L) are moving average with moving period of S and L, respectively:

   [Buy: if [p.sub.t] > maximum{MA(S), MA(L)} [Sell: if [p.sub.t] < maximum{MA(S), MA(L)} (1)

   [Buy: if [p.sub.t] > maximum{MA(S), MA(L)} [Sell: if [p.sub.t] < minimum{MA(S), MA(L)} (2)

   [Buy: if [p.sub.t] > minimum{MA(S), MA(L)} [Sell: if [p.sub.t] < maximum{MA(S), MA(L)} (3)

   [Buy: if [p.sub.t] > minimum{MA(S), MA(L)} [Sell: if [p.sub.t] < minimum{MA(S), MA(L)} (4)

   An illustrative example below shows how these four rules work.

   [p.sub.t] MA(S) MA(L) Rule #(1) Rule #(2) or MA(L) or MA(S) buy sell buy sell > max < max > max < min 1 3.5 7.5 sell sell 2 3.5 7.5 sell sell 3 3.5 7.5 sell sell 4 3.5 7.5 sell neither 5 3.5 7.5 sell neither 6 3.5 7.5 sell neither 7 3.5 7.5 sell neither 8 3.5 7.5 buy buy 9 3.5 7.5 buy buy 10 3.5 7.5 buy buy [p.sub.t] Rule #(3) Rule #(4) buy sell buy sell > max < max > min < min 1 sell sell 2 sell sell 3 sell sell 4 buy or sell buy 5 buy or sell buy 6 buy or sell buy 7 buy or sell buy 8 buy buy 9 buy buy 10 buy buy * Rule #(3) and #(4) end up the same decision In the fourth row, the current price is $4, MA(S)=$3.5 and MA(L)=$7.5, or MA(S)=$7.5 and MA(L)=$3.5. For Rule #(1), because the current price of $4 is less than max{$3.5, $7.5}=$7.5, a buy action is triggered. For Rule #(2), because the current price $4 is neither greater than max{$3.5, $7.5}=$7.5, nor less than min{$3.5, $7.5}=$3.5, the investor will neither buy nor sell the stock. For Rule #(3), because the current price $4 is greater than min{$3.5,$7.5}=$3.5, and less than max{$3.5, $7.5}=$7.5, the investor...