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Godwin Norris
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1 James Ofria MATH55 Introduction Since the first corporations were created people have pursued a repeatable method for determining when a stock will appreciate in value. This pursuit has been alchemy of the investment world. Theoretically this using any mathematical method to analyze historical data or time domain graphs to predict the future performance of stock is impossible because the future performance (output) is based on future values of each metric (input). In today s stock market the approach of mathematically analyzing metrics is called technical trading and in today s market more trades are executed by computers than by humans. According to a chart published by CNN Money in 212 more than 6% of all trades were executed automatically by computers. Moving average convergence/divergence (MACD) is a technical indicator derived from the share price belonging to a certain stock. Developed in the 197s by Gerald Appel and pronounced Mack Dee, it is used to find opportunistic changes in the strength and momentum of a company s shares. What is MACD and how is it calculated The MACD indicator is used by watching the interactions and performance of 2 signals in the time domain that are calculated from 2 exponential moving averages (EMA) of a company s closing share price. When the 2 signals cross each other or pass together from positive to negative this indicates a shift in strength and momentum. The two signals comprising a MCAD chart are referred to commonly as the MACD or difference and MACD signal. Figure 1

Exponential Moving Average An exponential moving average, abbreviated in the document as EMA, is a way of averaging a set of data in a particular domain.

2 Exponential Moving Average An exponential moving average, abbreviated in the document as EMA, is a way of averaging a set of data in a particular domain. In our case we are concerned with the time domain. EMA is a type of infinite impulse response filter that can be applied to an input signal to reveal the direction of momentum change as well as other trends. EMA works by applying different coefficients to each term begin averaged. This is done in a way that applies less weight to older data (time domain) in the dataset by applying ever smaller coefficients. See Equations below. The weights applied to each data point follow an exponential curve, which is where Exponential moving average received part of its name. See figure 2 for an example of coefficient values, in that example N = 15, that is to say in our application N = 15 days. Figure 2 EMA(P, t) = P(t) + (1 )P(t 1) + (1 )2 P(t 2) (1 ) + (1 ) 2 + Where: = N N = number of data points Historical Closing share Price = P(t)

3 MACD or difference The MACD or difference line is calculated by taking the difference of two separately calculated EMAs of a company closing share price. Closing share price is the price of one company share at the end of the regular trading day. The first EMA is calculated with a relatively short period and is often referred to as the Fast EMA, as a standard 12 days is used. The second EMA, called the Slow EMA, is calculated with a much longer period typically 26 days. Historical Closing share Price = P(t) MACD(t) = EMA 12 [P(t)] EMA 26 [P(t)] MACD signal The MACD signal is generated by taking the EMA of the MACD or difference curve over an even shorter period than the Fast EMA we took earlier of the closing market share price. MACD_Signal(t) = EMA 12 (MACD)

4 How MACD is applied to trading As mentioned earlier the MACD is used as a tool to show investors when there is an opportunistic shift the momentum of a stocks share price. The MACD indicator is typically represented as a chart with two curves or a histogram. MACD histograms usually show data points only where the events where action should be taken, and always convey less information. For this reason we will be focusing our analysis on the chart representation of the MACD indicator. If presented as a chart with two curves important and opportunistic events are identified when, MACD difference and MACD signal cross each other or when the MACD difference curve crosses from positive to negative values or vice versa. When this happens the MACD is said to have crossed zero. Additionally, if the two curves start to diverge from each other significantly this is an indicator that action should be taken. Figure 3 Excerpt from MACD analysis using CISCO share prices from 1/1/23 to 6/3/23 MACD difference crosses MACD signal As seen in figure 3 event one circled in red shows an example of the MACD or difference curve crossing the MACD signal curve. This type of cross event where the difference crosses below the MACD signal, indicates that the stock is bearish meaning that it might be a good time to sell. The next event where the difference curve crosses the MACD signal is event 3 seen on figure 3. This cross happens the opposite as the previous and indicates that the stock is at a good time to buy because it may be experiencing upward momentum.

5 MACD crossed zero or diverges In the second event shown in figure 3 of my analysis the difference curve crosses from positive to negative. This indicate that the momentum of the share price is changing from positive to negative. Conversely, as seen in the very beginning of event 4 the total momentum of the change in share price is shifting from negative to positive. Further, from both events 2 and 4 it can be seen that the difference and MACD signal curves are diverging from one another. This indicates that the shares are volatile and a change in momentum may be imminent. RESULTS: Does MACD really work? To find out how well this trading method actually works I simulated trading the shares using a MACD indicator using 1 years of daily historical data for large well-known tech companies. To help govern my automated MACD trader I set a series for rules for how it should handle things like bad trades that continue to cause a loss and what percentage of the total capital should be allocated to each trade as the total capital it has access to changes. See in table 1 below. Maximum capital to allocate per trade 25% Target profit per trade (when to liquidate shares) 25% Max loss to take per trade 5% Total starting Balance $1. Table 1 Below in charts 1 through 6 you can see the performance of the MACD indicator can be seen as compared to the overall performance of the company s share price. The orange line indicates the account balance of MACD trader, which starts at $1,. USD using the axis on the right. The blue line shows the price of a single share of the company s stock (use axis on left of chart). If the orange line finishes higher than the blue line then the MACD trader outperformed the company s growth.

6 4 CISCO vs Time $1, $1,. $8. $6. $4. $2. Chart 1 6 Adobe vs Time $1,4. 5 $1, $1,. $8. $6. $4. $2. Chart 2

7 9 SAP vs Time $1, $1,. $8. $6. $4. $2. Chart 3 IBM vs Time $2,. $1,8. $1,6. $1,4. $1,2. $1,. $8. $6. $4. $2. Chart 4

8 Apple vs Time 8 $1, $9,. $8,. $7,. $6,. $5,. $4,. $3,. $2,. $1,. Chart 5 12 Google vs Time $6,. 1 $5, $4,. $3,. $2,. $1,. Chart 6

9 Conclusion/Analysis of results From analyzing the above graphs it can be said that the MACD indicator does not necessarily make a for a good investment tool. The performance on trading stocks belonging to Cisco, SAP, and Google was over all very poor, because if instead of running the MACD trader an initial investment was made in each of those companies the final profit would have been greater. Further on stocks IBM and adobe the performance of the MCAD trader was approximately the same as performance of the stock. The MACD trader some made money but is was very close to the performance of investor who made a single investment and did nothing. Finally, apple shares were out performed by the MACD trader, but that shows that only one out of six times MACD works to produce significant profit. Three out of six time the MACD trader will be out performed by value investors who keep shares for many years. Finally, my results show that two out of six times the performance of the MACD trader will very nearly match that of the companies own organic growth. The results of my experimentation is very limited I only tested one sector (large tech companies), and I was also not able to account for events like splits, where the number of shares are doubled and share price halved. However, my results do show that the MACD indicator at face value is not landslide holy grail to tell the future of the market. With more complexity put into the simulation and addition algorithms to uncover corner cases where MACD might not be relevant could yield a more accurate analysis of the MACD indicator and will be have to be deferred to later works on this project.

Moving Averages, CrossOvers and the MACD

Moving Averages, CrossOvers and the MACD October 14, 2017 Introduction: Moving averages are the most widely used indicators in technical analysis, and help smoothing out short-term fluctuations (or volatility)