Wilder’s Parabolic SAR is a very good technical analysis tool that can show impartially if the trend, even in the very short term, is up or down. It can be used as a daily stop loss order. It works well with the SAR method to help investors profit from both uptrends and downtrends. It can also be used in day trading.
The Parabolic is a technical analysis tool that was introduced to the public in 1978 in the book New Concepts in Technical Trading Systems by the American Welles Wilder. In this book, Wilder described several new tools at the time: the Relative Strength Index (or RSI), the Directional Movement Index (or DMI) and the Parabolic SAR. The book also presented other tools, including one for volatility, but the three tools mentioned above are the best known.
How is the Parabolic used?
An example of the Parabolic is shown in Chart 1 of XIU (S&P/TSX60 Index in the form of an exchange-traded fund).
Note two types of dotted lines on the chart: lines below the price and lines above the price:
- When the dotted line is below the price, the trend is up.
- When the dotted line is above the price, the trend is down.
The first use of the Parabolic is as a trend indicator. It is impartial; it acts as an alert indicating a possible trend change.
Its second use is the very reason for its existence:
- When a dotted line below the stock price ends and gives way to a dotted line above the stock price, this means the price has dropped to the Parabolic price level.
- The investor sells his long position at this price.
- The investor then re-enters the market by selling short at this same price in order to profit from a probable decline.
- When a dotted line above the price of the stock price ends and gives way to a dotted line below the stock price, this means the price has risen to the Parabolic price level.
- The investor covers his short position at this price.
- The investor then takes a long position at this same price to profit from a probable rise.
The third use of the Parabolic is as a tool to indicate the price at which one should exit a market position. Let’s look at Chart 2:
- In the first week of January 2010, the stock began to decline after hitting a high of about $73.50. If we had sold the stock short close to this high, we could have subsequently covered our short at $63.50 (point B in the chart). That is the point at which the dotted line above the price gave way to the dotted line below the price. In this case, point B proved to be an effective indicator.
- In the first week of February 2010, the stock began to climb. After reaching a high of about $74.50, it began to decline. At point C, at around $72.00, the dotted line below the price gave way to a dotted line above the price. Here too, the Parabolic proved to be a good exit indicator.
- Note that we could have taken our long position at the exit price in point a above. This is an example of implementing the strategy in point 2b above.
- The Parabolic’s weakness. In mid-October 2009, we could have sold the stock short at the beginning of the decline, after the high of about $60.00. Two weeks later, the price hit a low of about $50.00. If we had waited for the Parabolic to give us an exit signal (i.e. to buy back the stock or exit the short position), we would have got the signal at around $56.00, at point A. In this case, the Parabolic would have given us a very disappointing exit signal, because it occurred $6.00 higher than the low and only $4.00 below the mid-October high.
If we compare the behaviour of the Parabolic signals at points A, B and C, we see that when the price reaches a low and creates congestion around this low (circled area B), or when the price reaches a high and creates congestion around this high (circled area C), the market exit signals are good because they are given close to the low and the high, respectively. Conversely, in circled area A, we see that the exit signal is poor, because the price, after reaching a low of about $50.00, climbs back quickly, without creating congestion around the low.
So there is a strong correlation between the quality of the signal and the amount of congestion around the highs and lows:
The rules for using the Parabolic also apply to day trading. An example is shown in Chart 3, using five-minute periods. Note that in this case too, the above observations apply: oval D shows congestion over several five-minute periods. The short-sell signal is given close to the high, at Friday’s open (at around $27.80). However, the Parabolic exit signal is given at around $26.60, an unfavourable price compared to the lower price of about $25.90 reached a little before 11:00 a.m. Note that in oval E, there is no congestion around the low, which explains the poor signal, as explained in point e above.
How the Parabolic is constructed
Before discussing the Parabolic, a word about the acronym SAR, which stands for Stop and Reverse. SAR is always mentioned when speaking about the Parabolic, but in reality SAR is a trading method that applies to various technical analysis tools. In fact, an investor has a choice of three stock trading methods:
- If a stock is rising, the investor can decide to enter the market by buying the stock and subsequently selling it. In this case, the investor only profits from price moves to the upside.
- If a stock is falling, the investor can decide to enter the market by selling the stock short and subsequently covering the short. In this case, the investor only profits from price moves to the downside.
- The investor can implement both of the preceding methods, to profit from both upswings and downswings.
This last method is the SAR method. For example, an investor starts off by buying 100 shares of ABC (symbol of a fictitious company) when a technical buy signal is given. When a sell signal is subsequently given, the investor sells 200 shares of ABC: 100 shares to close out the long position and 100 shares to take a short position in the stock). When another buy signal is given, the investor buys 200 shares of ABC: 100 shares to cover (close out) the short position and 100 shares to take a new long position to profit from the anticipated upswing. So from one signal to the next, the investor is always in the market, with either a long position or a short position. This enables the investor to profit from both upswings and downswings. This method is used with various technical analysis tools, such as the crossing of two moving averages, the DMI, momentum, etc.
To describe the Parabolic, it is practical to use Figure 1 and to present the formula as Wilder did in his 1978 book.
The horizontal axis in Figure 1 shows a series of market sessions and the vertical axis shows a series of prices of a fictitious stock. The series of bars in the chart depicts an uptrend, starting on day one. Each bar represents the price range during one session: the high and low of the session are at the extremities of each bar. The lowest price in the uptrend is $50 (day one). The SAR formula starts off as follows:
AF is the acceleration factor. Its numerical value, in the standard version of the Parabolic, is 0.02 in the starting calculation. To calculate the SAR on day five, the AF will be 0.02. On each successive day thereafter, the AF increases by 0.02. So on day six, it will be 0.04 and on day seven, 0.06. The AF stops increasing when it reaches 0.20, i.e. the equivalent of ten days of rising prices from the beginning of the calculation. Depending on the software used, the investor can change the AF (using a larger or smaller value) if the investor deems it suitable, based, for example, on the stock's volatility.
The subscript numbers 4 and 5 in the formula indicate day four and day five, respectively. The starting formula reads as follows:
The SAR signal price on day five is equal to the SAR signal price on day four plus the difference between the high on day four (H4) and the SAR on day four (SAR4) multiplied by the AF.
Note that the Parabolic calculation starts with day four. The SAR on day four (SAR4) is not the result of a calculation; it is simply the lowest price at the beginning of the uptrend. In Figure 1 it is $50.00, i.e. the lowest price on day one. Note that the SAR signal in an uptrend represents the exit price, when the stock price falls below the SAR price.
Inserting the numerical data from Figure 1 into the formula, the SAR5 calculation becomes:
The SAR6 is calculated with the following formula:
Inserting the numerical data, we get:
And so on and so forth for the subsequent days. On a chart, we end up with a dotted line below the stock price, as illustrated in Figure 1. The numerical calculation shown above and the chart in Figure 1 concern an uptrend. In the case of a downtrend, the formula is adjusted and the dotted line obtained will be above the stock price.