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# Profitable Trading (III) – Computerized Studies: PSAR

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### Introduction

The Parabolic Stop and Reverse system was presented by Welles Wilder in his classic book New Concepts in Technical Trading in 1978, and he originally calls it The Parabolic Time/Price System.

This system sets stops at points that are closer and closer to the price action as time passes. He calls it “parabolic” from the fact that the pattern forms a kind of parabola when charted. The main idea is to give the market room at the beginning of the trade and, as price moves in our favor, gradually tighten the stops as a function of time and price.

The PSAR stop always moves in the direction of the trade, as a trailing stop should do, but the amount it moves is a function of price because the distance the stop moves is computed in relation to the range the price has moved. It also gets closer to the price action regardless of the direction of the price movement.

### PSAR equation

If the stop is hit, the system reverses; therefore he calls each point a SAR: Stop and Reverse point.

The formula to compute it is:

SARTomorrow = SARToday + AF x (EPTrade – SARToday)

AF starts at 0.02 and is increased by 0.2 each bar with a new high until a value of 0.2 is reached.

EP is the Extreme Price point for the trade made. If long, EP is the highest value reached. If short EP is the lowest value for the trade.

Fig 1: magenta areas are winners, yellow break-even trades and pink areas are losers. As we might expect, in congestion areas the SAR system is a loser.

### PSAR as a trading system

PSAR as a naked system isn’t too good, since trades that go against the trend tends to fail, and all trades fail when the price moves in a tight corrective channel.

Sudden volatility peaks also fool PSAR. See Fig 1, point 18, where an unexpected downward peak reversed the trade in the wrong direction, cutting short a nice trade and transforming it into a big loser.

Fig 2a and 2b show the profit curve for longs and shorts in the EUR/USD 1 hour, for the latest 350 days. As expected, the long-trade graph presents more robustness than the short-trade curve. That is an example of how following the underlying trend grant traders an edge.

Fig 2a equity curve for long trades

Fig. 2b – Equity curve for short trades

Anyway, it’s awesome that using an entry system with absolutely no optimization could deliver such good results as the long side of this PSAR system! That shows, also, the power of a good trailing stop.

The naked system isn’t too good at optimizing profits, as well. A profit target makes it a lot better. Fig 3.a and Fig. 3.b shows the improvement after setting an optimal target for longs and shorts, especially relevant on shorts.

A small change in the AF parameter, lowering down to 0.18, to give profits more room run, and the use of profit targets, raised the percent profitable from 41.4% to 48.1. Max drawdown improved from -4.77% to -3.37%, as well, and the avg_win/avg_loss ratio went from 1.69 to 1.78. It seems not too much, but in combination with the increment in percent winners to 48.1% makes it an effective and robust system.

### PSAR as a trailing stop

In this section, we’ll study the Parabolic Stop and (not) Reverse system, as it might be called, as the exit part of a trading system.

As an exercise, let’s consider a simple moving average crossover. We’ll use the same market segment that we used in the naked PSAR case. For longs, we’ll use an 8-15 SMA crossover, while, for shorts, a 7-23 SMA will be taken, as this makes optimal crossovers for the current market.

Figs. 4a and 4.b show the equity curve for longs and shorts, respectively with just the crossover system, acting on its own.

As we might expect, the long equity curve behaved much better, that’s because the EUR/USD is currently trending up. On the short side equity curve, even when we’ve optimized its parameters, the crossover relationship is lousy.

Fig 5.a and 5.b show the effect of a PSAR trail stop. There’s almost no noticeable positive effect. The oddity that PSAR, as a system, is more profitable than when it acts as trail stop in another system is related to the entry signal. It’s evident that the SAR signal takes place earlier than the SMA crossover, so the PSAR stop isn’t able to extract profits from the entry signal. What it does, if we take a closer look, is it improves a bit the drawdown of the short side.

It may seem that the smart thing to do in a trending market such as the current EUR/USD trend is NOT to trade the short side, at least not mechanically.

But, it’s amazing how targets help us extract profits and reduce risk when trading against the trend. Let’s see the equity curves using long and short targets:

We may note that the long equity curve has a bit less drawdown, but, overall, it doesn’t change much. That was expected because the naked crossovers are very good at following a trend, so not very much may be added using targets.

The use of profit targets is much more noticeable on the short side equity curve. It not only presents a higher final profit, but it’s drawdown practically disappeared, allowing us to better extract profits against the prevailing trend. We have to be cautious, though if we detect a major trend change because we should move those targets accordingly.

### Conclusions

Throughout this article, we tried to understand and analyze the PSAR as, both, an entry-exit system and its behavior as trailing stop to be used with other entry systems. We spotted its strengths and its weaknesses.

In view of the results of our present study, we can conclude that:

• PSAR is a decent system if we combine it with a market filter and profit targets.
• Trailing stops, even sophisticated ones, such as PSAR, doesn’t solve our problem of whipsaws when we trade against the trend.
• By tweaking a bit the AF parameter down to .18 we were able to improve the trend following the nature of PSAR. Consequently, it’s advisable to adapt it to the current market volatility.
• The best tool we own to profit using counter-trend entries is profit targets, optimized to the current swing levels the market is showing.

References:

The definition of the PSAR is taken from New Concepts in technical trading, Welles Wilder.

The studies presented were made using Multicharts 11 trading platform programming capabilities and its results and graphs were taken from its System Performance Report.