Content uploaded by Andreas A Aigner
Author content
All content in this area was uploaded by Andreas A Aigner on Jun 15, 2020
Content may be subject to copyright.
15 June 2020
1/13
TREND TRADING
EXPLAINED
By Dr Andreas A. Aigner & Walter Schrabmair
Here we present a detailed summary for beginners of trend trading: How to use & When to use.
There is a plethora of different methodologies to trade stocks. Many are published in academic journals,
books, magazines, websites and online social trading platforms. The methods range from statistical models,
machine learning, artificial intelligence, to technical and fundamental analysis to name a few. We won’t
even attempt to make a comprehensive list. Amongst these methods are also mechanical trading systems,
which don’t have as many assumptions behind them. They simply follow an iterative rule that is determined
only by the price itself. Trend trading belongs to this category. The primary assumption that it makes is that
the stock stays in the trend it was in, unless the stock price exhibited such unusual behavior that it warrants
a trend reversal. In a previous paper we have gone over “The Philosophy of Trend Following” where you
can take an even deeper look at it [1].
Here we look at one particular method that we have found successfully used by several traders online and
by a number of hedge funds globally. It is really quite simple but still many explanations on how to do it
lack a comprehensive view at best or have errors at worst, not at least due to the unedited and unrevised
version in the textbook by the inventor of the method himself [2].
SECTION 1 – HOW TO USE
The trend trading method we will describe here is the ‘Volatility Method’ from Wilder’s book “New
Concepts in Technical Trading Systems” [2]. It essentially is simply a pair of conditions for holding a long
or short position
𝐿𝑜𝑛𝑔
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛
:
𝑃𝑟𝑖𝑐𝑒
>
𝑆𝐴𝑅
𝑆
ℎ
𝑜𝑟𝑡
𝑃𝑜𝑠𝑖𝑡𝑖𝑜𝑛
:
𝑃𝑟𝑖𝑐𝑒
<
𝑆𝐴𝑅
(Eq
1
)
The SAR stands for the “StopAndReverse” price and as long as either of these two conditions is valid the
position remains unaltered. Note that this level is always in the opposite side of your position. Meaning if
you are long you don’t want the price to fall below this SAR. If you are short you don’t want the price to
rise above this level. It essentially is a trailing stoploss price where you cut and reverse your position.
This SAR price is not a fixed price, instead it is a dynamically calculated value based on the price history
before. It is calculated by the following formula
𝑆𝐴𝑅
=
𝑆𝐼𝐶
−
𝐹𝑙𝑖𝑝
∗
𝐴𝐶𝐶
∗
𝐴𝑇𝑅
(Eq 2 )
Where SIC denotes the “Significant Close”, ACC is the “acceleration factor” and ATR is the “Average True
Range”. 𝐹𝑙𝑖𝑝 is simply a value that denotes the current trading direction being +1 when long and 1 when
short. Any kind of stoploss has this form and we could generalize this simply to write
A. Aigner & W. Schrabmair “Trend Trading Explained” 15 June 2020
2/4
𝑆𝐴𝑅
=
𝑆𝐼𝐶
±
Φ
(Eq
3
)
Where 𝑆𝐼𝐶 is some kind of reference price and Φ can be thought of as a margin of safety. This margin of
safety could be any measure but it makes sense to use some kind of measure of a trading range where
anything below this range is regarded as regular trading behavior and ignored. A measure of volatility is
one such measure and Wilder uses the Average True Range to calculate this measure. He uses a constant
as a multiplier ACC as a factor of this Average True Range. The Average True Range of Wilder [2] is
defined by
𝐴𝑇𝑅
=
𝑇𝑅
7
+
6
7
𝐴𝑇𝑅
(Eq
4
)
Where we TR is the Total Range which is defined as the maximum of three differences
𝑇𝑅
=
𝑀𝑎𝑥
𝑜𝑓

𝐻𝑖𝑔
ℎ
−
𝐿𝑜𝑤


𝐻𝑖𝑔
ℎ
−
𝑃𝑟𝑒𝑣𝐶𝑙𝑜𝑠𝑒


𝐿𝑜𝑤
−
𝑃𝑟𝑒𝑣𝐶𝑙𝑜𝑠𝑒

(Eq
5
)
The ATR in fact is calculated iteratively using the current Total Range and the previous value 𝐴𝑇𝑅 and
can be written like this
𝐴𝑇𝑅
=
𝛼
𝑇𝑅
+
(
1
−
𝛼
)
𝐴𝑇𝑅
(Eq
6
)
where 𝛼=1/7 is a smoothing factor. This recursive method is called an ‘exponential moving average’
and is a form of a simple moving average which has an infinite amount of terms but where the sum of the
weights do not sum up to 100% but instead approach 81.6% as a limit with the closest values having the
biggest weights and decreasing exponentially with distance/time going back from the latest value. This is
also known as a fixedpoint iteration or ‘relaxation’ since any linear equation 𝐴 𝑥= 𝑏 can be solved using
a fixed point iteration. For example, to highlight its behavior, consider a single impulse in time. An
exponential moving average would decay this single impulse exponentially in time. So the decay would be
exponential and the signal would have a corresponding halflife of 𝜖.
The last variable missing from this mechanical trading algorithm is the 𝑆𝐼𝐶, ‘Significant Close’. It is
defined as
𝑆𝐼𝐶
=
max
(
𝑆𝐼𝐶
,
𝑃𝑟𝑖𝑐𝑒
)
𝑖𝑓
𝑙𝑜𝑛𝑔
min
(
𝑆𝐼𝐶
,
𝑃𝑟𝑖𝑐𝑒
)
𝑖𝑓
𝑠
ℎ
𝑜𝑟𝑡
(Eq
7
)
What does this SIC represent? It is the highest close since the start of the current trend when the
algorithm is long and it is the lowest close since the start of the trend when the algorithm is short. It is
trailing the stock price and maximizing the profit of the current trend. It is preventing you giving you back
the gains you have already made, resetting closer and closer to the maximum profit for you. This is only
modified by the ‘margin of safety’ defined by Φ in Equations (2) and (3). The value of Φ scales with the
ATR as well as the ‘acceleration factor’ ACC which Wilder suggests using a value between 2.1 and 3.2. This
parameter ACC is actually a tuning parameter, set to a value where historically you were able to maximize
returns. The way to calculate this tuning parameter is to run models across thousands of stock prices and
look at the average profit and loss and determine where the maximum average profit was reached [3].
A. Aigner & W. Schrabmair “Trend Trading Explained” 15 June 2020
3/4
SECTION 2 – WHEN TO USE
An important criterion for the success of this trend following method is quite obviously the strength of
the trend. If there is no trend, if the stock has always the same price or hardly moves at all you won’t
benefit from this trend following strategy. You are looking to employ this method when there is a good
trend prevalent. How do you measure such a trend? In the paper “Power assisted Trend Following” [3]
we have derived a measure for the power of the trend which is called the Power Ratio and represents a
multiple of the current ATR. A sufficient multiple of the ATR is going to maximize the profit of this
strategy as was shown in this paper’s results. In the paper “The Power of Growth Stocks” [4] we have
looked a combination of Benjamin Graham’s formula for growth stocks and the use of the power ratio to
show also that you can optimize the trend following profit even further by selecting growth stocks which
we know are strong candidates for continued trending behavior. There are various other methods one
can think of to measure the trending behavior of a stock, for instance the annual stocks performance i.e.
the momentum or probabilities of being in a one directional trend. One further method to determine the
trending behavior is simply to look at the profit it is making in the past. If a stock has yielded consistent
profits in the past it is a fair assumption, it might continue to do so in the future. But as is usually
mentioned: performance in the past is never an indicator or guarantee of future performance, so it
depends on the trader’s risk tolerance and requires strict money management to adhere to, so that by
spreading out the risk your gains on your winners will outdo the losses you might have on your losers. It
only takes for 12 names to successfully stay in a trend to make outlandish gains on these stocks which
dwarf any losses you might have on an inconsistent trend.
Biography: Dr Andreas A. Aigner has a PhD in Mathematics from Monash University, Melbourne, Australia,
where he was born and studied. He spent a number of years in Research for various UK universities and
worked almost 10 years for Morgan Stanley in Controlling, Trading & Pricing for the Exotic Derivatives desk
in Hong Kong. He is now engaged fulltime in research and is building a signaling automaton (tradeflags.de)
together with his longtime friend and associate Walter Schrabmair, who works at the Medical University of
Graz and the Technical University of Graz in various research roles and as a computer whiz. Their contact
emails are andreas@tradeflags.at and walter@tradeflags.at
1. Andreas A. Aigner and W. Schrabmair, The Philosophy of Trend Following. 2020.
2. Wilder, J.W., New concepts in technical trading systems. 1978, Greensboro, N.C.: Trend
Research. 141 p.
3. Aigner, A. and W. Schrabmair, Power Assisted Trend Following. 2020: ResearchGate.
4. Aigner, A. and W. Schabmair, The Power of Growth Stocks, in Technical Analaysis of Stocks &
Commodities. 2020, Technical Analysis Inc. : USA. p. 813.