Evaluating the quality of your trading signals correctly.

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HOW GOOD ARE YOUR SIGNALS?

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HOW GOOD ARE YOUR SIGNALS? Evaluating the quality of your trading signals correctly.

Every algorithmic trading strategy has basically two dimensions: Trading signals and money allocation. The first one regards the type of orders the system generates and the time those orders should be taken whereas the second one regards the amount of the trading instrument to trade.

Most of the times the testing and evaluation of a system is performed by examining those dimensions together. If you want to know your system inside out and under-stand the reason behind its profitability (or its failure) you must study the system’s dimensions not only in unison but also separately. This Trading Tips issue focuses on constructing and gauging the performance curve of a system‘s trading signals in-and-of themselves thus completely disregarding the system‘s money allocation dimension.

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USUAL EQUITY CURVES MAKE NO DIFFERENCE BETWEEN SIGNAL AND MONEY MANAGEMENT.

There are two popular equity curves to evaluate the performance of a trading strategy. I call them CumulativeProfit and MultFracProfit. The CumulativeProfit assumes that you trade one unit (or a constant number of units) of the trading instrument for every signal whereas the MultFracProfit curve assumes that you reinvest the profits of each trade.

CUMULATIVEPROFIT Regarding the CumulativeProfit, if you trade the same number of units of the trading instrument every time a signal is generated then you invest much more money when the price of the trading instrument is high than when its price is low.

b Example: If you buy 100 shares of a stock each time a buy signal emerges then if the price of the stock is $30 you invest $3,000 in the signal whereas if the price of the stock is $3 you invest $300 in that signal.

b Result: The CumulativeProfit fails to eliminate the money allocation dimension of the system.

MULTFRACPROFIT Regarding the MultFracProfit curve, the involvement of money allocation is more obvi-ous since you indirectly assume that you start with an initial capital and you reinvest the profits of previous trades.

b Result: In effect you will put much more money in signals that follow a stream of profitable trades and you put less money in signals that follow a stream of losing trades.

CONCLUSION: In short, the CumulativeProfit and MultFracProfit curves are incapable of isolating and gauging the performance of the system’s signals dimension from the system’s money management one.

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CumulativeProfit%n= a1 + a2 +···+an where αi i i is the profit from trade i based on the notional investment of $1

THE SOLUTION:APPRAISING THE SIGNALS OF USING THE CUMULATIVEPROFIT% CURVE.

An effective way to evaluate the performance of a system’s signals themselves is by what I call the CumulativeProfit% curve. This curve is constructed by practically assuming that you always invest a notional 1$ in each and every trade proposed by the trading signals.

Suppose that you have a buy signal at price Pbuy and a later sell signal at price Psell. The profit you would have got assuming you followed the signal by in-vesting $1 is (Psell − Pbuy)/Pbuy. If the sell signal was first, the profit would be (Psell − Pbuy)/Psell.

The CumulativeProfit% curve is constructed using the cumulative sum of such profits so the value of CumulativeProfit% after the completion of trade n (where n≥1) is:

This formula gives the values of CumulativeProfit% at the closing of each position. The values of CumulativeProfit% between the actual closings of positions are defined assuming that you close them prematurely. Once you have constructed the CumulativeProfit% curve you can plot it below the trading instrument‘s chart and have a direct visual comprehension of how your signals performed historically.

Thus you get …

b A clear overview of the historical performance and b A number of gauges to quantify the risk and reward profile

… of all of your trading signals.

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IMPLEMENTATION IN TRADESIGNAL WITH EQUILLA.

Tradesignal’s versatile formula language Equilla offers the opportunity to plot the Cu-mulativeProfit% curve and compute gauges which appraise the signals of a strategy.

You can find the full code in our workspace which can be downloaded on our website.

DOWNLOAD WORKSPACE FOR TRADESIGNAL HERE:

Try the new workspace which is provided here for both Thomson Reuters and Bloomberg data. More workspaces can be downloaded at

www.intalus.com/workspaces.

TIP: Open the workspace, save the code and then drag and drop it in a chart which has a strategy attached to it.

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6 RISK AND REWARDS GAUGES.

Moreover, in the statistics tab of the performance report you will find six gau-ges which describe the risk and reward profile of the signals as implied by the CumulativeProfit% curve. These are:

HISTORICAL EDGE OF THE SIGNALS (CPP_Edge)This is simply the last value of CumulativeProfit% curve divided by the number of trades. It shows you the historical edge you are given by the signals. The higher the edge, the better the signals.

b Example: If the last value of CumulativeProfit% is say 5 and the number of trades is 100 then the edge of the signals is 0.05 (or 5%). This means that – on average – the signals gave you a 5% edge every time you followed them. Assuming you have used a long history of the trading instrument in various market conditions and the signals generated many trades this gives you an estimate of what you can expect to gain by following the signals. An edge of 0.05 (or 5%) means that if you always invest 100 000 Euro in the trades generated by the signals, you expect to get (on average) 5 000 Euro from each one of them.

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MAXIMUM DRAWDOWN (CPP_MaxDD)The Maximum Drawdown (or MaxDD for short) is the largest peak-to-trough distance in the CumulativeProfit% curve. The lower the MaxDD, the better the signals. Again, assuming that you have used a long history of the trading instrument and the signals generated many trades the MaxDD practically shows you the least you should expect to lose at some point following the signals.

b Example: If for example MaxDD is 5 then this means that if you planned to invest 100 000 Euro in the trades generated by the signals and you started following the signals at the worst possible time in the CumulativeProfit% curve then you should have 600 000 Euro ready because you would have to experience a loss of 500 000 Euro and you would also need an extra 100 000 to follow the next signal.

PROFIT TO MAXDD RATIO (CPP_ProfitToMaxDD)This is simply the last value of CumulativeProfit% divided by the MaxDD. The higher this ratio, the better the signals.

LONGEST DRAWDOWN (CPP_MaxRecoveryBars)This is the highest number of consecutive bars the underwater equity of Cumulati-veProfit% was below zero. The smaller this number, the better the signals.

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𝑆𝑆𝑆𝑆𝑆𝑆𝑘𝑘(𝑅𝑅𝑅𝑅𝑅𝑅����������������� )𝑆𝑆𝑆𝑆𝑆𝑆𝑘𝑘(𝑆𝑆𝑅𝑅𝑆𝑆𝑅𝑅𝑆𝑆(𝑅𝑅𝑅𝑅𝑅𝑅))

k = SharpeAndSortinoPeriod

𝑆𝑆𝑆𝑆𝑆𝑆𝑘𝑘() = simple moving average of k-bars

Ret = difference between the value of the CumulativeProfit% and its value k bars ago.

The ( � ) accent refers to the mean and the StDev() refers to the standard deviation.

More precisely, to calculate the values of 𝑅𝑅𝑅𝑅𝑅𝑅����������������� and 𝑆𝑆𝑅𝑅𝑆𝑆𝑅𝑅𝑆𝑆(𝑅𝑅𝑅𝑅𝑅𝑅) for the N-th bar loaded in a chart (call that bar B) we define 𝑛𝑛 to be equal to the integral part of the fraction 𝑁𝑁

𝑘𝑘 so 𝑛𝑛simply shows how many k's fit inside 𝑁𝑁 (if for example N=3000 and k=21 then 3000/21=142.85 so n=142).

𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 = value of 𝑅𝑅𝑅𝑅𝑅𝑅 at the bar which is (𝑖𝑖 − 1) ∙ 𝑘𝑘 bars behind B.

Then, the values of 𝑅𝑅𝑅𝑅𝑅𝑅����������������� and 𝑆𝑆𝑅𝑅𝑆𝑆𝑅𝑅𝑆𝑆(𝑅𝑅𝑅𝑅𝑅𝑅) for the bar B are:

𝑅𝑅𝑅𝑅𝑅𝑅����������������� =∑ 𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖𝑛𝑛𝑖𝑖=1𝑛𝑛

and

𝑆𝑆𝑅𝑅𝑆𝑆𝑅𝑅𝑆𝑆(𝑅𝑅𝑅𝑅𝑅𝑅) = �∑�∑� [𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 − 𝑅𝑅𝑅𝑅𝑅𝑅����������������� ]�𝑛𝑛𝑖𝑖=1

𝑛𝑛

A MODIFIED SHARPE RATIO (CPP_ModSharpe)This is a modified version of the classic Sharpe Ratio so the higher it is, the better the signals. It requires a period parameter (namely: SharpeAndSortinoPeriod) which is a positive integer and can be changed via the Indicator properties. The default value for the SharpeAndSortinoPeriod is 21¹. The short formula for the modified Sharpe Ratio is:

¹ Depending on the chart you apply the CumulativeProfit% indicator you can change the SharpeAndSortinoPeriod parameter

(that is, the k) to represent annual, monthly, weekly or whatever period you wish. For example, if you are interested in the annual

Sharpe in a daily chart then you should set the parameter to 252 since a year has approximately 252 trading days. If the chart is

weekly then you should set this parameter to 52 (a year has approximately 52 weeks).

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𝑆𝑆𝑆𝑆𝑆𝑆𝑘𝑘(𝑅𝑅𝑅𝑅𝑅𝑅����������������� )𝑆𝑆𝑆𝑆𝑆𝑆𝑘𝑘(𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑅𝑅𝐷𝐷(𝑅𝑅𝑅𝑅𝑅𝑅))

where DownDev(Ret) is defined as:

𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝐷𝑅𝑅𝐷𝐷(𝑅𝑅𝑅𝑅𝑅𝑅) = �∑�∑� [min (𝑅𝑅𝑅𝑅𝑅𝑅𝑖𝑖 − 𝑅𝑅𝑅𝑅𝑅𝑅����������������� , 0)]�𝑛𝑛𝑖𝑖=1

𝐷𝐷

A MODIFIED SORTINO TYPE RATIO (CPP_ModSortino)This is a modified version of the Sortino Ratio so the higher it is, the better the signals. Like the modified Sharpe Ratio it depends on the SharpeAndSortinoPeriod parameter. Both the modified Sortino and the modified Sharpe ratios are reward/risk metrics. Their difference is that the modified Sharpe regards risk as both upward and downward volatility of performance whereas Sortino regards risk as only downward volatility of performance (see our Trading Tips 16: www.intalus.com/trading-tips).

PRACTICAL EXAMPLE:DEFAULT EQUITY CURVE VERSUS CUMULATIVEPROFIT% CURVE.

Now we come to a practical example. Figure 1 shows (next page) the Akamai share on a daily chart with the trading strategy “Bollinger Band Entry” applied. In addition to the conventional equity curve (middle) the CumulativeProfit% curve is displayed (bottom). The SharpeAndSortinoPeriod parameter is 21 and the ShowIndividualStatsInPortfolio parameter is set to ‘False’.

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Figure 1: Default equity curve (orange) vs. CumulativeProfit% equity curve (blue)In this example the “Bollinger Band Entry” strategy was applied in Akamai shares. Due to the low price levels after the crash in the years 2000 to 2002 the default equity curve (middle subchart) – despite the sharp increase in 2003 – shows little change. The CumulativeProfit% equity curve (lower subchart) delivers a realistic picture of signal quality.

When the price of the trading instrument has gone from very low levels to very high ones (or vise-versa) the differences in the Tradesignal‘s default equity curve and the CumulativeProfit% curve are noticeable:

b The price of Akamai Technologies was close to $300 near the beginning of 2000 and ended up close to $0.5 during the fall of 2002.

b The default equity curve (middle sub chart) calculates profits assuming buying/selling the same number of shares all the time. Due to the low absolute price level there is very little change despite the strong upmove during 2003 The equity curve downgrades the performance of the signals after 2002.

b The CumulativeProfit% on the other hand clearly depicts that the signals of the strategy had a superb performance in 2003. The equity curve now reflects the real quality of the trading signals.

CONCLUSION: The default equity curve shows the combined performance of the trading strategy, while the CumulativeProfit% curve reflects the performance of the trading signals themselves.

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Figure 2: CumulativeProfit% in Performance Report All metrics of the CumulativeProfit% Indicator are displayed in the performance report.

PRACTICAL EXAMPLE:RISK RETURN GAUGES APPLIED TO A PORTFOLIO.

Besides the SharpeAndSortinoPeriod and the ShowEquityUnderWater parameters, the CumulativeProfit% indicator has one more input parameter which is of True/False type (namely: ShowIndividualStatsInPortfolio). It enables you to activate or deactivate the display of all key figures, which are reflected in the performance report. They each start with the abbreviation “CPP_”.

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Figure 3: CumulativeProfit% Indicator with all gauges (equity portfolio) In this example the CumulativeProfit% indicator and all other gauges are calculated on the basis of the strategy “Bollinger Band Entry” for 10 shares from the Nasdaq Composite. For this purpose, the input ShowIndividualStatsInPortfolio needs to be set to “Yes” in the properties window.

If you want calculate the values of the six key figures and compare them for several securities, please proceed as follows:

b Create a portfolio with several securities b Apply a trading strategy of your choice b Insert the CumulativeProfit% indicator b Set the input ShowIndividualStatsInPortfolio to “Yes”

All key figures are then displayed in separate columns in the portfolio table for every symbol (see Figure 3).

This will give you a quick and convenient overview of the risk return spectrum of the chosen trading strategy on individual stocks.

That’s it for today. Take care, take profit and “Eις το επανιδείν”.Giorgos Siligardos

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EVALUATE THE QUALITY OF YOUR TRADING SIGNALWITH THE CUMULATIVEPROFIT% CURVE.

DOWNLOAD WORKSPACE FOR TRADESIGNAL HERE:

Try the new workspace which is provided here for both Thomson Reuters and Bloomberg data. More workspaces can be downloaded at

www.intalus.com/workspaces.

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© 2015 Intalus – www.intalus.com

Distribution allowed under a Creative Commons Attribution-Noncommercial license:

http://creativecommons.org/licenses/by-nc/3.0/

Tradesignal® is a registered trademark of Tradesignal GmbH. Unauthorized use or misuse is specifically prohibited.

All other protected brands and trademarks mentioned in this document conform, without restriction, to the provisions of applicable

trademark law and the copyrights of the respective registered owners.

www.intalus.com/vimeo www.intalus.com/youtube

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ABOUT THE AUTHOR.Giorgos Siligardos, PhD

Giorgos Siligardos holds a PhD in Mathematics and a Market Maker certificate on derivatives from the Athens Exchange. He is a financial software developer and co- author of academic books on finance.Giorgos has also been a research and teaching fellow to the University of Crete as well as a teaching fellow to the Department of Finance and Insurance at the Technolo-gical Educational Institute of Crete for many years teaching math and financial courses and supervising Masters dissertations.

You may contact Giorgos atgiorgos.siligardos@intalus.com

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Part 1: The Toolbox for Traders.

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CLEAR STRATEGIES NOT GUT REACTIONS.Act smart and always use objective and clear signals.Tradesignal. Überlegen handeln. Made in Germany.

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