Starting A Strong Equity Curve

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Equity Curve

An equity curve is a graphical representation of the change in the value of a trading account over a time period. An equity curve with a consistently positive slope typically indicates that the trading strategies of the account are profitable, while a negative slope shows that they are generating a negative return.

Breaking Down Equity Curve

Since it presents performance data in graphical form, an equity curve is ideal for providing a quick analysis of how a strategy has performed. Also, multiple equity curves can be used to assess various trading strategies performance and risk.

Equity Curve Calculation

Assume a trader’s starting capital is $25,000 and his or her first trade of 100 shares had an entry price of $50 and an exit price of $75. Commission on the trade is $5

The trade is recorded in a spreadsheet as follows:

Starting capital = starting capital – ((entry price x qty of shares) – commission)

  • $25,000 – (($50 x 100) – $5)
  • $25,000 – ($5,000 – $5)
  • $25,000 – $4,995
  • $20,005

Starting capital = starting capital – ((exit price x qty of shares) – commission)

  • $20,005 + (($75 x 100) – $5)
  • $20,005 + ($7,500 – $5)
  • $20,005 + $7,495
  • $27,500

Repeat the above process for each new trade.

Trading the Equity Curve

All trading strategies produce an equity curve that has winning and losing periods. The visual representation is similar to a stock chart. Traders can apply a moving average, either simple or exponential, to their equity curve and use it as an indicator.

A simple rule could be introduced to stop the strategy trading if the equity curve falls below the moving average. Once the equity curve moves back above the moving average, the trader may want to start trading the strategy again. Trade automation software allows traders to backtest their strategy to see how it would have performed on historical data. This typically includes the ability to generate an equity curve for each strategy used.

Trading signal rules could be strengthened by adding another moving average to the equity curve and waiting for a crossover of the two lines before a decision is made to stop or start the strategy. For example, if the fast moving average crosses above the slow moving average, the trader would begin or recommence their strategy, and if the fast moving average crosses below the slow moving average, they would halt their strategy.

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Trading the Equity Curve

A popular method for determining if a strategy should be kept trading is trading the equity curve. What this means we apply an indicator, say 200-day moving average, to the equity curve. When the equity curve falls below this value we stop trading. We then continue to paper trade the strategy until it gets above the moving average and then trade it live again. The general idea being that you get out when the strategy is doing poorly and get back in when it is doing well. Also once a strategy breaks, this gives you a simple way of getting out of it.

In this example we would stop trading during the blue oval because the equity curve is below the moving average.

Often people will pick an indicator to use and then trade the equity curve live without seeing how the backtested results may have changed. Conceptually I like trading the equity curve because it is potentially good way of getting out of a strategy that is no longer working. But for strategies doing fine but simply going through a drawdown, what kind of effect does it have?

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If one trades using the equity curve, one should test using the equity curve.

The Strategy

We will be using the ConnorsRSI strategy from this post. The test period is from 1/1/2001 to 12/31/2020. The reason for testing so far back is I wanted to give the equity curve signals lots of triggers. Here are the baseline results without trading the equity curve.

The Methods

These are the methods I will test. If you have other ideas, put them in the comments below. If I get enough new ones, I will test them.

  • The curve is above the (50,100,200) day moving average for last 5 days
  • The 50-day moving average is above the 200-day moving average
  • The 20-day moving average is above the 50-day moving average
  • The 50-day moving average is above the 100-day moving average
  • The (6,9,12,18) month return is greater than zero, (ROC)

The two most popular that I have seen are the equity curve being above the 200-day moving average and the 50-day moving average above the 200-day moving average. Which I have tested in the past on my own.

When the equity curve test is not true, we stop taking new trades. Any currently open trades we simply exit as they normally would.

The Results

Click for larger image.

My first observation is that all the stats got worse or stayed about the same, CAR, MDD, Ulcer Index, Sharpe Ratio. Clearly using equity curve trading does not improve your strategy. Using the MA200 has a 29% reduction in CAR.

What I like is that using the 1 year return (ROC252) above zero had only 15% reduction in CAR with about the same MDD. For protection from a broken strategy this could be worthwhile. The 1.5 year rule had eve better results.

The MA50>MA200 rule did a good job. If you used the C>MA50 rule. Your results would have been greatly reduced. This is why we test ideas. You never know which ones will work and which won’t.

Different Set of Parameters

Let us see if this pattern holds up with a different set of parameters. I choose these parameters to have more volatility in the strategy and trying to see if that would make using the equity curve better.

Click for larger image.

Again, we see the one year (ROC252) and the 1.5 year (ROC378) return above zero doing well. After that the returns really drop.

Broken Strategy

I went looking for an old strategy I traded for a few years that I stopped trading because I thought it was broken. Here are the results of that strategy since 2001 without using an equity curve.

Click for larger image.

You can see that starting 2020, it stopped working. Could using the equity curve stopped the bleed those years? Reduce the max drawdown?

Click for larger image.

At first glance this looks good. The ROC252>0 method reduces drawdowns and increases returns. The 2020 to 2020 results are better. What worries me a little is the difference between the 9 month(ROC189>0) and 18 monthROC378>0) methods as compared to the ROC252>0. Then comes the problem of how long do you give it to get back? I still believe the strategy is broken and would not start trading it again.

Spreadsheet

Fill the form below to get the spreadsheet with all the results and additional stats. I also ran with many more parameters in the ConnorsRSI strategy.

Final Thoughts

Clearly using equity curve to stop trading can have a dramatic negative change in your results. This is why you should test with this vs simply saying that is what I will do in live trading. Depending on your method you may reduce your returns by as much as 50%.

I currently don’t use this. But I like what I see for the ROC252>0 method. I must investigate this more. The big advantage of using the equity curve is that it gets you out of a broken strategy and that makes me want to investigate this more.

Backtesting platform used: AmiBroker. Data provider: Norgate Data (referral link)

Trading the Equity Curve – More Ideas

A couple posts ago, I looked at Trading the Equity Curve and found interesting results but nothing that made me decide this works for me. Using the equity curve to decide when to stop trading a strategy just sounds like it should work. But for me it is always about testing. I cannot count how often I thought an idea would help the results only to see them dramatically hurt them. Remember test everything!

I have been thinking about other methods to use to trade the curve. I also wondered maybe it is the strategies I tested against that caused less than stellar results. I am working on a SP500 weekly mean reversions strategy with an average hold of three months. Maybe new methods of trading the curve or the different strategy will give better results.

The Strategy

No rules will be given. Here is the general concept. Buy S&P500 stock when it is a weekly pullback. Of course, there is a market timing filter to keep out of bad markets. Then exit with a profit target or maximum loss. These are the baseline results without trading the equity curve.

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Clearly this strategy has not had problems. Now can we add trading the equity curve and not dramatically change the results for the worse?

The Methods

These are the methods I will test. If you have other ideas, put them in the comments below. If I get enough new ones, I will test them. The first two ideas are similar to what I tried on the previous post. The drawdown idea resonated with me and was curious to see how it would work out. The last rule I decided to simply try combing two rules that did well from last time.

  • The curve is above the (100,200) day moving average
  • The (50,100,200,252) day return is greater than zero, (ROC)
  • The current drawdown is less than (10,15,20,25)%
  • The 252 day return is greater than five percent
  • The 252 return is greater than 0 or the equity is above the 200 day moving average

When the equity curve test is not true, we stop taking new trades. Any currently open trades we simply exit as they normally would. When the equity curve test is true again, we can take trades

Results of Trading the Equity Curve

Two columns need explaining. # trades skip, is the number of trades the strategy did not take because of the equity curve rule. As you can see the top row missed no trades and this is basically the original strategy results. My goal is no more than a 10-15% reduction in CAR. At 15%, this cut off is 15.69, which only one version beats. This version, drawdown 0. It has been 10 days since this has been true and the cutoff value is 50. Our allocation to the trade is

New allocation = Normal Allocation * (1- (days since equity rule true)/(rule cutoff)

New Allocation = (10%)*(1-10/50) = (10%)*(.8) = 8%

Each day the potential size shrinks. When it has been more days the cutoff value, then the strategy stops shrinking the trade and starts skipping trades.

Shrinking Position Sizing Results

How we have several results with CAR greater than 15.69. Off these, I like the RO252>0 and DD 0 method these two years are worse. The DD

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Interesting post. Thanks for sharing.

Here’s one thing that I do that is very simple and works much better for me than actually trading the equity curve per se, but it is based on a very similar concept: recent performance of the strategy potentially gives you information that you can use to improve the strategy.

First of all, I take all trades. The magic is in the position sizing. I look at the profitability of the last two trades. There are four combinations: WW, WL, LW, LL. I adjust the Risk Weight for the next trade between 0.5 and 1.5 for each of the four states, based on backtesting. To keep it simple, I use only three values: 1.0 (the default), 0.5 and 1.5.

I have found, almost across the board, that I can improve my strategy’s performance, as measured by profit factor, by 0.10 to 0.25 points, and I can usually have larger net profitability compared to the baseline strategy. I take all trades, so I don’t have to mess with code that simulates taking a trade and factoring it into a synthesized equity curve.

This is actually a modified version of what I started doing which was just looking at the last trade. What I found for most mean-reverting strategies (and many trend strategies) was that the trade results were also mean-reverting. So typically I would bet 1.5X after a loss and 0.5X after a win. Try this. It really works well, and I have found it to be robust in actual trading across a lot of strategies.

The reason I modified the approach from just looking at the last trade and instead using the last two trades was that I didn’t want to get into a death spiral with a broken strategy that just kept losing. Since I was betting 1.5X after each loss, I didn’t want to get into a situation where I had X losses in a row and was getting killed by exacerbating that with larger than normal sizing each time. So with monitoring the last two trades, I don’t allow the LL combination to be set to a risk weight greater than 1.0, and it would be ideal if it came in at 0.5 in the backtesting. The other three combinations (WW, WL and LW) each can go up to 1.5X, but not the LL combination. For most of my live strategies, I have found that limiting LL to no more than 1.0 has actually improved the profitability and stability of the equity curve.

What you also have to do with this approach is adjust how you use your system metrics because you might have a strategy that backtests with these as the optimal settings:

WW: 0.5
WL: 1.5
LW: 1.5
LL: 1.0

In this case, the sum of the four risk weights doesn’t add up to 4.0, so we are actually risking a little more money overall with these settings than if we were doing 4 X 1.0 for the baseline. So with more money at risk, I usually look at the profit factor rather than the net profit or average trade to gauge how performance compares to the baseline.

While I have not experienced that this approach is too curve-fitted, I’d be curious to hear if your gut/experience or your testing supports that conclusion or contradicts it.

It took me a while to trust this effect that I noticed when testing, but it was so consistent, especially with mean-reverting strategies, that I just went with it and then expanded on it. I like it. It’s pretty simple. It almost feels too simple. That’s probably why I still don’t trust it as much as I’d like, but I trust it enough to incorporate it as a component into all of my 75+ live strategies.

One reason I decided to start working along these lines was that I truly hate the hard decision that always comes with most indicators or trading approaches, and that is how many lookback trades or bars to use as an input parameter. I hate that, so I avoid it if I can. For me, comparing the equity curve to its moving average is just too complicated and too much work to code. I have also found in my testing that approach that the robustness just isn’t there when I try to optimize/test through different parameter settings for the number of trades to look back in the moving average.

Equity Curve Money Management

Amongst a wide variety of money management methods that have evolved over the years, a perennial favorite is the use of the equity curve to guide position sizing. The most common version of this technique is to add to the existing position (whether long or short) depending on the relationship between the current value of the account equity (realized + unrealized PL) and its moving average. According to whether you believe that the equity curve is momentum driven, or mean reverting, you will add to your existing position when the equity move above (or, on the case of mean-reverting, below) the long term moving average.

In this article I want to discuss a slightly different version of equity curve money management, which is mean-reversion oriented. The underlying thesis is that your trading strategy has good profit characteristics, and while it suffers from the occasional, significant drawdown, it can be expected to recover from the downswings. You should therefore be looking to add to your positions when the equity curve moves down sufficiently, in the expectation that the trading strategy will recover. The extra contracts you add to your position during such downturns with increase the overall P&L. To illustrate the approach I am going to use a low frequency strategy on the S&P500 E-mini futures contract (ES). The performance of the strategy is summarized in the chart and table below.

(click to enlarge)

The overall results of the strategy are not bad: at over 87% the win rate is high as, too, is the profit factor of 2.72. And the strategy’s performance, although hardly stellar, has been quite consistent over the period from 1997. That said, most the profits derive from the long side, and the strategy suffers from the occasional large loss, including a significant drawdown of over 18% in 2000.

I am going to use this underlying strategy to illustrate how its performance can be improved with equity curve money management (ECMM). To start, we calculate a simple moving average of the equity curve, as before. However, in this variation of ECMM we then calculate offsets that are a number of standard deviations above or below the moving average. Typical default values for the moving average length might be 50 bars for a daily series, while we might use, say, +/- 2 S.D. above and below the moving average as our trigger levels. The idea is that we add to our position when the equity curve falls below the lower threshold level (moving average – 2x S.D) and then crosses back above it again. This is similar to how a trader might use Bollinger bands, or an oscillator like Stochastics. The chart below illustrates the procedure.

The lower and upper trigger levels are shown as green and yellow lines in the chart indicator (note that in this variant of ECMM we only use the lower level to add to positions).

After a significant drawdown early in October the equity curve begins to revert and crosses back over the lower threshold level on Oct 21. Applying our ECMM rule, we add to our existing long position the next day, Oct 22 (the same procedure would apply to adding to short positions). As you can see, our money management trade worked out very well, since the EC did continue to mean-revert as expected. We closed the trade on Nov 11, for a substantial, additional profit.

Now we have illustrated the procedure, let’s being to explore the potential of the ECMM idea in more detail. The first important point to understand is what ECMM will NOT do: i.e. reduce risk. Like all money management techniques that are designed to pyramid into positions, ECMM will INCREASE risk, leading to higher drawdowns. But ECMM should also increase profits: so the question is whether the potential for greater profits is sufficient to offset the risk of greater losses. If not, then there is a simpler alternative method of increasing profits: simply increase position size! It follows that one of the key metrics of performance to focus on in evaluating this technique is the ratio of PL to drawdown. Let’s look at some examples for our baseline strategy.

The chart shows the effect of adding a specified number of contracts to our existing long or short position whenever the equity curve crosses back above the lower trigger level, which in this case is set at 2xS.D below the 50-day moving average of the equity curve. As expected, the overall strategy P&L increases linearly in line with the number of additional contracts traded, from a base level of around $170,000, to over $500,000 when we trade an additional five contracts. So, too, does the profit factor rise from around 2.7 to around 5.0. That’s where the good news ends. Because, just as the strategy PL increases, so too does the size of the maximum drawdown, from $(18,500) in the baseline case to over $(83,000) when we trade an additional five contracts. In fact, the PL/Drawdown ratio declines from over 9.0 in the baseline case, to only 6.0 when we trade the ECMM strategy with five additional contracts. In terms of risk and reward, as measured by the PL/Drawdown ratio, we would be better off simply trading the baseline strategy: if we traded 3 contracts instead of 1 contract, then without any money management at all we would have made total profits of around $500,000, but with a drawdown of just over $(56,000). This is the same profit as produced with the 5-contract ECMM strategy, but with a drawdown that is $23,000 smaller.

How does this arise? Quite simply, our ECMM money management trades as not all automatic winners from the get-go (even if they eventually produce profits. In some cases, having crossed above the lower threshold level, the equity curve will subsequently cross back down below it again. As it does so, the additional contracts we have traded are now adding to the strategy drawdown.

This suggests that there might be a better alternative. How about if, instead of doing a single ECMM trade for, say, 5 additional contracts, we instead add an additional contract each time the equity curve crosses above the lower threshold level. Sure, we might give up some extra profits, but our drawdown should be lower, right? That turns out to be true. Unfortunately, however, profits are impacted more than the drawdown, so as a result the PL/Drawdown ratio shows the same precipitous decline:

Once again, we would be better off trading the baseline strategy in larger size, rather than using ECMM, even when we scale into the additional contracts.

What else can we try? An obvious trick to try is tweaking the threshold levels. We can do this by adjusting the # of standard deviations at which to set the trigger levels. Intuitively, it might seem that the obvious thing to do is set the threshold levels further apart, so that ECMM trades are triggered less frequently. But, as it turns out, this does not produce the desired effect. Instead, counter-intuitively, we have to set the threshold levels CLOSER to the moving average, at only +/-1x S.D. The results are shown in the chart below.

With these settings, the strategy PL and profit factor increase linearly, as before. So too does the strategy drawdown, but at a slower rate. As a consequence, the PL/Drawdown ration actually RISES, before declining at a moderate pace. Looking at the chart, it is apparent the optimal setting is trading two additional contracts with a threshold setting one standard deviation below the 50-day moving average of the equity curve.

Below are the overall results. With these settings the baseline strategy plus ECMM produces total profits of $334,000, a profit factor of 4.27 and a drawdown of $(35,212), making the PL/Drawdown ratio 9.50. Producing the same rate of profits using the baseline strategy alone would require us to trade two contracts, producing a slightly higher drawdown of almost $(37,000). So our ECMM strategy has increased overall profitability on a risk-adjusted basis.

(Click to enlarge)

CONCLUSION

It is certainly feasible to improve not only the overall profitability of a strategy using equity curve money management, but also the risk-adjusted performance. Whether ECMM will have much effect depends on the specifics of the underlying strategy, and the level at which the ECMM parameters are set to. These can be optimized on a walk-forward basis.

EASYLANGUAGE CODE

MALen(50),
SDMultiple(2),
PositionMult(1),
ExitAtBreakeven(False);

Var:
OpenEquity(0),
EquitySD(0),
EquityMA(0),
UpperEquityLevel(0),
LowerEquityLevel(0),
NShares(0);

OpenEquity=OpenPositionProfit+NetProfit;a
EquitySD=stddev(OpenEquity,MALen);
EquityMA=average(OpenEquity,MALen);
UpperEquityLevel=EquityMA + SDMultiple*EquitySD;
LowerEquityLevel=EquityMA-SDMultiple*EquitySD;
NShares=CurrentContracts*PositionMult;
If OpenEquity crosses above LowerEquityLevel then begin
If Marketposition > 0 then begin
Buy(“EnMark-LMM”) NShares shares next bar at market;
end;
If Marketposition 1 then begin
Sell Short (“ExBE-LMM”) (Currentcontracts-1) shares next bar at market;
end;
If Marketposition

Trading the Equity Curves ☆

Abstract

Nowadays, financial markets are no longer only for “big players”. Also small investors and traders have strong presence. Each of them uses their own strategy and therefore there are countless strategies. Each trading strategy has an equity curve, which gives us very important inside of how good or bad this strategy is. Aim of this paper is to look at the equity curve gained from the one specific trading strategy and find out, if it is possible to improve it (improve the final return, recovery factor, sharp ratio etc.) by applying some most used technical indicators on it. In other words, will we gain better performance by trading the equity curve itself? The used strategy is built on the well known idea of trading the divergences and the rules are applied on various currency pairs. In the results there is comparison of raw equity curves (unmanaged) and managed equity curves of this trading strategy.

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Selection and peer-review under responsibility of Asociatia Grupul Roman de Cercetari in Finante Corporatiste.

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