#### Why a Trend Follower Uses Portfolio Realised Balance rather than Portfolio Equity for Position Sizing

When it comes to allocating capital to each of our trade bets when trading a systematic diversified trend following portfolio, a question is frequently posed by the practitioner about which is the preferable equity treatment to use as a basis for calculating position size. Is it better to use the Realised Equity Balance of our trading account, or should we use the Current Equity Balance of our trading account, as a basis for calculating position size?

The difference relates to whether we should only refer to the realised balance of our trading account, **which is known with certainty**, or whether we should use the current equity of our trading account which may include current open trades **whose future is currently uncertain**.

Now given our ‘uncertainty about certainty’, you have probably already guessed our preferred treatment. We have no opinion about the ultimate destination of our current active trades, and to presuppose that the current equity is a reflection of what will transpire with certainty can lead us to false assumptions and unnecessarily introduce unwanted risk from excessive leverage into a portfolio.

For example, let us assume that we currently have a significant unrealised equity balance of say $100,000 (which is entirely possible in riding outliers that may last many years) in addition to a closed current realised equity balance of $300,000. Our equity now is therefore $400,000 whereas our Realised Balance is only $300,000. **The difference is material in nature** when calculating the position size of our next trades we take. For example, assuming we risk 0.5% or 50 basis points per trade based on these differing equity levels, then we risk $2,000 per trade using our $400,000 equity or $1,500 per trade using our Realised Balance. The difference in dollar risk allocation to any new trades that we take can be significant in how we introduce unnecessary risk into a portfolio.

The issue surrounds the uncertain destination of all currently active trades that represent the unrealised equity component of our portfolio. There is no guarantee that our unrealised equity would materialise if the trends associated with the outliers that we are currently riding suddenly reverse back to their trailing stop. Under this *very* possible scenario we would find that our position sizing treatment then compromises the risk we add to our portfolio from the most recent trades taken, as their risk contribution calculation is based on far higher levels of equity that turn out to be an illusion. However, based on this illusion of any additional equity being added to our capital, we now find that these new trades are inappropriately scaled in terms of their total risk contribution to the overall portfolio.

Obviously, we prefer the most conservative risk treatment to our method of position sizing treatment which does not add unwanted ‘leverage to our portfolio’ through unduly sized trades. We therefore adopt the stance that it is more prudent to adopt the equity amount represented by the Realised Balance which is known with certainty at the time of calculating the position size of any new trades. This value therefore only comprises the total value of Opening Equity including the summation of all our Closed Trades at the time we calculate the position sizes for any new trades.

This post is now going to dig a bit deeper into the nuts and bolts of this more conservative assumption by providing a comparative example of both approaches made to a sample small portfolio. But before we start our comparison, we should discuss why we do not use more ‘sexy’ alternate position sizing techniques such as the Kelly Criterion for our position sizing method.

You see we avoid any method such as the “Kelly Criterion” or “Optimal f” technique which presupposes that our historical track record is a representative distribution to use to place an ‘optimal bet size’ for each future trade. As you are all aware by now, we are suspect about the conclusions we can draw from a historic record. We view our track record as circumspect and only one possible path of many possible paths that price may have taken in an unfolding complex adaptive system. We feel that this flimsy track record offered by a backtest does not have a sufficient solid footing to allow for any ‘ form of predictive guarantee’ to be placed on position sizing for an uncertain future.

So, we avoid any method that uses data mining as a basis for position size determination and we reduce our choice to a very simple one. Our simple position sizing technique is based on the application of a standard percent amount of risk we wish to make of our Realised Equity Balance. This method allows two broad objectives to be achieved. Firstly, it importantly allows for the** compounding of our wealth** which does most of the heavy lifting of our equity growth over time, and secondly, it ensures that we adopt a **standardised procedure for allocating risk **to all current trades that we wish to take so that each of our risk bets at any moment in time is equal…independent to the return stream that we are considering in our global portfolio.

In this game where we are seeking the fruits of wealth that are delivered by outliers over a large sample size, **it is the normalised small bet size that is our ultimate aim. **We have no idea about which trades are going to turn into outlier trades, but we know that over a large sample size, there is going to be a greater probability that a few of them could be. This is unlike alternative position sizing techniques that infer from the historical trade sequence that current trades need to be overweight or underweight in terms of their possible contribution to the overall portfolio.

If the outliers arise and we can participate in them, then they are of such great magnitude in relation to normal single trade events that their impact dwarfs the impact of the many small bets we have placed while patiently waiting for them. We do not need to scale our individual bets to ‘predict’ their impact on the portfolio. Rather we apply a very simple process that does not adopt any predictive judgement and treats each trade equally. When encountering an outlier, then our simple process capitalises on this market feature.

So having made the reader aware of the reason why we elect to use a method of position sizing that is naively simple for a very good reason, we can move on to comparing the differing methods of either using the Equity Balance or the Realised Balance as the basis for allocating a trade risk % for position sizing purposes.

In this example we are going to apply a classic trend following breakout system to CADJPY over a long-term back test starting in 1972 and going to current day.

So, we start our journey back in the early 70’s and note the following from the equity curves produced.

**Figure 1: Comparison Between Non-Compounded Realised Balance and Equity Balance in the early Years of a Trend Following Portfolio**

In the first year, the results are effectively random with only 9 standard trades under our belt with an absence of any outlier. You will note the **green curve represents our total equity** at any point in time which oscillates above and below our starting equity balance of $50,000. The **blue curve on the other hand represents the realised balance** of all closed trades at any point in time. Now it is line ball which is the more conservative measure to use now. There is simply an insufficient trade sample size to form any conclusions at this point in time about which holds better value in being used for position sizing calculations. Both would be ‘almost’ equal in their impact if applied under compounded treatment.

Now this initial phase of a trend following portfolio where we cannot infer anything about the power of the approach is a typical phenomenon associated with our game which hunts for outliers. We cannot determine if our systems are working as intended, **until we meet the Outlier head on**. You may find that it takes a few years from inception before you meet an outlier, so until this point in time, capital protection is paramount, but you might feel that despite your merciless treatment of all losses that you are getting nowhere with your method in capturing profits. This is where you need enduring faith in your method.

If you wanted to nit-pick about which method to adopt, **at least from Fund inception until the outliers arrive**, then the most prudent course of action would be to adopt a position sizing method that **chooses the lower of either** the Equity Balance or the Realised Balance for position sizing purposes at this early stage in the game.

But now let us move on in our trade sample path and revisit the example where we get to meet our first outlier trade. Let us now see what happens to the comparative result between Equity and Realised Balance.

**Figure 2: Comparison Between Non-Compounded Realised Balance and Equity when Meeting the First Outlier**

In Figure 2 we can now visually observe the impact of meeting the first outlier event in the trade series. The first thing to notice is how the magnitude of the outlier event dwarfs the previous perturbations of the trade history making them effectively ‘random perturbations’. You would need to now use a magnifying glass to observe any material impact on overall equity arising from the trade history preceding this ‘outlier’ event in the record.

Also notice how the Equity curve (in green) rapidly accelerates in advance of the Realised Balance (in blue). This is attributed to the unrealised equity that is exponentially magnified when we successfully ride this outlier event. The Realised Balance lags behind the Equity curve and only catches up when the outlier event has ended (the ‘trend ultimately bends’).

Now this is the classic effect of ‘positive skew’ taking hold in our trade series which we have discussed in a prior Blog post. The impact of this outlier on the trade series is to significantly positively skew the entire trade distribution to reflect the bias of the series that this event has on the trade history.

Let us now continue on with our backtest to reveal how this positive skew takes a lead role in influencing the future performance result.

**Figure 3: Comparison Between Non-Compounded Realised Balance and Equity over a Large Trade Sample**

Now we refer to a long term backtest of Figure 3 with a helicopter view surveying the entire performance record. The first thing to note is that the impact of the outliers do not seem so profound with this zoomed out view….but that is misleading as discussed in our prior Blog dealing with the impact of outliers. It is the outliers themselves that lead to the entire positive performance of the backtest. If we put our magnifying glasses back on and refer to the trade events between Trade 12 and 14 of Figure 3 which signify the material impact of a single outlier, we can now see how the equity “steps” in the Equity curve are entirely the result of outliers. It is the helicopter view itself that makes it appear that the performance results are produced from ‘most trades’, when in fact the performance results are attributed to only a few ‘extreme trade events’.

Now of course the results we have seen in Figures 1 to 3 are the results from a non-compounded treatment (after applying 1 lot per trade to each trade event in the backtest). So let us now review a compounded result using either the Realised Balance or the Equity Balance as our basis for applying position sizing treatment.

In the following Figure we visually compare the performance results of both treatment methods using a small % risk allocation of 0.5% or 50 basis points per trade for either the Equity Balance (in green) or the Realised Balance (in red).

**Figure 4: Comparison Between Compounded Realised Balance and Equity over the entire Backtest History**

We can now understand why the Equity Balance line sits **above** the Realised Balance result. The leading impact of unrealised equity from outliers’ ‘lifts’ the curve and then a compounded treatment magnifies this slight bias over the entire result. The bias attributed to compounding is predominantly due to the lag between relative position sizes adopted by the different methods. In other words, the significant material impact of unrealised equity during an outlier move that might take 2 to 3 years to convert into realised equity (when the outlier ends) is sufficient to accelerate the impact of compounding through the position sizing treatment.

For example, let us refer to Figure 2. You will notice that at the time of trade 13, the equity curve sat at $173,188 in Equity whereas the Realised Balance at the time of Trade 13 was only $97,635. If we applied say 0.5% trade risk to each of these levels, you can now see how position sizing is ‘leveraged by the ‘Position Sizing Treatment’ when compared to the Realised Balance curve.

So, under positive skew, the Equity method of position sizing treatment accelerates leverage applied to the return series leading to greater profits **but this comes at a cost** as ,if we look very closely, we also find that this increased leverage exacerbates the volatility in the return series by virtue of this method of treatment. It turns a fairly smooth non compounded equity curve into a “pogo stick” if the leverage impact on position sizing becomes too extreme.

So here is how we can observe the impact of this applied leverage unfold when things get more volatile.

Have a look at the risk adjusted metrics of the compounded results when we lift the trade risk % applied to position sizing from the prior 0.5% per trade to now 5% per trade.

**Figure 5: Comparison Between Compounded Realised Balance and Equity with Enhanced Leverage at 5% Trade Risk**

You will notice that as we increase our position sizing treatment to the trend following models under both scenarios, that the **Equity Method deteriorates in its MAR ratio under higher leverage**. This is a sign that fundamentally, the Equity method produces an inferior equity curve to the Realised Balance method and is only a symptom associated with ‘window dressing’ associated with leverage from the applied method.

It may be difficult for the reader to understand the fundamental issue surrounding this symptom of exacerbated volatility under leverage, but it becomes exceedingly important when dealing with the consolidated impact of this return stream to the global portfolio. We have only looked at the impact of one market in the portfolio and have clearly seen a material difference in the robustness of each method. Now magnify this with the effect of 100 different markets that might reside in a portfolio. You could imagine that the method itself could lead to swamping the global portfolio with excessive risk from leverage.

If, however we included the return stream arising from the Realised Balance method into our global portfolio, we would see that the Portfolio possessed far lower overall leverage which becomes exceedingly important under compounding due to the nonlinear impact that starts to pervade the portfolio over the longer term. The Equity balance method unduly increases the volatility of the Global portfolio by virtue of the position sizing method itself as opposed to the inherent ‘unlevered’ risk signature that fundamentally lies at the heart of a trend following strategy.

Remember that it is at the **Global Portfolio level where we apply the global leverage lever** to increase or reduce the leverage of the entire portfolio….not at the level of the individual return stream. So, once we have compiled our Diversified Trend Following Portfolio using the Realised Balance method of position sizing, we can then confidently increase the global lever of trade risk % applied to all constituents of the portfolio, with a reduced concern that the impacts of increased leverage is going to fundamentally undermine the risk signature of the entire portfolio leading to a “pogo stick in the long term performance record”.

**Trade well and prosper**

**The ATS mob**