A Specific Trading Question That is Actually Wide Ranging

This article originally appeared in the Ask Jack column on Bidnessetc.com. Each article answered a question submitted by readers.

Note to Readers: If you don’t quite understand the following question or think it doesn’t pertain to you, read on anyway. The question will become clarified in the course of the answer, and, if you are a trader, you should find the answer quite relevant.

I am confused on how one is to implement position size rebalancing based on changing volatility. For example, if I have 5 positions open and each were sized on a 1% of equity at risk and 100-day ATR times a factor of 3; how would I actually rebalance?

Your question is an interesting one because while it outwardly appears to be quite specific, it touches on four essential elements of practical risk management:

1. Where to place protective stops.
2. Equity risk per trade.
3. How to adjust trading for changing volatility conditions.
4. Portfolio risk effects.

I will discuss each of these elements and then will use this information to specifically answer your question.

Where to Place Protective Stops

I can’t do any better in answering this question than quoting a segment of my Hedge Fund Market Wizards interview with Colm O’Shea, the manager of COMAC Capital, a London-based global macro hedge fund. I quote this section in its entirety because it is filled with what I consider extremely valuable advice.

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Do you ever have a problem getting out of a losing trade?

I start by deciding where the market would have to go for me to be wrong. That’s where I place my stop. That means that it’s not difficult for me to get out of a position if the market goes there. The most common money management error I see is people setting stop losses that are really pain thresholds. When the market reaches their stop, they don’t really want to get out because they still think they are right. They will get out because their stop is hit, and they are disciplined. But very soon afterwards, they will want to get back in because they don’t think they were wrong. That’s how day traders in NASDAQ in 2000 and 2001 lost a ton of money. They were disciplined, so they would close out their positions by the end of the day. But they kept on repeating the same trading mistake. They failed to recognize that they were completely wrong because we were in a bear market.

So the disciplined use of stops that are set too close could lead to the proverbial death by 1000 cuts.

Yes, and that is why I think trading books that provide specific rules can be quite dangerous. They can lead to the illusion that you are being controlled and disciplined. And it is true that you are restricting yourself from a single catastrophic loss, but it doesn’t prevent repeated losses on the same idea.

Sometimes a close stop may be appropriate. If it is a short-term technical idea, and you don’t like the trade anymore if the market breaks a level, then getting out on a close stop is fine. If, however, it is a fundamental idea that needs a long time to play out, then a short-term stop makes absolutely no sense. If your entry and exit strategy is out of sync with the reason you like to trade, then you don’t have an internally consistent money management plan, which means it will fail.

So, you need to decide where you are wrong before you determine the stop point.

First, you decide where you are wrong. That determines where the stop level should be. Then you work out how much you are willing to lose on the idea. Last, you divide the amount you’re willing to lose by the per-contract loss to the stop point, and that determines your position size. The most common error I see is that people do it backwards. They start with position size. Then they know their pain threshold, and that determines where they place their stop.

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I can’t improve on O’Shea’s advice on how to place stops, which can be summarized as a three-step process:

1. Decide where you are wrong. This is your stop point.
2. Decide how much you are willing to lose on the trade idea.
3. Divide the amount you are willing to risk by the per contract (or per share) loss to the stop to determine the position size.

Equity Risk Per Trade

How much to risk per trade is ultimately a personal choice. What may seem conservative to one trader can be wildly aggressive to another or vice versa. Just as there is no single correct slope choice for a skier—a novice skier might find a green circle trail challenging, while an expert skier could consider a single black diamond trail overly tame—there is no single correct risk choice per trade. The correct choice can vary widely, and each trader must determine what risk level per trade is personally appropriate.

Having said this, most traders tend to choose a risk level that is too high. Bruce Kovner, the founder of Caxton Associates and one of the best traders of our time, believes most novice traders trade too large. His advice to traders is, “Undertrade, undertrade, undertrade….Whatever you think your position ought to be, cut it at least in half. My experience with novice traders is that that they trade three to five times to big. They are taking 5 to 10 percent risks on a trade when they should be taking 1 to 2 percent risks.”

No trader ever went broke by choosing a risk per trade level that is too low, but many traders go broke choosing risk levels that are too high. In fact, mathematically, choosing a risk point that is too high can reduce total profits even if your method has a positive edge for every trade. (Readers interested in this last point can research the Kelly Criterion, with the caveat that the optimal bet size indicated by the Kelly Criterion will represent excessive risk in all trading circumstances—a tangent too lengthy to explore in this article.) And, there is even a risk-per-trade point where you will mathematically guarantee ruin of the account, again, even if you have a positive edge in all your trades.

Personally speaking, when in my first Market Wizards book some traders, such as Larry Hite, mentioned their rule of never risking more than 1% on a trade, that amount sounded conservative to me. Now, I consider 1% per trade extremely aggressive and find myself typically risking only about one-tenth that amount. While that amount may sound ridiculously low, keep in mind that risk is determined by the aggregate of all trades—that is, the portfolio. So if you have a lot of trades, even a small risk per trade can aggregate to a significant level, particularly if the trades are correlated (more on that later).

How to Adjust Trading for Changing Volatility Conditions

A common mistake many traders make, especially beginning traders, is to trade the same position sizes through sharply varying volatility conditions. Using a static position sizing approach means you will be undertaking larger and larger risk if market volatility expands. The failure to reduce position size exposures sufficiently, or even at all, when market volatilities exploded in 2008 was one of the reasons why so many traders and investors suffered such large losses in that year. Although many markets witnessed huge declines in late 2008, their volatility levels also exploded. If market participants, particularly long-only traders, had cut their position sizes proportionately, their losses would have been dramatically reduced.

If volatility changes cause stops to widen proportionally—as, for example, would be the case with an ATR-based stop implied by your question—and assuming you still want to keep the dollar risk per trade the same, despite the volatility change, then position size would have to be decreased proportionate to the increase in volatility. This action follows directly from the previously cited three-step summary of O’Shea’s process for setting stops.

Portfolio Risk Effects

Setting individual position stops and adjusting position sizes for changes in volatility is still insufficient to assure proper risk management. Even if the stop on every position is kept to a prudent risk level and position sizes are reduced when volatility increases, total portfolio risk can still be excessive if there are too many positions, especially if these positions are significantly correlated. So a critical last step is to have some sense of the risk implied by all positions in the portfolio.

A worst-case estimate for portfolio risk can be derived by simply adding the risk-to-stop of all the individual positions—that is, the total loss that would be realized if every position in the portfolio was stopped out. If this implied total loss is not excessive, then the risk is well contained. However, the reverse situation—an excessive worst-case portfolio risk estimate—does not necessarily imply that actual risk is too high. The degree of correlation between positions is critical to the portfolio risk level. For example, there is a huge difference between a 20-stock long portfolio, risking 1% per position, and a 20-stock portfolio, consisting of 10 long and 10 short positions, risking the same 1% per position. In the former case, adding the risk of all the individual positions may be a reasonable proxy for total risk, whereas in the latter case, it would greatly overstate risk.

So how can one gauge portfolio risk? There is no simple answer. The simplest case is one where the individual positions are significantly correlated, such as a long stock portfolio. In this case, as mentioned before, adding all the individual risks, although a bit overly conservative, is a reasonable portfolio risk proxy.

The next simplest case is a portfolio where the individual holdings are significantly correlated to a common benchmark—for example, a long/short, large cap stock portfolio, using the SPY (the ETF for the S&P500) as the benchmark. In this case, each position can be translated into the beta-weighted equivalent of the benchmark (e.g., SPY). Beta indicates the percentage price move that can be expected for the individual stock, given a 1% move in the benchmark. For example, if a stock has a beta of 0.8 to the SPY, it means that if the SPY is down 1%, a long position in the stock is expected to be down 0.8%. If the stock is trading at $100 and the SPY is trading at $200, a 500-share long position in the stock would be approximately equivalent to a 200-share SPY position (0.8 x ½ x 500), or, equivalently, the $50,000 stock position would be equivalent to a $40,000 SPY position. Short positions would have negative betas, of course, since they would be expected to go down when the benchmark goes up. Since long and short positions will offset each other, in a long/short portfolio, the dollar value of the beta-weighted equivalent benchmark position will be far smaller than the total dollar value of the individual positions.

How would you translate the beta–weighted equivalent benchmark position (e.g., SPY) into a portfolio risk number? Easy. Assume your individual stock stop points tend to be about 2%-4% away from the current share price. To be conservative, you can take the upper number of this range (4%) and multiply it by the dollar value of the beta-weighted equivalent benchmark position to get a short-term portfolio risk measure. For example, if the total of your beta-weighted positions were equivalent to 1000 SPY shares and the SPY was trading at $200, the implied short-term portfolio risk implied by this approach would be $8,000. This number will be much lower than the total risk implied by summing the losses that would be realized if all your position stops were hit, and this make sense because whichever direction the broad market moves, on balance, your short and long positions are likely to move in opposite directions. The method just described provides only a short-term risk gauge—an estimate of the portfolio risk implied by the next market swing being adverse to the net beta-weighted position. Over time, the broad market could move up, stopping out shorts, and then down stopping out longs, or vice versa, and the total risk could be much larger.

If the positions in the portfolio are not significantly correlated to a single benchmark, then deriving a portfolio risk measure becomes much more difficult. There are approaches, such as Value at Risk (VaR), which are designed to measure portfolio risk. However, even a brief discussion of the different methods of calculating VaR and the potential benefits and pitfalls of this approach would require a far too lengthy tangent for this article.

If there is no benchmark that can be used against all, or at least most, of the positions, then all you easily determine is the worst-case risk, as previously explained. The less correlated the positions in your portfolio are too each other, the more overstated this risk number will be.

ATR Defined

Before finally answering your specific question, I need to define the ATR for readers who are unfamiliar with this metric. The ATR, also referred to as ADTR, stands for the Average (Daily) True Range. The daily True Range, which is averaged to get the ATR, adds the overnight price move, if any, to the day’s range to get a more accurate gauge of the market’s daily price movement. Specifically, the True Range can be defined as the maximum of yesterday’s close and today’s high minus the minimum of yesterday’s close and today’s low. So, for example, if yesterday’s close was 100, today’s high was 99, and today’s low was 98, the daily range would be 1, but the True Range would be to 2. Similarly, if yesterday’s close was 100, today’s high was 102, and today’s low was 101, the daily range would be 1, but the True Range would be to 2. The 100-day ATR would be the average True Range during the past 100 days (sometimes calculated as an exponential average). The ATR is, effectively, a volatility measure.

Finally, Your Question

First, you are apparently following O’Shea’s three-step process for placing stops:

1. Decide where you are wrong—Your approach defines an exit if the market moves three times the ATR against your position.
2. Decide how much you are willing to lose on each trade—You have defined this amount as 1% of equity.
3. Determine the position size—Once you define your stop point and dollar risk per trade, the position size is automatically implied.

Your approach also incorporates volatility by using the ATR to determine your stop point because stops will be wider when volatility (as measured by the ATR) is higher. And if your risk per trade remains fixed at 1%, wider stops directly imply smaller positions. So, effectively, your approach will have you trading smaller positions when markets are more volatile, which again is consistent with sound money management.

Your question about position rebalancing in response to changes in ATR is clearly directed at open positions. However, you don’t specify whether you are using the ATR to define a fixed or trailing stop, and it makes a difference. You also don’t mention using ATR levels for rebalancing the size of new positions, which is actually the most important application. Therefore, I will address the rebalancing question for three separate cases:

1. Open Position with Fixed ATR-Based Stop—In this case, you wouldn’t necessarily do anything, since the stop was well-defined at the point of trade entry and contained within the desire maximum risk level.
2. Open Position with Trailing ATR-Based Stop—As an example of this type of case, let’s say you use a trailing stop that is three times the ATR below the highest price since entry (assuming a long position). Here, there is a reasonable argument to be made that if the market volatility has increased (i.e., an increase in the ATR), then the stop should be wider to avoid getting stopped out on meaningless price swing in the new, more volatile price environment. If a trailing stop is widened in response to an increase in the ATR, then the position size needs to be reduced proportionately in order to keep the risk per trade contained to the same level (1% in your case). So if the ATR doubles, causing the distance to the stop point to double, then the position size would need to be halved. Since we are talking about an existing position, it would also be reasonable to instead choose to maintain the full position and not widen the stop in response to a higher ATR. Both methods stay consistent with the fixed 1% risk criterion, and it is a matter of personal choice which approach to use.
3. New Positions—In regards to new positions, a higher ATR would unambiguously imply a wider stop given your implied stop-loss method. So here, your position for a newly implemented trade would decrease proportionately to the increase in the ATR—e.g., a doubling in ATR would indicate a halving of positions size.

In regards to how the portfolio might affect rebalancing (e.g., you mention the example of five positions), it doesn’t make a difference. The actions for each case described above would be the same whether you had one position, five positions, or 50 positions. What I would stress, however, is that even the combination of a sensible stop-loss placement strategy and the adjustment of trading exposure in response to changes in volatility is not sufficient to define an adequate risk management strategy. The trader also has to consider the aggregate risk of all positions, as was previously detailed in the section, Portfolio Risk Effects.

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jschwager@fundseeder.com