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## The Primary Trade Size Forumla

Position sizing is something that comes up ALL THE TIME in the discussions among new and developing traders. Everything starts with the size of the risk we’re looking to take and works up from there.

Here is the basic formula:

Position Size = Amount at risk /(Number of Points or Pips being risked x Value ofÂ  Each Point or Pip)

Amount at risk comes from looking at the fraction of your account that you want to be exposed to loss on the given trade. So if you have a \$5000 account and want to risk 2% then that would be \$100.

The number of points or pips being risked is basically how far away from your entry point your initial stop will be. If you’re getting long at 100 and your stop is at 95, then the point risk is 5.

The value of each point or pip will depend on the market you’re trading.

Thinking in stock market terms where the value of a point is \$1.00 per share (adjust for your own currency), the formula would be as follows:

Shares = \$ to be risked / (Points risked)

So if you want to risk \$1000 and your point risk is 10 you would trade 100 shares: \$1000/(10 x \$1)

If you’re trading a fixed size contract market such as futures or forex (lots), then it would look like this:

Contracts (Lots) = \$ to be risk / (points risked x point value)

In the case of e-mini S&P 500 futures, the point value is \$50, so if we want to risk \$1000 and have a 10 point stop, we would trade 2 contracts: \$1000/(10 x \$50)

If we are trading micro lots of EUR/USD where the pip value is \$0.10 and we are risking \$1000 with a 125 point stop, we’d trade 80 contracts: \$1000/(125 x \$0.10)

Notice that nowhere in here did I bring up the question of appropriate leverage. It only matters if you don’t have enough available to you to put on the trade you’re looking to do.

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## A little quiz on trading returns

A book I’m currently reading (which will be reviewed later) presents a set of choices to the reader in terms of picking which sequences of market returns is the better choice. Let’s see how well you do.

1) Which set of returns produces the better final return?
A) -30%, +30%, -30%, +30%
or
B) -10%, +10%, -10%, +10%

2) What if we switch the sequence around?
A) +30%, -30%, +30%, -30%
or
B) +10%, -10%, +10%, -10%, +10%

A) -30%, +30%, -30%, +30%, +15%
or
B) -10%, +10%, -10%, +10%, 0%

4) What about if there are no negatives?
A) +10%, +10%, +10%, +10%
or
B) +20%, 0%, +20%, 0%

If you answered B, B, B, and A then congratulations!

If you did not, then you probably fell victim to thinking of the returns as being additive rather than multiplicative. By that I mean the final returns for question 1 are derived as follows:

A) 1 x (1-0.3) x (1+0.3) x(1-0.3) x (1+0.3) or 1 x 0.7 x 1.3 x.7 x 1.3 = 0.8281 or -17.19%
B) 1 x (1-0.1) x (1+0.1) x(1-0.1) x (1+0.1) or 1 x 0.9 x 1.1 x0.9 x 1.1 = 0.9801 or -1.99%

And because it doesn’t matter which order you do the multiplication in, the results for question 2 are exactly the same.

In the case of question 3, the added 15% return in period 5 isn’t enough to overcome the prior period’s ups and downs as 0.8281 x 1.15 only brings it back up to 0.9523.

For question 4 it’s again a simple pair of calculations

A) 1 x 1.1 x 1.1 x 1.1 x 1.1 = 1.4641 or +46.41%
B) 1 x 1.20 x 1 x 1.20 x 1 = 1.44 or 44%

The point the book authors are trying to make is the volatility impacts performance. The extension from there is that using risk management to at least reduce the size of your losers can increase your returns significantly.

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## Maintaining a Position Mindset in a Portfolio

I met with the head of a PhD program yesterday. We had a good discussion of markets and trading, and he brought up a subject that I thought was working a blog post.

This professor talked about how a trader or investor’s mindset can change when going from dealing with individual trades to managing a portfolio of positions. Specifically, he observed how someone who would be very diligent about risk management and following a specific plan of action when managing one specific position could let all that slide when managing one position among many.

For example, a trader whose only position is a long in XYZ stock could be very good about exiting that position on a stop if the market goes against him. If, however, XYZ is only one of ten holdings in a portfolio, the trader might do more rationalizing of letting the position run if the rest of the portfolio is doing well. And you could flip that around to a poorly performing portfolio by dumping positions before they should be sold.

Yes, there are at least some academics who allow for psychological influences on trading decision-making. đź™‚

Of course the point is that unless you specifically have a combination of trades that are meant to work together (hedges, pair trades, etc.) then each individual position should be managed based on its own merits.

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## Rogue trading isn’t just an institutional issue

A recent discussion of rogue traders looks to address the reasons why they do what they do.

Those reasons include:

1) The qualities which make them attractive as employees (can thrive in highly competitive environments, remain calm under intense pressure and have the ability to take risks) are the same that lead to rogue trading.

2) They are motivated by money and thatÂ  motivation turns to greed, leading them to take greater risks.

3) The traders’ managers benefit from their risky trades in that their bonuses and such are often a function of the groups’ performance.

4) The trader tries to cover up a mistake to protect both their compensation and their reputation.

Now, most readers of this blog probably won’t be in a position to become a rogue trader in the classic sense. That doesn’t mean, though, that these points don’t have value at the individual level.

Consider just one aspect of the rogue trader thing noted above, the part about reputation. If your trading has an ego and reputational element to it – meaning you gain personal and/or social status enhancement from your trading performance – then you are at risk of become a rogue trader in your own way.

Imagine how you would feel being in a position of having made a big bad trade, the result of which would cause a reduction in your social standing. Can you see how you might hide that loss and/or trade your way out of it (usually to very negative effect)?

If we accept the view that the traits that lead to trading success are those which also sow the seeds of rogue trading – which we don’t necessarily have to do, but let me go with this for a moment – then that means all of us who trade the markets have the potential in us to blow up spectacularly. Just one more reason why risk management is such a big deal.

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## Quick and Dirty Position Sizing Rule for Traders

There’s all kinds of discussion and advice about how much risk should be taken on a trade-by-trade basis. Figures like 1%-2% are often tossed out in the active trader community.Ă‚Â William OĂ˘â‚¬â„˘Neil suggested 8%Ă‚Â in his book How to Make Money in Stocks. If you really want to do it right, and you have the appropriate statistics, you can come up with a risk level based on your strategy’s/system’s win rate and the relative sizes of the winners to the losers. We don’t always have a really good set of performance metrics to work with, though, so here are a couple of quick and dirty ways to get to per trade risk.

Fixed Risk
If you’re planning on taking the same nominal risk (say \$100) then it’s very simple. You take the maximum amount you’re willing to risk over a given period and divide that by the number of trades you expect to make in that period.

Let’s say you’re maximum risk for the week is \$500 and you expect to make 10 trades. Take \$500, divide that by 10, and you come up with \$50 risk per trade.

Alternately, if you want to think in percentage terms, let’s say you want to set your max risk at 5% for the week and will do 10 trades. In this case you’re per trade risk would be 0.5% (5%/10).

Fixed Ratio
The math gets a bit more complicated when you start talking about setting your risk as a percentage of your account equity. This means, for example, that if you decide to risk 5% and your first trade was a loss, your second trade would mean risking 5% of the now 5% smaller account equity (95% of the initial value). That would be 4.8% of the initial account balance (95% x 5%). This sort of strategy means as your account balance falls from a series of losing trades you’ll actually take smaller and smaller risks through aĂ‚Â negative compounding process.

Let’s bring back the 5% risk for the week and the 10 expected trades.

We can figure out what the per trade risk would be by using this base formula in Excel:

=1-((1-r)^(1/n))

Where r is the total risk for the period we’re looking at and n is the number of trades expected for that period.

Plugging in our 5% total risk and 10 trades we get:

=1-((1-0.05)^(1/10))

or

= 1 – (0.95^0.1)

Which works out to 0.512% for the per trade risk.

Note that this is actually slightly larger than what we got in the fixed risk calculation above. That’s because of the negative compounding involved.

Scale it Up!
Note that you can use this same sort of process for setting up your per period risk limits. For example, you could figure out what your per week risk limit should be given where you want your per month risk cap to be. It’s the same math, just scaled up from trades to time periods.

Very Conservative
Now, in both of the sets of calculations above we’re going on the assumption of a worst case scenario where every one of our trades in the period in question is a loser (or in the case of time periods, that each of the smaller ones sees a maximum loss). That makes it inherently very conservative in nature. To that end, it’s good for setting the floor in terms of how small you should trade. As such, new traders can make very good use of these quick and dirty calculations to keep them trading conservatively during the learning processĂ‚Â (so long as they are pretty close in their estimates of how many trades they’ll do). More experienced traders will want to adjust up based on rational assessment of performance.

How do you set your risk?
I like to use the quick and dirty stuff above when looking at more position-oriented trades. They are inherently less frequent, so as such more subject to strings of losses because the law of large numbers cannot necessarily come in to play.

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## Taxes and Cutting Your Losers

I’ve been doing quite a bit of reading on the subject of Behavioral Finance of late (and will only being doing more and more in the future). I haven’t been in the academic finance arena since I did my MBA in the late 90s, so some of what I’m going it refreshing my knowledge base and reaquainting myself with the academic viewpoint. It’s really easy to slip away from that when you’re focused very closely on real world markets and regularly interacting with real-world traders, not just the ones imagined in the academic literature. (On the Behavioral Finance subject, I encourage you to watch Mind Over Money.)

One of the things that has come up fairly frequently in the articles and papers I’ve been reading is the idea of cutting your losses and letting your profits run. Now this is an academic discussion, so it has relatively little to do with what most traders think when that sort of advice is being offered. Instead, the academics are referring to the tax implications, especially since they most often are referring to stock trading/investing.

Here’s the logic
When you close a position you trigger a tax event. If you exit a profitable position you’ll have a tax liability – obviously – so it behooves one to hold on as long as possible to defer that event. This is particularly true near year-end when a shortly extended holding period can defer a tax bill by 12 months or more.

As for cutting your losses early, that’s the flip side. When you take a loss you reduce your tax liability. That means it behooves you to book your losses quickly. In effect, the tax impact reduces your net loss. For example, if you’re tax rate is 20% and you’ve taken a \$1000 trading loss, you’ve effectively only lost \$800. In other words, your account is effectively worth \$200 more if you take that loss than if you hold on to the trade. The academics I’ve read seem genuinely incredulous that traders and investors would hold losing positions for exactly that reason.

Know the Law
Now there are all kinds of different tax rules in the global array ofĂ‚Â jurisdictions and markets. For example, in the US securities (stocks, bonds, options, etc.)Ă‚Â fall under normalĂ‚Â capital gains where the tax impact is only felt when a trade is closed. Futures and forex are treated differently in that your positions are marked-to-market at year-end. That means the timing of your exits doesn’t really matter. The rules are different in other countries, though, especially when you bring in things like spreadbetting, so make sure you know how your country’s tax laws impact your bottom line.

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## Correlation analysis for trading position diversification

I got the following inquiry from the ever-curious Trader Rod.

A few questions concerning correlation between two instruments for the purpose of diversification:

1. When calculating the correlation coefficient, given my time frame is daily, should I focus on daily closing prices or daily returns?

2. If the answer to previous question is to focus on returns, and the average holding period for a position is one week, should I calculate the coefficient using series of weekly returns?

3. What is a good threshold for diversification, i.e. at which point do I decide the two instruments are too highly correlated, e.g. anything below 0.7 is acceptable ?

Correlations have been gaining in focus of late, no doubt in large part due to the very obvious and public linkages between the dollar and stocks. It’s hardly a new thing, though. It’s been used in the type of work Rod is describing here for decades. Modern Portfolio Theory, for example, is heavily involved with correlation analysis. In other words, this isn’t a new field of analysis, so if it’s something you have a mind to explore there’s plenty of reading you can find on the subject. Make sure you do take a half approach, though. Using correlations without understanding what they are, what they mean, and how they can change can be extremely dangerous. Just ask the blown up banks and hedge funds who didn’t make it through the credit crisis.

As for Rod’s specific questions:

1) You should always use returns. They are how you can compare two instruments in a standardized fashion. Otherwise, differences in the prices of the securities can create comparison problems.

2) A holding period of only a week makes correlation application challenging. They tend not to be that stable in the short time frames. At best I’d say look at a rolling 5-week correlation and use it as a rough guideline. But realize that it’s only rough. There’s likely to be considerable deviation.

3) To achieve true diversification between two securities you need to have a near zero or negative correlation.