The Nature of Returns

Through the years I have sought to improve my returns. Initially I sought market knowledge; then I focused on self-awareness and knowledge of self – I especially looked for ways to improve my decision making skills. Nowadays, I focus at improving my net returns by delving into the nuances of the Expectancy Return and Expectancy Ratio.

There are quite a few variations of both formulae floating around. For Expectancy Return I use:

(Avg$ Win x Win Rate) – (Avg$Loss x Loss Rate) = expected $ Return.

Where:

  • Avg$Win = Profitable $ Returns/Total Winning Trades
  • Win Rate = Total number Win Trades/Total Trades
  • Avg$Loss = Losing $ Returns/Losing Trades
  • Loss Rate = Total number Losing Trades/Total Trades

I have explained elsewhere (The Art of Position Sizing) that I prefer to normalize my results by using percentage of the price that initiated the trade. But for this blog. let’s use the idea with which most are comfortable: $ Return.

Note also that the above formula can be summarised to (Total-Losing$)/Total Trades; but while the results would be the same, the first rendition separates two important components:

  1. The Avg$Win and Avg$Loss: these are the result of our entry and exit and are totally within our control. And,
  2. The WinRate and LossRate: these are more a factor of the interaction of the Ebb and Flow of our plan and the Market. (For ‘Ebb and Flow’, see (The Art of Position Sizing).

If we understand how important (1) is to our being profitable, we’ll tailor our trade management and position sizing according to its statistical history.

Most times we manage trades based on our perception of the technical and/or the fundamental picture. The Ray Wave, for example, provides an objectively definable edge in identifying where a swing structure may end. (See The Ray Wave I). But maximization of our profit lies less with the Ray Wave’s intricacies than with understanding our profit/loss profile.

For example if we have a 40% hit rate; and Avg$Win of $75.00 with an Avg$Loss of $50, we have no edge i.e. over a large sample size, we’ll not make or lose money. But if we can raise the Avg$win to $100, we can expect to make $10.00 per trade.

We can take the Expectancy Return and turn it into a ratio:

(Ave$win x WinRate)/(Avg$Loss x Loss Rate) = Expectancy Ratio

Now taking that information we reconcile the idioms:

  1. Never let a winning trade turn into a loss. And,
  2. Let your profits run

Once we know the minimum ratio we need to provide an edge of ‘x’, we don’t have a winning trade until the minimum ratio is reached. For example, if our minimum ratio for an edge is 1.5, and we have risked $100 on this trade, we need to see at least $150.00 in open profits before we can say we have a winning trade. Once that objective is attained we implement our defensive strategies to let our profits run. The strategies may involve partial exits (like my Rule of 3) or bringing the trailing stop to breakeven etc.

This is not to say that on occasions, we’ll not exit a position before attaining our minimum ratio – there will be times when we perceive that market conditions have changed and we need to exit. The key words are, ‘on occasions’. If we consistently take profits before attaining our minimum historical ratio, then, in the long run, we must be unprofitable.

Tomorrow I’ll examine how these ideas have led to the amending of my Rule of 3 See (Rule of 3); I’ll also examine their application to John Sweeney’s Maximum Adverse and Maximum Favourable Excursions.

Position Sizing 2

Yesterday we defined our subjective risk thresholds. Today we’ll look at the metrics – the objective approach to defining them.

There are certain key numbers that I collect from my equity journal. Remember that while I will be speaking in terms of ‘dollars’, I also collect the numbers for ‘% of initiating price’ (see The Art Of Position Sizing):

  • Average Dollar Win
  • Win Rate
  • Average Dollar Loss
  • Loss Rate
  • Maximum Drawdown
  • Maximum Positive Return
  • Maximum Consecutive Wins
  • Maximum Consecutive Losses
  • Average Number of Consecutive Wins
  • Average Number of Consecutive Losses
  • Standard Deviation of Monthly Returns.
  • Average annual return

The information provides the objective bedrock for estimating my normal position size. Let’s illustrate my approach by way of example let’s say subjectively I accept a 4% as my maximum risk. My maximum number of consecutive losses is 3 and the average loss is 1%. I can now estimate that the objective maximum percentage loss.

I multiply my maximum number of consecutive losses by 3. So now the number is 9. So my possible worst case drawdown on average would be a 9 x 1% = 9%. I then multiply the standard deviation of monthly returns by 3. Let’s say that comes out at 27%. I now have the boundaries for my worst case scenario: 9% to 27%.

I can now estimate how long it would take me to recover from a worst case scenario since I know my average annual return. If it’s around 25%, then a 27% loss would take me a year.

The idea is to play with the numbers so you know the most comfortable normal risk for you. This number is partially subjective and partially objective. Once you have this number, you can then adopt a position-sizing algorithm. There are as many algorithms as there are successful trading methodologies. Our job is to find a comfortable one for us.

We need one more factor before using a position sizing algorithm: a measurement of the volatility of the market e.g. the Average True Range (ATR) of ‘x’ days. With this we can have a look at some position sizing formulas.

One of the simplest is the Turtle formula.

(% Capital to Risk x Capital)/$value of Average True Range (ATR)

The ATR is the volatility component that the market brings to the equation, we bring the rest. Notice that too often the ‘% Capital to Risk’ is a figure plucked out of the air e.g. 2%. But if you don’t do the work, you will not know whether that figure is appropriate to you and your style of trading. The purpose of position sizing is balance ‘maximization of profitability’ with ‘minimization of risk of ruin’. If we adopt a random figure we’ll never know whether we have struck the appropriate balance for us. Moreover by doing the numbers we have a ‘feel’ for our run of losses and wins. In this way, we prepare for the drawdowns (and the accompanying anxiety) and exuberant profits (and the accompanying euphoria).

One other point. The ‘Capital’ is the cash you have at the end of your measuring period (weekly, monthly, quarterly) +/- open profits as measured from the stop loss. For example: your cash is $100k and you have an open position profit of +$5k. However, your current stop is at -$3k. Your ‘Capital’ is $100 – $3k, not $100k + $5k.

I recommend you set a measuring period rather than calculate the ‘Capital’ on a trade by trade basis. Accompanying the measuring period, you set a high threshold and a low one which, if hit. you would re-calculate the “Capital’. I use a monthly measure and a threshold of 50% of my average annual return as the upper threshold and 25% of ‘three times the standard deviation of monthly returns’ as my lower threshold. This means I reduce normal size more quickly than I increase it.

So now you have a normal size position. But this is not the end of the story. I believe that the position size should be varied depending on the context of the trade. To do this, I use the standards:

  • Probability of Success
  • Where I am in the Ebb & Flow

Of the two, the Ebb & Flow is the more important factor.

The probability of success is easy enough to understand. You can calculate the probability of success for your rule (setup) if your equity trading journals record the Rule number for a trade (and yours should). This historical probability will be tempered or enhanced by the current context.

So lets’ say that your ‘313 Outside’ setup has a 68% probability of success (normal position size). But on this occasion all the timeframes line up and you feel that this raises the probability to 85%. You may want to raise the position size to 1.5 times normal.

The Ebb & Flow is based on my view of the markets and trading plans. I see our plans as an inlet onto which the waves (the market) wash. Sometimes they only partially fill the inlet. This is the norm. It means we win some, lose some. In this situation, we use normal position sizing. Sometimes the waves cover all the inlet. At those times, we can do no wrong; so we’ll look to increase our size. Sometimes the waves have all but totally receded. At those times, we can do no right; so we’ll look to reduce position size.

We identify the Ebb & Flow by our trading results. If we start to see losses above the norm, especially if we have increased size after a prolonged exuberant profitable run, we’ve moved from flow to ebb. It’s important to understand that, like selling the top or buying the bottom, we’ll always be slightly late in the identification. In other words, we won’t know until after the first few ‘environment changing’ trades that a transitional stage is happening. That’s OK; it’s better than not catching it at all.

In my next blog, I’ll look at the USDJPY and include a position sizing example.

Position Sizing 1

Thanks to all who put pen to paper yesterday. My purpose was to make clear my reasons for writing and I am happy so many share them with me.

In this series, I’d like to talk about position sizing and suggest certain formulas.

Position sizing is part of the Money Management factor in the factors for trading success: Written Plan with an Edge x Effective Money Management x Winning Psychology. The multiplication sign is important. It emphasizes that you need to be competent in all three areas – incompetence in any one area will lead to failure. As an extreme example, if you have ‘0’ competence in any area, then your dollar return must be ‘0’.

I feel that much of what is written about money management misses the point – the authors speak of measuring the outcome in dollar terms. Yet, a dollar outcome fails to account for the differing volatilities which differ in the same instrument over different timeframes, and among different instruments. Hence, I believe we need to have a section in our reports that normalizes results. Now sometimes the position sizing formula itself will do the normalizing e.g. the Turtle formula I’ll speak about that later in the series; but most times, we need to input it somewhere in our spreadsheet.

I know of two ways of normalizing:

  • Using the ATR or
  • Expressing the outcome of the trade as percentage of the initiating price. We do this on a one contract basis. For example: if I sell three contracts of the ES at 1358 and cover at 1348, I have made 10 points per contract. This is a result of (10/1358)% = 0.74%

Either way does the job.

So step one in a management algorithm is to normalize your output.

Step two is to decide on the amount of risk to take per trade. This is both a subjective and objective exercise. The subjective one is more difficult to assess. One of the more interesting ways of doing this is via a visualization question and answer process:

  • Select an amount of money that represents a significant return to you but that is within reach. It could be US$100k or US$1M or US$1b.
  • Select an amount of money whose loss would mirror (1) except you’d feel pain rather than pleasure. Express this as a function of your capital.
  1. Assume you have an indeterminate amount of black and white balls in a jar. If you pull the black ball, you lose (b); if you pull the white, you win (a).
  2. Starting at a percentage you know will be painful – for me it would be 30 & ask: would I choose the game (where I stand to win $X or lose Y%) or not play. If the latter, choose a lower percentage and keep playing until you chose the game. The percentage before you chose the game is your subjective risk threshold. For example: Say at 3% I chose the game, and the percentage before that was 4%, 4% is my threshold.

This provides the threshold for an individual trade, you now repeat the same exercise for consecutive losses and again for portfolio risk. It’s important to do this because each measures a different impact. For example your pain threshold per trade may be 4% but 20% for consecutive losses; and it may be 12% for portfolio loss. In other words, you may not be happy losing more than 4% on any one trade but it would be OK to lose up to 20% of you lost it because you lost on five trades, each losing 4%.

You may be thinking – that’s illogical! I agree but we are talking here of subjective risk assessment, logic has little to do with it. By identifying and keeping below the subjective risk threshold, we ensure we reduce anxiety and thus ensure we keep to our rules.

For the process to work, you need to vividly imagine the pleasure and pain – in short engage your emotions!

So now you have your subjective risk threshold, part of the process to determine the maximum risk per trade. Tomorrow I’ll continue with this thread and look at the objective risk thresholds.

The Art Of Position Sizing

Today I want to talk about a subject that normally causes participants to doze – it’s a very unsexy subject. Unsexy but very important. So bear with me.

There are two issues I have with many commercial position sizing software:

  1. The software allows only testing on an instrument by instrument basis.
  2. It reports only on dollar results

There is no problem with testing on an instrument by instrument basis if you are trading one instrument. But if you are trading a basket of instruments, then serious problems rear their heads.

One of the main issues lies in the fact, that unless you can test on a portfolio basis, you cannot assess the damage a drawdown will do to the portfolio. For example, in a diversified portfolio, a drawdown in one instrument may be saved by a profitable run in another. Or, if all instruments suffer a drawdown simultaneously, then their drawdown would have a much greater impact on capital.

The commercial package I like best is the successor to Trading Recipes: Mechanica Standard Edition

http://www.mechanicasoftware.com/products.htm

I don’t own a copy (I had my own program written) but I have seen it work and I am impressed with it.

The second issue arises because all dollar results are treated equally. But in the real world of trading, this is clearly not the case. The volatility of the market plays an important role in assessing the reasonableness of the return. For example, a risk of $1000 would be very different in an instrument that has an Average True Range of $3000 to one that has an Average True Range of $200.

The Expectancy Formula I quoted in previous blogs is not the one I use for this reason. The formula quoted has been:

(Avg$Win x Win Rate) – (Avg $Loss x Loss Rate) = Exepectancy

I prefer to normalize the result by dividing the result on a one contract basis by the initiating price. Let’s say I bought gold at US$850 and sold it at US$930. The Initiating Price % result would be:

((930-850)/850)x 100 = 9.4%

What I am doing is substituting the $ expectancy with a % of initiating price then translating that to dollars.

For example, let’s say my long-term expectancy is 10%. I enter the ES tonight at 1377. My expectancy for the trade would 1377 x .10 = 137 points x 50 x number of contracts. If I were trading gold and my entry is 890, my expectancy would be 890 x .10 = 89 x 100 x number of contracts.

I find using the % of initiating trade price a more accurate way of assessing expectancy than dollar values.

So then, the Expectancy Formula I use is:

((AvgWin%IPrice x WinRate) – (AvgLoss%IPrice x Loss Rate)) = % Expectancy

Trading and Making Money

Two trades in Crude Oil illustrate my approach to making money in the trading game. If there is a Holy Grail in trading, it’s reflected in the formula:

(Avg$Win x WinRate) – (Avg$Loss x Loss Rate) = > $0

In other words, what is important ( taking the win rate into consideration) is for our $ win to be greater than our $ loss.

To maximise the difference, I seek to exit a position BEFORE my stop is hit. So when I say that my trade has an 80% of success, this does not mean that I have an 80% probability of making money. Given that my win rate fluctuates between 47% and 55%, the comment “80% probability of making money” would be sheer nonsense. What the statement means for me: if I exit before my stop is hit, I have an 80% chance of being right. This means that in 80% of the time, if I had not elected for early exit, my stop would have been hit.

Figure 1 shows my results for 2006, my trading year is from September 1 to August 31. My aim is to make around 25% per annum. In 2006 I had a better than average result even though my win rate was slightly below 50%.

2006-results.jpg

Figure 1 2006Results

But early exit comes at a price: there will be times that when exiting a position means I’ll re-enter at a more adverse price. This is what happened with the most recent Crude Oil trades.

Figure 2 shows a classical “Negative Development” buy setup and entry (For Negative Development see previous posts and Nature of Trends). Note that I use CSI’s Perpetual contract for analysis and the appropriate nearest futures month for stops and entry levels.

crude-oil-perpetual.jpg

FIGURE 2 Negative Development

What I expect following Negative Development setup is strong continuation. Instead, we had two inside days. So, on Dec 11, I exited the position with a 0.36% loss. I exited not because the trade had done anything wrong, but because it wasn’t doing what I expected.

I did plan a re-entry on a breakout and this was triggered last night. This second trade can’t lose because I exited 1/3 at last night’s close, moved my stop to breakeven on the second 1/3 and left unchanged the initial stop on the last 1/3.

The early exit cost 0.36%. When you consider the difference between my initial exit and breakout entry, my loss on the trade was 0.42%. But I am happy to wear the loss which with hindsight need not have occurred. But that’s the point: only precognition of last night’s breakout would have kept me in the trade. And since I don’t have that skill, I was happy to bail and happy with the way I managed the trade.

The Expectancy of a Trade & Your Trading Plan

The Expectancy Return formula identifies the key area on which we need to focus.

Most newbies focus on the win rate. But the win and loss rate are less under our control than the Avg$win and Avg$Loss. This post will explore the reasons for this.

No matter how good a trader we may be, we will experience drawdown periods – where everything we do is wrong. On the flip side, we have long-term losing traders with periods where all they do turns to gold. I believe the reason for the phenomena lies in the nature of free markets. I liken the market to waves within a limitless circle; and I liken our market knowledge and trading plans as a rectangle within the circle. As long as the waves wash into our rectangle, we enjoy success; the more our rectangle is filled, the more success we enjoy.

But when the waves recede from our rectangle, we experience drawdown periods. In this metaphor, we have little control over our win/loss rate; it depends entirely on whether or not the tide is in our rectangle. Sure we can increase the size of rectangle (i.e. increase our self and market knowledge); but since the circle is limitless, we can never know enough to prevent the drawdown periods.

On the other hand, the Avg$Win and Avg$Loss is totally within our control because they are dependent on our entry and exit. By focusing on expanding the difference between our Avg$Win and Avg$Loss, we create our profitability.

By the way, it’s easier to decrease the loss than to increase the profit. When I take a trade I ask a series of questions whose answers prepare an exit before my stop is hit. One of the questions I ask myself is: “What does the trade have to look like for me to remain in the trade?”. Another question is: “What does the trade have to look like for me to exit?”.

The attached JPG of my personal account shows the difference between a good trading month and a poor one. October was a poor month: my total Win Rate and Loss Rate were almost equal (+17 to -16); but the $Loss was 1.3:1 to 1.0 $Win; and as a result, I lost (3%) for the month. Now have a look at Feb 2006.

In Feb I made only $5000.00 more than October, but my losses were ($38,000) compared to October’s ($114,000.00). As a result, I made a whopping +6.9% ROI!

My results for 2006 to 2007 show we’ll make money if we focus on our entries and exits and thus increase the difference between our profits and losses. The alternative is to focus on improving our Win Rate and that is much harder to achieve.

Monthly Results 2006 - 2007

The Expectancy of a Trade

A most important formula for our trading is the Expectancy Formula. Its basic formulation is in dollars terms.

(Average Dollar Win/Win Rate) – (Average Dollar Loss/Loss Rate) = Expected Profit per Trade

Let’s say:

  • My AVG$win is $750.00
  • My Win rate is 48%
  • My Avg$ loss is $183
  • My Loss rate is 52%
  • My avg trades per year is 300

My expected $ profit would be:

$((750 x .48) – $(183 x .52)) x 300 =

$(360 – 95) x 300) = $79452

The interesting thing is when using the formula in this way I seldom came close to the actual profit. I looked into the problem and found that the reason lay with the mix of instruments. If the mix remained the same, then the formula would come close to the actual results; but most times, my mix altered and when that happened, the results skewed.

It’s not hard to see why: a $300 profit in Oats is not the same as a $300 profit in the EUUS given the different volatilty of the two instruments.

I knew that if I wanted to take the formula to the next level, I had to find a way of normalizing the results across instruments. I chose to normalize the results by reference to the open on a one contract basis:

(close price of the trade – open price of the trade)/close price of the trade = % of open price of the trade

Thus I am now able to compare apples with apples. By doing it this way, I am able to anticipate more accurately the return per trade.

VISION and Trading

Yesterday I wrote that VISION, goals etc had their counterpart in out trading.

VISION is found in two components:

Our trading philosophy. Consciously or unconsciously our philosophy, Ayn Rand’s ‘sense of life’, governs our actions. So too with our trading, consciously or unconsciously, our trading philosophy governs our actions from the plans we choose to our position size to the actions we take to execute consistently our trading plan.

I adapted the statement of my philosophy when I first read it in Trader Vic – Methods of a Wall Street Master by Victor Sperandeo. The articulation there of Sperandeo’s philosophy strongly resonated with my values. So with a small amendment, I adopted it:

  • Preservations of Capital
  • Consistent Execution (leading to consistent profitability)
  • Superior Returns

You’ll see the three ideas reflected in all that I do. Our trading philosophy forms one part of our VISION.

The other component is found in the rational for a trading plan. We need a trading plan for two reasons:

  1. Before entry: it tells us when the probabilities favour our trade
  2. After entry: it tells us when the probabilities are no longer in our favour and we should quit a trade.

Both components are essential to our trading success. The key analytical insight to our success is found in the expectancy formula; the formula that tells us we can expect to make, on average, on each trade. Unless the sum is positive, we don’t have an edge i.e. we are doomed to fail in the long run. The most basic formulation of the formula finds its expression in:(Avg$Win x WinRate) – (Avg$Loss x Loss Rate) = Expected Trade Result

Where:

  • Avg$Win = Total $ profits/Total number of Winning Trade
  • WinRate = Total number of Winning Trades/Total Trades taken
  • Avg$Loss = Total $ losses/Total number of Losing Trade
  • LossRate = Total number of Losing Trades/Total Trades taken.

Most newbies focus on the Win and Loss Rate. But in my view, this is the more difficult part of the equation to control. Why this is so is best described by a story I heard about while learning Drummond Geometry (P&L Dot):

One day an ex-floor trader was told by an apprentice he had taken under his wing: ‘The 1-1 support WILL hold this decline”! The market was heading south towards what P&Lers called 1-1 support.

The ex-floor trader replied: “What are the probabilities?”

The apprentice said: “It WILL HOLD, I am certain!”

The ex-floor trader said not a word; instead, he picked up the phone and said: “Sell me 3000 Dec contracts at market”

Needless to say, the market went through the 1-1 support like knife through butter. “Remember this” said the ex-floor trader, “ we think in probabilities not certainties”.

This is a great tale. It tells us that the trading is in the realm of probabilities and as such the win/loss rate is less under our control than the Avg$Win and Avg$Loss. Both of these depend entirely on our decisions to enter and exit.

Notice that the formula explains why someone with a 90% win rate can still lose money. Let’s see why. Let’s say the Avg$Win is $10 and Avg$Loss is $100 and the win rate is 90%. The sum of the formula is:

($10 x .90) – ($100 x .10) =

(S9) – ($10) = -$1.00

So over the long term, over a large sample size, each trade we take will lose -$1.00.

Our VISION allows us to imagine a number of critical events:

  1. What does a trade need to look like – what does it have to do after entry – for me to remain in a trade?
  2. What does a trade need to look like for me to exit a trade?
  3. What does a trade have to look like for me to stop and reverse?

By visualizing the answers to these questions allows me to exit trades BEFORE my stop is hit. The technique allowed me to return 46.64 on capital (ROI) for 2007 an average dollar profit per trade of US$181.00.

By keeping detailed statistics, I am able to CANI (constant and never-ending improvement) my entry and exit. This is not to say I won’t have losses; of course, I will. My loss rate for 2007 of 50.44 attests to that. But by keeping a margin of 2:1 for my Expectancy Ratio (same formula except we divide the Avg$Win component by the Avg$Loss), I was able to return a fabulous 46.64% ROI.

In the next post, I’ll look at a trading plan and its components.