Position sizing is one of the most important but least understood components of any trading system.
The Turtles used a position sizing algorithm that was very advanced for its day, because it normalized the dollar volatility of a position by adjusting the position size based on the dollar volatility of the market. This meant that a given position would tend to move up or down in a given day about the same amount in dollar terms (when compared to positions in other markets), irrespective of the underlying volatility of the particular market.
This is true because positions in markets that moved up and down a large amount per contract would have an offsetting smaller number of contracts than positions in markets that had lower volatility.
This volatility normalization is very important because it means that different trades in different markets tend to have the same chance for a particular dollar loss or a particular dollar gain. This increased the effectiveness of the diversification of trading across many markets.
Even if the volatility of a given market was lower, any significant trend would result in a sizeable win because the Turtles would have held more contracts of that lower volatility commodity.
Volatility – The Meaning of N
The Turtles used a concept that Richard Dennis and Bill Eckhardt called N to represent the underlying volatility of a particular market.
N is simply the 20-day exponential moving average of the True Range, which is now more commonly known as the ATR. Conceptually, N represents the average range in price movement that a particular market makes in a single day, accounting for opening gaps. N was measured in the same points as the underlying contract.
To compute the daily true range:
True Range = Maximum(H-L,H-PDC,PDC-L)
where:
H – Current High
L – Current Low
PDC – Previous Day’s Close
To compute N use the following formula:
N = (19 × PDN + TR) / 20
where:
PDN – Previous Day’s N
TR – Current Day’s True Range
Since this formula requires a previous day’s N value, you must start with a 20-day simple average of the True Range for the initial calculation.
Dollar Volatility Adjustment
The first step in determining the position size was to determine the dollar volatility represented by the underlying market’s price volatility (defined by its N).
This sounds more complicated than it is. It is determined using the simple formula:
Dollar Volatility = N × Dollars per Point
Volatility Adjusted Position Units
Thus, a unit for a given market or commodity can be calculated using the following formula:
Unit = 1% of Account / Market Dollar Volatility
or
Unit = 1% of Account / N × Dollars per Point
Examples
Heating Oil HO03H:
Consider the following prices, True Range, and N values for March 2003 Heating Oil:
Date High Low Close True Range N
11/1/2002 0.7220 0.7124 0.7124 0.0096 0.0134
11/4/2002 0.7170 0.7073 0.7073 0.0097 0.0132
11/5/2002 0.7099 0.6923 0.6923 0.0176 0.0134
11/6/2002 0.6930 0.6800 0.6838 0.0130 0.0134
11/7/2002 0.6960 0.6736 0.6736 0.0224 0.0139
11/8/2002 0.6820 0.6706 0.6706 0.0114 0.0137
11/11/2002 0.6820 0.6710 0.6710 0.0114 0.0136
11/12/2002 0.6795 0.6720 0.6744 0.0085 0.0134
11/13/2002 0.6760 0.6550 0.6616 0.0210 0.0138
11/14/2002 0.6650 0.6585 0.6627 0.0065 0.0134
11/15/2002 0.6701 0.6620 0.6701 0.0081 0.0131
11/18/2002 0.6965 0.6750 0.6965 0.0264 0.0138
11/19/2002 0.7065 0.6944 0.6944 0.0121 0.0137
11/20/2002 0.7115 0.6944 0.7087 0.0171 0.0139
11/21/2002 0.7168 0.7100 0.7124 0.0081 0.0136
11/22/2002 0.7265 0.7120 0.7265 0.0145 0.0136
11/25/2002 0.7265 0.7098 0.7098 0.0167 0.0138
11/26/2002 0.7184 0.7110 0.7184 0.0086 0.0135
11/27/2002 0.7280 0.7200 0.7228 0.0096 0.0133
12/2/2002 0.7375 0.7227 0.7359 0.0148 0.0134
12/3/2002 0.7447 0.7310 0.7389 0.0137 0.0134
12/4/2002 0.7420 0.7140 0.7162 0.0280 0.0141
The unit size for the 6th of December, 2002 (using the N value of 0.0141 from the 4th of December), is as follows:
Heating Oil
N = 0.0141
Account Size = $1,000,000
Dollars per Point = 42,000 (42,000 gallon contracts with price quoted in dollars)
Unit Size = (0.01 × $1,000,000) / (0.0141 × 42,000) = 16.88
Since it isn’t possible to trade partial contracts, this would be truncated to an even 16 contracts.
You might ask: “How often is it necessary to compute the values for N and the Unit Size?” The Turtles were provided with a Unit size sheet on Monday of each week that listed the N, and the Unit size in contracts for each of the futures that we traded.
The Importance of Position Sizing
Diversification is an attempt to spread risk across many instruments and to increase the opportunity for profit by increasing the opportunities for catching successful trades. To properly diversify requires making similar if not identical bets on many different instruments.
The Turtle System used market volatility to measure the risk involved in each market. We then used this risk measurement to build positions in increments that represented a constant amount of risk (or volatility). This enhanced the benefits of diversification, and increased the likelihood that winning trades would offset losing trades.
Note that this diversification is much harder to achieve when using insufficient trading capital. Consider the above example if a $100,000 account had been used. The unit size would have been a single contract, since 1.688 truncates to 1. For smaller accounts, the granularity of adjustment is too large, and this greatly reduces the effectiveness of diversification.
Units as a measure of Risk
Since the Turtles used the Unit as the base measure for position size, and since those units were volatility risk adjusted, the Unit was a measure of both the risk of a position, and of the entire portfolio of positions.
The Turtles were given risk management rules that limited the number of Units that we could maintain at any given time, on four different levels. In essence, these rules controlled the total risk that a trader could carry, and these limits minimized losses during prolonged losing periods, as well as during extraordinary price movements.
An example of an extraordinary price movement was the day after the October, 1987 stock market crash. The U.S. Federal Reserve lowered interest rates by several percentage points overnight to boost the confidence of the stock market and the country. The Turtles were loaded long in interest rate futures: Eurodollars, TBills and Bonds. The losses the following day were enormous. In some cases, 20% to 40% of account equity was lost in a single day. But these losses would have been correspondingly higher without the maximum position limits.
The limits were:
Level Type Maximum Units
1 Single Market 4 Units
2 Closely Correlated Markets 6 Units
3 Loosely Correlated Markets 10 Units
4 Single Direction – Long or Short 12 Units
Single Markets – A maximum of four Units per market.
Closely Correlated Markets – For markets that were closely correlated there could be a maximum of 6 Units in one particular direction (i.e.6 long units or 6 short units). Closely correlated markets include: heating oil and crude oil; gold and silver; Swiss franc and Deutschmark; TBill and Eurodollar, etc.
Loosely Correlated Markets – For loosely correlated markets, there could be a maximum of 10 Units in one particular direction. Loosely correlated markets included: gold and copper; silver and copper, and many grain combinations that the Turtles did not trade because of positions limits.
Single Direction – The maximum number of total Units in one direction long or short was 12 Units. Thus, one could theoretically have had 12 Units long and 12 Units short at the same time.
The Turtles used the term loaded to represent having the maximum permitted number of Units for a given risk level. Thus, “loaded in yen” meant having the 16 maximum 4 units of Japanese Yen contracts. Completely loaded meant having 12 Units. Etc.
Adjusting Trading Size
There will be times when the market does not trend for many months. During these times, it is possible to lose a significant percentage of the equity of the account.
After large winning trades close out, one might want to increase the size of the equity used to compute position size.
The Turtles did not trade normal accounts with a running balance based on the initial equity. We were given notional accounts with a starting equity of zero and a specific account size. For example, many Turtles received a notional account size of $1,000,000 when we first started trading in February, 1983. This account size was then adjusted each year at the beginning of the year. It was adjusted up or down depending on the success of the trader as measured subjectively by Rich. The increase/decrease typically represented something close to the addition of the gains or losses that were made in the account during the preceding year.
The Turtles were instructed to decrease the size of the notional account by 20% each time we went down 10% of the original account. So if a Turtle trading a $1,000,000 account was ever was down 10%, or $100,000, we would then begin trading as if we had a $800,000 account until such time as we reached the yearly starting equity. If we lost another 10% (10% of $800,000 or $80,000 for a total loss of $180,000) we were to reduce the account size by another 20% for a notional account size of $640,000. There are other, perhaps better strategies for reducing or increasing equity as the account goes up or down. These are simply the rules that the Turtles used.
Original Turtle Trading Rules: Foreword
Original Turtle Trading Rules: Introduction
Original Turtle Trading Rules: Chapter 1: A Complete Trading System
Original Turtle Trading Rules: Chapter 2: Markets: What the Turtles Traded
Original Turtle Trading Rules: Chapter 3: Position Sizing
Original Turtle Trading Rules: Chapter 4: Entries
Original Turtle Trading Rules: Chapter 5: Stops
Original Turtle Trading Rules: Chapter 6: Exits
Original Turtle Trading Rules: Chapter 7: Tactics
Original Turtle Trading Rules: Chapter 8: Further Study
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