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Compounded Time Weighted Rate of Returns

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The Forex Smart Tools Trade Log uses Compounded Time Weighted Rate of Returns to accurately calculate all equity values shown. Read on to understand how amazing this is… !

Why do you need this fancy accounting method for your trading record?

If you never deposited or withdrew funds into your account over time, you wouldn’t need this approach.

If you never combined two or more accounts that had different starting dates you wouldn’t need this approach.

These are situations that do occur all the time in the life of active traders, so the need for greater accuracy is required.

Watch this movie for a full explanation if you like
How Do The Pros Track Their Equity Changes?

This is the ‘correct approach as recommended by the NFA, the National Futures Association, the organization which governs all Forex CTAs in the United States.

Don’t get scared about the math here. This approach is built into the Forex Smart Tools Trade Log for you so if you use the Log you will automatically have full advantage of this powerful reporting function even without understanding it at all. For those who like to understand or are not yet using the Log and want to figure this out by hand, read on.

What are the accounting options to use when figuring out equity?

It turns out there are actually many different ways to express your gains and losses from your investment into your trading. Each way has a certain application. The choices include:

  • Simple Return
  • Compound Return
  • Average Return
  • Time Weighted Return
  • Money Weighted Return
  • Unit Valuation Return
  • Internal Rate of Return

There are probably other ways too, but by the time we looked at all of these to decide what’s the best way to set up the Trade Log, our heads were spinning. And we had discovered what we wanted (which indeed turned out to be what the NFA told us too):
Compounded Time Weighted Rate of Returns.

This is the methodology that the Trade Log uses. The reason this is the method of choice for you as a trader is that a compounded time weighted rate of return accommodates how you probably interact with your trading account in real life. You probably pull money out of your account as you make profits, and put more money in as your confidence increases or funds become available to you. The timing of your additions and withdrawals is probably random and is not based on a set schedule. These kind of events can play havoc on other methods of computed return. Let’s see why…

Here’s a simple example:

The basic formula for Time Weighted Rate of Return (TW ROR) over one period of time is:

(MV1 – MV0 + W1 – A1) ÷ MV0

  • MV1 is our market value of our account at the end of the time period we are looking at.
  • MV0 is our market value of our account at the beginning of the time period we are looking at.
  • W1 is the withdrawal we have made from our account in this time period.
  • A1 is the addition of more funds into our account in this time period.

So in essence we are adding back in our withdrawals and subtracting back out our additions.

Let’s take a simple example…

Say you open a new account with $1000. You trade on it for a few weeks and the net result of all your trades is a profit of $100. Well done! What is your TW ROR now?

  • MV1 is $1100. This is the ending balance of your account today.
  • MV0 is $1000. This was the market value of your account at the beginning of the time period.
  • W1 0. You did not make any withdrawals from your account in this time period.
  • A1 is 0. You did not make any additions into your account in this time period.

So you have (1,100 – 1,000 + 0 – 0) ÷ 1000. This then is 100 ÷ 1000, which is 0.1, or 10%.

Let’s take another example…

  • Let’s say you open a new account with $10,000;
  • You trade for a couple months and show $1,500 in profit so you take out $1,000 as salary;
  • Another month goes well and you’ve made $900 in profit, and decide to take $500 as salary;
  • You have a great few weeks and see $1,200 in profit in your trades. It’s your birthday and your favorite Uncle Benny gives you $800, which you decide to add to your trading account;
  • The next month is tougher and you lose $400 in trading.

Now you want to step back and get one rate of return that summarizes all this activity. How are you going to do that?

Map it out – Separate each event like this:
Trade Results Additions /
Ending of Period

Would it be correct to simply take the [ (ending value – beginning value) ÷ beginning value ] ? That’s how Simple Returns are calculated, and you’d come up with (12,500-10,000) ÷ 10,000 = 25%.

That is one way to do the math, but it’s not very satisfying or super-accurate for our purposes because it does nothing to separate out our trading profits from our salary or our gift from Uncle Benny. It’s fast and easy, but it’s not how a professional would think. This example shows us why we really need a much more sophisticated approach to calculating our return percentage. Let’s see how…

Holding Periods

Each Addition or Subtraction Creates a New Holding Period

Each time you add or withdraw funds from your account as a manual adjustment, you bring one “Holding Period” to a completion. Within the Trade Log you do this by clicking Edit Equity next to an account listing, then clicking the link Add a manual adjustment. You can see two such examples highlighted in pink in this screen shot:

screenshot from the Forex Smart Tools Trade Log

That’s all you have to do to close off a Holding Period. Behind the scenes, the powerful Trade Log takes over and starts to do the math for you. The Log then calculates the TW ROR for each holding period separately:

Holding PeriodBeginning of PeriodTrade ResultsAdditions / WithdrawalsEnding of PeriodTW ROR
Now Compound

The next step in coming up with the Compounded Time Weighted Rate of Return is to compound these individual holding periods into one combined number. Again, the Trade Log is doing this automatically for you. But if you wanted to do it manually, here is the formula for compounding (HPR means holding period return):

[(1 + HPR1)*(1 + HPR2)*(1 + HPR3) … *(1 + HPRN)] – 1

In our example above, we’d take [ (1+.15) x (1+.0857) x (1+.1101) x (1-.031) ] -1 = 34.31%

This is a very accurate value and really represents the results of all this activity in our account. Now you’re getting the results that a professional trader would expect and demand.

Combining Accounts

The above example was certainly complex, but think of this: it all took place within one account. What if you have multiple accounts you want to consider all at once and each account may have been funded at different dates, with different amounts and different activity within each.

Or what if you are a professional money manager and want to track your individual clients’ activity with great accuracy. Each of your clients may be adding or pulling their own funds at different dates, and new clients may come on board at different times.

The powerful Trade Log will handle all these situations for you with ease in the same manner. The compounded time weighted rate of return is the appropriate metric for measuring these situations.

You can choose Manage Accounts within the Broker Account dropdown menu on the Summary page. From that dialog you can set up any number of groups that you wish. Each group can be composed of any number of accounts. If you are a professional fund manager, you can set up individual accounts for each one of your clients, and use this feature to create an aggregate group of all your clients together to see and report on the result of all your trading. This approach also makes it easy to generate individual reports for each of your clients, giving them their trade results with Compounded Time Weighted Rate of Return accuracy.

Screenshot from the Forex Smart Tools Trade Log
Let’s Take An Example…
  • Let’s say you open a new account with broker GoForBroke with $4,000;
  • You trade for a couple months on this account and show $1,000 in profit;
  • You decide things are going well and you want to diversify. You open an account with broker Where’sMyMoney with $2,000;
  • In the next couple months you make $800 on the GoForBroke account and $300 on the Where’sMyMoney account;
  • You want to cash in on some of your profits in the GoForBroke account so you take a salary of $200. At the time you do that you are up $850 in GoForBroke and $350 in Where’sMyMoney;
  • You’re ready to retire from your day job and trade full time. You take an early-retirement bonus of $9000 and deposit it all into a new account with broker GoodLuck;
  • At the time you funded GoodLuck, you were up $600 on the GoForBroke account and $100 on the Where’sMyMoney account.
  • Now you ask the Trade Log to spit out a Rate of Return or Equity % for all this activity. You create a new broker grouping with these three accounts and specify a time period to look at that spans the initial funding date of the first account all the way up until today. Let’s see what the Trade Log does with this information:

Notice by the way how obviously wrong a “simple return” approach would be to this challenge. To take the $18,600 you have at the end and simply subtract the $4,000 you had at the beginning, divided by the beginning, would give you an answer of 365%, which is totally meaningless in this case. We clearly need a more sophisticated approach to the problem!

Each Addition, Subtraction or Account Creation Ends a Holding Period

In the table below, the event which triggers the end of a holding period is highlighted in blue.

The first holding period begins when the first brokerage account (GoForBroke) is created. (It could also be the case that we query the Trade Log for a report for a specific time frame, like “last year”. In that case, the first holding period begins at the first date of whatever date range we specify).

The first holding period closes when the second account is created (with broker Where’sMyMoney).

The second holding period closes when you pull the $200 salary. It doesn’t matter which account this happens on. Any addition or withdrawal triggers the end of one holding period and the beginning of a new holding period.

The third holding period closes when you open account GoodLuck.

When the new account(s) are funded, those are treated like additions to the fund.

Map it out – Separate each account and each event like this:
TimeBeginning GoForBrokeBeginning Where’sMy$Beginning GoodLuck Trade ResultsAdditions / WithdrawalsEnding of Period
20000850 + 350-2008,000
Now calculate the TW ROR for each individual holding period:
(end – beginning + withdrawals – additions) / beginning
TW ROR Result
1( 7000 – 4000 + 0 – 2000) / 400025%
2( 8000 – 7000 + 0 + 200) / 700017.14%
3( 17,700 – 8000 + 0 – 9000) / 80008.75%
And now… compound each period into one net return figure:
[ (1+.25) x (1+.1714) x (1+.0875) ] – 1 = 59.24%

What Joy for a Fund Manager !

So if you were a fund manager who trades for several individual clients, what you do is just like the above example in which an individual trader has several different accounts that they traded all at once. Change the name of each broker in the above example to Tom, Dick or Harry – your three clients – and you get the idea.

Without this sophisticated approach that the Trade Log automatically provides, it becomes very difficult to be able to give each of your clients an accurate report for their own trading results, and a comparative report for the fund as a whole. The Trade Log can handle this challenge with ease now using Compounded Time Weighted Rates of Return.

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