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Monday, October 17, 2016

Capitalism Baby


How using non-compounded returns can actually make you look better. 
More smoke and mirrors when bragging about returns.

A clever way to confuse not so knowledgeable traders when talking about performance is to just report "returns" and specify that they are "non-compounded" returns. Implying something like "Imagine if I were compounding them. It would be even better".

In our minds, the term "compounded" has connotations of greatness and we have a tendency to believe that, if you are talking to me about non-compounded returns, then, man, thanks for doing that and being so honest and punishing yourself because you could make yourself look so much better if you showed your compounded results.

However, as with many other areas in trading, you always have to do your homework. But first, let's remember what compounding is.

According to Investopedia:
"The compound return is the rate of return, usually expressed as a percentage, that represents the cumulative effect that a series of gains or losses have on an original amount of capital over a period of time."

...And you didn't see much difference there.

Let's go with an example:

Let's say you have a $10,000 account.
After two months of trading it, the account balance is $11,449

Your account growth is +14.49%
Your compounded return (on a monthly basis) is 7%:

First month    : +7% (from $10,000 to $10,700)
Second month: +7% (from $10,700 to $11,449)

Your average monthly return (7.245% = 14.49 / 2) is in fact better than your compounded monthly return.


Trader A can be talking about his non-compounded returns, and Trader B can be talking about his compounded returns. Trader A mentions a greater return than Trader B, however both accounts have grown by the exact same amount. Here's the case:

Both traders start the year with a $100,000 account.

Trader A (non-compounded)
January:   +$3000  (+3%)
February: +$4000  (+4%)
Final account balance: $107,000. Real account growth: +7%

Trader B (compounded)
January:   +$3000  (+3%)
February: +$4000  (+3.88%)
Final account balance: $107,000. Real account growth: +7%. (Even though you'd get 6.88% if you arithmetically add 3 and 3.88)


Trader A always calculates his monthly returns in respect with the original $100,000 amount at the beginning of the year. That's why he reflects +4% in February.

Trader B always calculates monthly returns in respect with the account balance at the end of the previous month. That's why February's +$4000 only represents +3.88% in respect with the account balance at the end of the previous month $103,000.

In both cases, both traders have grown their accounts by the same amount of dollars ($7,000). Yet, if you were not seeing a total amount in dollar terms you are almost guaranteed to get confused. Smoke and mirrors folks.

Most websites out there simply show a percentage number for each month. So, you typically see twelve percentage numbers for an entire year. If Traders A and B posted their returns on their websites, you would see January +3%, February +4%, and then you'd see January +3%, February +3.88%. Without any other context, you immediately think that the first case is better than the second one. Furthermore, if Trader A, in addition to this, tells you: "By the way, my returns are non-compounded returns (imagine if I were compounding them)". Now you are totally convinced that Trader A doesn't have slightly better but MUCH better results than Trader B. In reality, they are both performing equally.

This always leads me back to my point that, there are so many ways to confuse people with fancy maths, that the cleanest, most honest way to talk about performance is to say: hey, I started with a $10,000 account, and it is now a $13,000. I am up 30%. That's it. No last names. No fancy financial terms.

For more information on reporting performance numbers and other clever tricks that exist all over the Internet, read my article Measuring Portfolio's Performance. You will be a much harder to deceive trader going forward.

Cheers,
LT

Related Articles:
Trading with realistic expectations
How much capital do you need to trade for a living
Measuring Portfolio's Performance


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