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# weird annualized rule about return?

Discussion in 'Strategy Building' started by yoyo2000, Oct 3, 2005.

1. ### yoyo2000

I met a weird annualized rule:
as usual,in order to annualize a monthly return,one should multiplies this monthly return with square root of 12,but when a guy compounds his capital,this rule become weird:
Suppose a system's monthly return is 100%,so his yearly return should be (100%+1)^12-1= 4095% with compounding his capital,but in square root of 12 rule,his year return is 100%*square root(12) = 346% ,the difference is so huge!

what's wrong?

2. ### acrary

You multiply by the square root of 12 to annualize the monthly standard deviation, not the return.

3. ### Thunderdog

You are not quite correct in that a 100% monthly return results in an annualized return of 409,500% if compounded monthly. Your formula is correct:

(1+1.00)^12-1=4,095. However, you forgot to multiply the result by 100 in order to present the annualized return in percentage terms.

Anyone who disagrees can prove it to himself by doing it by hand by simply doubling the starting capital 12 times. It only takes a moment or two. Starting with capital of only \$1,000 at the beginning fo the first month you will reach \$4,096,000 at the end of the year. Subtract from the total the original \$1,000 capital base, and you have a net profit of \$4,095,000 which is an annualized return of 409,500%

As for the second part of your post, it also works backwards, remembering to present the percentage return in decimal terms in the equation (dividing by 100):

(4,095+1)^(1/12)-1=1.00. This 1.00 represents the 100% monthly return (in decimal terms), and is the geometric mean rather than the arithmetic mean. You must use the geometric mean to account for the monthly compounding effect. This is a simple time value of money calculation.

Please confirm the validity of my calculations since it has been 21 years since I completed my MBA and I have never encountered scenarios with such astronomical returns in my previous life as a banker. Those decimal points can get lost in such lofty numbers, eh?

As an aside, this is why I think that people who claim to be able to double their money on a monthly basis are well and truly quite full of shit.

It depends on what they mean. If they are pulling the original amount out every month, then it is absolutely possible. But compounding at 100% may not be a likely scenario; although anything is possible.

5. ### Thunderdog

There is a wide chasm between possible and even remotely likely. Why would someone want to take out his money when it can earn so much so quickly in his trading account? Living expenses?! Of course, the markets will not allow such a trading god to compound to the moon because of liquidity constraints and all the other usual reasons, but why not take it to the limit of what the markets and his method can tolerate? There are a number trading billionaires whose returns never came even remotely close to those kinds of monthly returns. So why is the guy who makes 100% a month not among them? Why would he need to pull out the original amount every month and prevent himself from owning the world in just a few short years?

Since even the greatest trading legends have never consistently made 100% monthly returns, I think I will stick to my guns and confidently assume that such poseurs on ET and elsewhere are well and truly quite full of shit.

6. ### Thunderdog

Since ES is doing very little at the moment (and I'm bored), let us explore the matter a bit further. Let me present a gross exaggeration first to make a point, and then a relatively more "plausible" scenario.

First the outrageous scenario. Consider a chess board, which has 64 squares. Imagine that you place a single penny on the first square (the corner of your choice). If you then subsequently double the amount of the preceding square, by the time you reach the 64th square you will have theoretically achieved more wealth than all the wealth of this world. In dollar terms, the last square will have a value of \$1.84467 x 10^17. I believe this is in the quadrillions (which come after trillions). If each square were to represent one month, then the theoretical wealth will have been achieved in just over 5 years.

Of course, this example is patently absurd. Therefore, let us pare it down to more "reasonable" levels based on your assertion that it is "absolutely possible" to consistently make 100% monthly returns. You are not comfortable with the idea of monthly compounding, presumably for the reasons I mentioned in my prior post (liquidity, etc.). Therefore, let us consider the possibility that he does reinvest all his winnings and seeks to expand the markets he trades in to overcome liquidity issues. He can do so by expanding to international markets and by hiring other traders to trade his method. Even so, the growing size of his account will likely degrade his method and his strategy will no longer be able to achieve 100% monthly returns because he is reinvesting (compounding). Therefore, let us assume that he is only able to achieve a quarter of his earlier performance, a "mere" 25% monthly return when reinvested. This would mean that if he were to start with only \$10,000, he would have net profits before overheads of almost \$16 Billion after only 64 months. Not bad if you can get it. Just as a matter of interest, if he could "only" achieve a monthly return of 20% (which is reinvested), he would have profits before overheads of over \$1.1 Billion. A 30% reinvested return would yield profits before overhead of over \$196 Billion. You choose.

So, my question to you is this: where are all these traders who are able to make 100% monthly returns and why are they not reinvesting, regardless of the degradation of their methods? Presumably, if they only applied themselves they could displace the Soros, PTJs, Cohens, and all the other legends of the trading world in a matter of a few years. Even those guys never even dreamed of consistent 100% monthly returns and look where they are.

Therefore, I will continue to abide by the conclusions of my 2 earlier posts: BS.

7. ### yoyo2000

Well,100% return per month just an example to magnify the effect of calculation.

8. ### TheStudent

Never heard of using square roots to annualize return.

Returns expand geometrically with time.

Volatility, however, expand geometrically with the square root of time.

9. ### yoyo2000

it's very weird,I saw that there are 7 reply to my post from list,but when I enter,I couldn't find only 3,how can I see other 4 reply,please?

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