Thoughts on measuring percentage gains:

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Thoughts on measuring gains:

If the index is up 1% and you are up 10%, are you doing ten times better than the index? I don’t think so. Let’s take it back a step for a simple view, and have the index flat but you are up 10%. So if someone else started with $100 invested in the index, and the index was flat they’d now still have $100. You are up 10% to $110. Are you doing infinitely better than the index? No way! You are 10% ahead of the guy who invested in the index.

And if the index was up 0.1%, are you suddenly doing 100 times better than the index with your 10%? No, our friend has $100.10 and you have $110.00, and you are 9.9% better off than he is.

So going back to the initial question, if the index is up 1% and you are up 10%, are you doing ten times better than the index? You’ve got it now. The guy who invested in the index has $101 and you have $110 so you are 110/101 or 8.9% better off than him.

Thinking of it otherwise gives you some strange results. For example, our friend is up 1% and you are up 50%. Are you doing 50 times better? If so, and if you are both up 1% today, so he’s up 2% and you are up 51%. Are you suddenly doing only 25.5 times better. Again, no way! When our friend is up 1% and you are up 50% he’s got $101 and you have $150 so you are 48.5% better off than he is, not 50 TIMES better off. And when he’s at $102 and you are at $151, you are doing 48.0% better than him.

And if your favorite investing newsletter (fictional) is up 500% since inception, and the index is up 400% in the same time, is the newsletter doing 100% better than the index? This is not a trick question! The investor in the index has grown his $100 to $500. You have grown your $100 to $600. You are 20% better off than he is, not 100%.

I was thinking about this because of a newsletter ad that said that they were up 1000% more than the S&P in a given amount of time. First of all, that impressive sounding 1000% is just 10 TIMES. So you need to know how much they are talking about. If the index was up just a tenth of a percent, they could crow about that with a gain of one whole percent, which would be insignificant. If the index was up by 1%, they just need a 10% gain, which is somewhat better. If the index was up 50%, and they were up 500%, that would be impressive! But in all three cases they could say that they were up 1000% more than the S&P.

The message is to pay attention to what you are being told and figure out what it really means.

Best,

Saul

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First of all, thanks for the clear post on a tricky topic.

I am kinda sorta a math geek, but my wife really is (informal vs. formal education), and it constantly amazes us how people not only do math incorrectly but interpret the results incorrectly. And I think you meant your post to be on the serious side, but it had me laughing and/or chuckling the whole time.

I call what you are getting at common sense (or cents?), but I have heard it described as critical thinking.

Fun games can, and are, had with numbers, especially statistics and percentages. My wife would have a bunch of corny (to me even) jokes about this subject, but I cant think of any now.

You are a wise sage to us on this board Saul, and I for one appreciate your posts and thoughts. I say that with a bit of levity because I don’t really know you, and don’t know whether that will go to your ego and eventually end up with negative consequences to all involved, but there is some truth to it even so.

respectfully,
Robert

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First of all, thanks for the clear post on a tricky topic… You are a wise sage to us on this board Saul, and I for one appreciate your posts and thoughts.

Hi Robert,

Thanks for your kind words.

Best,

Saul

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If the index is up 1% and you are up 10%, are you doing ten times better than the index? I don’t think so. Let’s take it back a step for a simple view, and have the index flat but you are up 10%. So if someone else started with $100 invested in the index, and the index was flat they’d now still have $100. You are up 10% to $110. Are you doing infinitely better than the index? No way!

Dividing by zero is generally frowned upon. B^)

Generally speaking - at least from this relative novice’s perspective - comparative gains seem to be measured with a “if I put the same amount of money in each instrument, what would I have later?” approach. To me, that makes the most sense.

Manipulating percentages for the sake of a comparison might be rewarding, but - as you point out - it can be highly deceptive and not terribly informative.

Good post.

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I missed one of the best examples: If the index was up 1% after six months and a newsletter recommendations were up 2%, would it make any sense for them to say they were up 100% more than the index??? Or up “twice as much” as the index. They are at $102 and the guy who invested in the index is at $101 ! The absolute value of the numbers matter. The $101 and $102 could reverse tomorrow. If it was $125 and $150 that would be more meaningful at least.

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