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S&P Average Total Returns by Month Going Back to 1926
By JLP | October 2, 2009
The above graphic shows the average total returns for the S&P 500 Index* by month of the year going back to 1926.
Notice the only month to have a negative average return is September (-.75%). February, with it’s average total return of .06% (that’s six-tenths of one percent) is the second worst month. The two best months on average are July and December with average returns of 1.83% and 1.75%, respectively.
What I found interesting was that the average monthly return from January 1926 through September 2009, was .93%. Not too bad. But…that only tells part of the story. The real story is the standard deviation of those monthly returns, which is 5.56%. This means that two-thirds of the time, the monthly total return can fall between -4.63% (.93% – 5.56%) and 6.48% (.93% + 5.56%). In other words, these returns are quite volatile.
UPDATE: BG, in the comments below, brought up an important point. I mentioned the monthly average of .93% for all the months from January 1926 through September 2009. That’s the average, which is not what you would have received as your rate of return for the 1,005 months. Rather, your actual rate of return over those 1,005 months would have been .77% (not adjusted for inflation). That’s A LOT smaller number than .93%. How much smaller? Let’s see:
compared to…
Average rates of return grossly overstate actual returns. And, the greater the time period, the greater the exaggeration.
Thanks for bringing up the discrepancy, BG.
*The S&P 500 was composed of 90 stocks prior to February 1957.
Topics: S&P 500 Index | 8 Comments »
October 2nd, 2009 at 6:47 pm
I noticed that you are using arithmetic mean (average) for this chart — did you do the same for the underlying data?
A +50% return and a -50% return (in any order) has an arithmetic average of 0%, but it’s geometric average is -13%…
October 2nd, 2009 at 6:54 pm
Yeah, I meant to mention that the geometric mean for ALL the monthly data is .77% (compared to the average of .93%). I understand the shortcomings of using averages for computing purposes.
October 3rd, 2009 at 1:34 pm
JLP) Are the individual monthly averages you have listed in the chart the arithmetic or geometric average? Are there more red months other than September?
For your other readers who may not understand geometric averages: A 20% drop requires a gain of 25% to offset. This means that -20% and +25% have a geometric average of 0% (break-even).
October 3rd, 2009 at 2:55 pm
The monthly numbers are average numbers because it wouldn’t make sense to do a geometric average for that data. In other words, what I was trying to illustrate with the data is the average return for each month going back to 1926. The only way a geometric average would be beneficial to know in this case is if a person was planning on investing in one particular month.
The geometric average for all the months is more beneficial and useful.
October 3rd, 2009 at 6:04 pm
Although the actual return brought the numbers down a lot i would not worry too much about it and think that you can beat the index. The SD from month to month is a lot higher than i had expected I admit it is a lot more volatile on a monthly basis that i had expected. I always look at the SD on a yearly basis good information! Thanks you
October 3rd, 2009 at 8:19 pm
JLP said: “The monthly numbers are average numbers because it wouldn’t make sense to do a geometric average for that data.”
I disagree, example:
Month A: +10%, -10%
Month B: +20%, -20%
By using the arithmetic average, you are concluding that Month A is no better or worse than Month B (both are averaging 0%).
Using geometric means, I would say that Month A is better than Month B because Month A ends the simulation with more money in your account (what really matters).
You said: “Average rates of return grossly overstate actual returns. And, the greater the time period, the greater the exaggeration.” I agree with that statement completely, and you are currently “grossly overstating” the monthly returns because you are relying on arithmetic averages. Unless your intent _is_ to grossly overstate the monthly returns…
October 4th, 2009 at 6:32 pm
Now I’m under the impression that it isn’t necessarily the time period that throws of the difference of the two ways of calculating returns, it’s the negative returns. If you have no negative returns they should be about the same. The more negative returns or even just one big negative return is what makes the biggest exaggeration. Does that sound right to you?
October 5th, 2009 at 11:29 am
#7) The only reason time comes into play is because you have 1005 months for the error to compound (exponential error). A seemingly tiny difference, compounded 1005 times becomes a huge difference. For the monthly averages, you have 83 chances (1005/12) for the errors to compound.
As for negative numbers only causing the error, not necessarily true:
$100 invested at +15%, +15% yields: $132.15
$100 invested at +10%, +20% yields: $132.00
In the case above, both have arithmetic averages of 15%, but the geometric means are 15% and 14.89% respectively. That tiny 0.11% difference will compound over a large timeframe.
Negative rates using arithmetic averages will cause larger errors than otherwise, as you suspect — but the error is there whether you have negative returns or not.
http://en.wikipedia.org/wiki/Exponential_error