## Monthly return vs annual return for investment growth analysis?

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Topic Author
schrute
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### Monthly return vs annual return for investment growth analysis?

Does it make sense to look at investment growth based on monthly deposits or annual deposits? If I look to make \$1,000 monthly deposits (\$12,000 annually) for 10 years at a rate of 8% annual return, I yield the following:

Monthly deposits (additions made 12x per year based on the above): 182,946.04
Annual deposits (addition made 1x per year and calculated at the end of compounding period): 173,838.75
Difference: ~\$11,000

That means compounding .667% per month. I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
David Jay
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### Re: Monthly return vs annual return for investment growth analysis?

You have created a “selection” artifact.

If instead you were to calculate the annual deposit at the beginning of the compounding period, “Annual Deposits” would outperform monthly by a similar amount. If you calculate the annual deposit as June 30, the two numbers will be within a whisker of each other (tiny variations from year to year, averaging out over, say, analysis periods of more than 5-10 years).

It’s “time in the market”.
Prediction is very difficult, especially about the future - Niels Bohr | To get the "risk premium", you really do have to take the risk - nisiprius
Topic Author
schrute
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### Re: Monthly return vs annual return for investment growth analysis?

David Jay wrote: Tue Sep 01, 2020 8:28 pm You have created a “selection” artifact.

If instead you were to calculate the annual deposit at the beginning of the compounding period, “Annual Deposits” would outperform monthly by a similar amount. If you calculate the annual deposit as June 30, the two numbers will be within a whisker of each other (tiny variations from year to year, averaging out over, say, analysis periods of more than 5-10 years).

It’s “time in the market”.
Well, isn't "time in the market" based on the culmination of investments which in this example would be monthly?
David Jay
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### Re: Monthly return vs annual return for investment growth analysis?

If you want to calculate monthly, that’s fine. It’s just 12 times more entries.

But the long term results will be almost identical to a June 30 annual deposit (because average time in the market of 6 months for the entire year’s deposits is the same as 12 monthly deposits).
Prediction is very difficult, especially about the future - Niels Bohr | To get the "risk premium", you really do have to take the risk - nisiprius
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### Re: Monthly return vs annual return for investment growth analysis?

schrute wrote: Tue Sep 01, 2020 8:13 pmThat means compounding .667% per month. ... is this a more "accurate" representation to look at monthly vs annual deposits?
If you expect to invest monthly, then it would be more accurate to model that way. But you should not use one-twelfth of 8% as the monthly rate. That would compound to about 8.3% annually. The following shows formulas for computing the future value with yearly or monthly investments made at the start, end, or middle of each period using the Excel FV function. (The formulas in cells C5:C7 are copies of the formulas in cells B5:B7.)

Code: Select all

``````Row       Col A    Col B    Col C   Formulas in column C
1               Yearly  Monthly
2        Rate  8.0000%  0.6434%  =(1+B2)^(1/12)-1
3     Periods       10      120  =B3*12
4  Investment   12,000    1,000  =B4/12
5    At start  187,746  181,283  =FV(C2,C3,-C4,0,1)
6      At end  173,839  180,124  =FV(C2,C3,-C4,0,0)
7   At middle  180,659  180,703  =FV(C2,C3-1,-C4,-C4,0)*(1+C2)^(1/2)``````
Cell B7 confirms David Jay's observation that making the entire annual investment at mid-year produces about the same result as making one-twelfth of it each month.
FiveK
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### Re: Monthly return vs annual return for investment growth analysis?

schrute wrote: Tue Sep 01, 2020 8:13 pm I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
The greatest inaccuracy is likely to be the return itself, whether you specify monthly or annual. E.g., compare annual returns of 6% vs 8% vs 10%, regardless of whether you use monthly or annual compounding.
Topic Author
schrute
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### Re: Monthly return vs annual return for investment growth analysis?

FiveK wrote: Tue Sep 01, 2020 11:34 pm
schrute wrote: Tue Sep 01, 2020 8:13 pm I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
The greatest inaccuracy is likely to be the return itself, whether you specify monthly or annual. E.g., compare annual returns of 6% vs 8% vs 10%, regardless of whether you use monthly or annual compounding.
What do you mean? That annual returns won't be exactly 6, 8, or 10% because of variations or that can't really predict future returns?
FiveK
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### Re: Monthly return vs annual return for investment growth analysis?

schrute wrote: Wed Sep 02, 2020 1:00 am
FiveK wrote: Tue Sep 01, 2020 11:34 pm
schrute wrote: Tue Sep 01, 2020 8:13 pm I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
The greatest inaccuracy is likely to be the return itself, whether you specify monthly or annual. E.g., compare annual returns of 6% vs 8% vs 10%, regardless of whether you use monthly or annual compounding.
What do you mean? That annual returns won't be exactly 6, 8, or 10% because of variations or that can't really predict future returns?
The latter.

Topic Author
schrute
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### Re: Monthly return vs annual return for investment growth analysis?

FiveK wrote: Wed Sep 02, 2020 1:18 am
schrute wrote: Wed Sep 02, 2020 1:00 am
FiveK wrote: Tue Sep 01, 2020 11:34 pm
schrute wrote: Tue Sep 01, 2020 8:13 pm I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
The greatest inaccuracy is likely to be the return itself, whether you specify monthly or annual. E.g., compare annual returns of 6% vs 8% vs 10%, regardless of whether you use monthly or annual compounding.
What do you mean? That annual returns won't be exactly 6, 8, or 10% because of variations or that can't really predict future returns?
The latter.

Fair point, but if you're not withdrawing and instead depositing, this should be less of a concern in this case, right?
FiveK
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### Re: Monthly return vs annual return for investment growth analysis?

schrute wrote: Sat Sep 05, 2020 5:49 pm
FiveK wrote: Wed Sep 02, 2020 1:18 am
schrute wrote: Wed Sep 02, 2020 1:00 am What do you mean? That annual returns won't be exactly 6, 8, or 10% because of variations or that can't really predict future returns?
The latter.
Fair point, but if you're not withdrawing and instead depositing, this should be less of a concern in this case, right?
Sequence of returns matters just the same - only the effect is reversed. When depositing, one wants the early returns to be negative, and the later returns to be above average.
dbr
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### Re: Monthly return vs annual return for investment growth analysis?

schrute wrote: Tue Sep 01, 2020 8:13 pm Does it make sense to look at investment growth based on monthly deposits or annual deposits? If I look to make \$1,000 monthly deposits (\$12,000 annually) for 10 years at a rate of 8% annual return, I yield the following:

Monthly deposits (additions made 12x per year based on the above): 182,946.04
Annual deposits (addition made 1x per year and calculated at the end of compounding period): 173,838.75
Difference: ~\$11,000

That means compounding .667% per month. I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
You "look" at what you actually do. If the question is do you have more money in the end if you put in \$1000/mo rather than \$12,000 at the end of a year, then you will because the money is in the account a little longer. If you put in that \$12,000 at the beginning of each year then you would have more. You also have to decide if the monthly contributions are at the beginning of the month or at the end. Check out the format for the Excel function FV(rate,nper,pmt,(pv),(type)) type=0 end of period type=1 begin of period.
Topic Author
schrute
Posts: 337
Joined: Wed Nov 05, 2014 2:27 pm

### Re: Monthly return vs annual return for investment growth analysis?

dbr wrote: Sat Sep 05, 2020 6:40 pm
schrute wrote: Tue Sep 01, 2020 8:13 pm Does it make sense to look at investment growth based on monthly deposits or annual deposits? If I look to make \$1,000 monthly deposits (\$12,000 annually) for 10 years at a rate of 8% annual return, I yield the following:

Monthly deposits (additions made 12x per year based on the above): 182,946.04
Annual deposits (addition made 1x per year and calculated at the end of compounding period): 173,838.75
Difference: ~\$11,000

That means compounding .667% per month. I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
You "look" at what you actually do. If the question is do you have more money in the end if you put in \$1000/mo rather than \$12,000 at the end of a year, then you will because the money is in the account a little longer. If you put in that \$12,000 at the beginning of each year then you would have more. You also have to decide if the monthly contributions are at the beginning of the month or at the end. Check out the format for the Excel function FV(rate,nper,pmt,(pv),(type)) type=0 end of period type=1 begin of period.
No, I guess what's an accurate way to forecast the growth? At the beginning, of course it will be bigger. Instead, does just dividing /12 the annual interest make more sense? While imperfect and not indicative of actual market performance, at least that average is a 'better' reality of returns over the year? Of course there can be losses, but these are deposits only for now.
abuss368
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### Re: Monthly return vs annual return for investment growth analysis?

schrute wrote: Tue Sep 01, 2020 8:13 pm Does it make sense to look at investment growth based on monthly deposits or annual deposits? If I look to make \$1,000 monthly deposits (\$12,000 annually) for 10 years at a rate of 8% annual return, I yield the following:

Monthly deposits (additions made 12x per year based on the above): 182,946.04
Annual deposits (addition made 1x per year and calculated at the end of compounding period): 173,838.75
Difference: ~\$11,000

That means compounding .667% per month. I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
A monthly return is almost meaningless and the same argument could be made for an annual return. Honestly I stopped calculating years ago and focused instead on looking for ways to increase the savings rate. That is your better strategy.
John C. Bogle: “Simplicity is the master key to financial success."
dbr
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### Re: Monthly return vs annual return for investment growth analysis?

schrute wrote: Sat Sep 05, 2020 6:49 pm
dbr wrote: Sat Sep 05, 2020 6:40 pm
schrute wrote: Tue Sep 01, 2020 8:13 pm Does it make sense to look at investment growth based on monthly deposits or annual deposits? If I look to make \$1,000 monthly deposits (\$12,000 annually) for 10 years at a rate of 8% annual return, I yield the following:

Monthly deposits (additions made 12x per year based on the above): 182,946.04
Annual deposits (addition made 1x per year and calculated at the end of compounding period): 173,838.75
Difference: ~\$11,000

That means compounding .667% per month. I realize actualities are different (sometimes investments go down some months), but is this a more "accurate" representation to look at monthly vs annual deposits?
You "look" at what you actually do. If the question is do you have more money in the end if you put in \$1000/mo rather than \$12,000 at the end of a year, then you will because the money is in the account a little longer. If you put in that \$12,000 at the beginning of each year then you would have more. You also have to decide if the monthly contributions are at the beginning of the month or at the end. Check out the format for the Excel function FV(rate,nper,pmt,(pv),(type)) type=0 end of period type=1 begin of period.
No, I guess what's an accurate way to forecast the growth? At the beginning, of course it will be bigger. Instead, does just dividing /12 the annual interest make more sense? While imperfect and not indicative of actual market performance, at least that average is a 'better' reality of returns over the year? Of course there can be losses, but these are deposits only for now.
You forecast growth of actual investments by invoking a statistical model and calculating a distribution of possible outcomes. Uncertainty is reflected in the breadth of the distribution and there is additional uncertainty in trying to estimate the parameters of the distribution including the fact that successive returns are not completely independent and that the imagined distribution changes in time as well. Even what sort of distribution might be a good model for investment returns is a question. Even so at least a picture of the structure can be obtained this way. There are many models both using historical data and using Monte Carlo methods to try to do these things. An old but easy to use example is www.firecalc.com You have to look through the options for how to set up the model depending on what you want to see, starting with savers enter that expenses are zero and use the "not yet retired" tab.

What is it you actually want to know or try to estimate?