Different Ways to Calculate Rates

[InsaneZane1]

userque posted a comment in another thread in this forum about different ways to calculate return rates. I believe he didn't seek out to stir up trouble, and that he only really meant to make others more aware that there are different ways to calculate rates. I'm going to use my 2013 month-to-month returns as an example:

Jan = 5.82% = 1.0582
Feb = 0.85% = 1.0085
Mar = 3.66% = 1.0366
Apr = 2.28% = 1.0228
May = 1.44% = 1.0440
Jun = (1.17%) = 0.9883
Jul = 5.89% = 1.0589
Aug = (2.13%) = 0.9787
Sept = 0.66% = 1.0066
Oct = 2.41% = 1.0241
Nov = 2.15% = 1.0215
Dec = 1.94% = 1.0194

Here are a few methods I know of to calculate EOY return rates:

Method 1: Simple addition
This is nothing more than finding the sum of all of the percentages above. I get 23.80%.

Method 2: Factor in Monthly Compounding
As userque suggested in the other thread, this is more complicated, but the simple explanation is to do the following:
1. Multiply all of the monthly returns together (e.g., 1.0582 x 1.0085 x 1.0366 x ......) = 1.2619
2. Subtract 1 from result achieved in step 1: 1.2619 - 1 = 0.2619
3. Multiply result of step 2 by 100: 0.2619 x 100 = 26.19%

You can also get info on how to do this from the TSP site at https://www.tsp.gov/PDF/formspubs/oc05-16w.pdf .

Method 3: Divide current balance (or balance at end of year in question) by sum of total contributions made and EOY balance of previous year
1. Obtain EOY balance from previous year by logging into TSP account and setting "Balance As Of..." date to the last day of December in the previous year. In my case, it would be the balance from 12/31/2012.
2. Obtain YTD/EOY total contributions for year that you are calculating for. In this case, I would use "Balance As Of..." 12/31/2013 and obtain total contributions made from the Contributions tab.
3. Divide EOY balance for 2013 by sum of numbers obtained in steps 1 and 2. --> EOY Bal / (P-EOY Bal + Cont)
4. Subtract 1 from result of step 3
5. Multiply result of step 4 by 100. Using this method I came up with 24.30% for my own account.

So, using the 3 different methods above, I came up with 3 completely different results:
1. Simple Addition = 23.80%
2. Compounded = 26.19%
3. EOY-(P-EOY+CONT) = 24.30%

I believe what userque was alluding to was that Method 2 is technically the more accurate way of calculating the return rate. Perhaps userque can chime in, however, and clarify whether this is indeed the case, or if a method I did not explain above is more "technically correct".

[chpwolf]

I have to question method 2 as being the most accurate, or even accurate at all.

Here are the numbers from my 2014:


Jan
1.1802


Feb
1.2445


Mar
1.2073


Apr
1.172


May
1.1918


Jun
1.2368


Jul
1.1408


Aug
1.1914


Sep
1.0848


Oct
1.074


Nov
1.0713


Dec

1.0338


(* all)

5.372357


(sub 1)

4.372357


* by 100

437.2357




Am I missing something?

[Cactus]

I don't think your monthlies are correct. You are saying you made 18% in Jan and then 24% in Feb on top of that, etc.

I'd be happy to get that in a year. I can't see getting that in a month.

[chpwolf]

I thought I replied, but do not see it.
It could very well be that I'm using incorrect numbers. I was using the 12 month PIP that TSP shows every ~3rd day of the month. Should I use something else or calculate a monthly return in a different manner?

[Boghie]

userque posted a comment in another thread in this forum about different ways to calculate return rates. I believe he didn't seek out to stir up trouble, and that he only really meant to make others more aware that there are different ways to calculate rates. I'm going to use my 2013 month-to-month returns as an example:

Jan = 5.82% = 1.0582
Feb = 0.85% = 1.0085
Mar = 3.66% = 1.0366
Apr = 2.28% = 1.0228
May = 1.44% = 1.0440
Jun = (1.17%) = 0.9883
Jul = 5.89% = 1.0589
Aug = (2.13%) = 0.9787
Sept = 0.66% = 1.0066
Oct = 2.41% = 1.0241
Nov = 2.15% = 1.0215
Dec = 1.94% = 1.0194

Here are a few methods I know of to calculate EOY return rates:

Method 1: Simple addition
This is nothing more than finding the sum of all of the percentages above. I get 23.80%.

Method 2: Factor in Monthly Compounding
As userque suggested in the other thread, this is more complicated, but the simple explanation is to do the following:
1. Multiply all of the monthly returns together (e.g., 1.0582 x 1.0085 x 1.0366 x ......) = 1.2619
2. Subtract 1 from result achieved in step 1: 1.2619 - 1 = 0.2619
3. Multiply result of step 2 by 100: 0.2619 x 100 = 26.19%

You can also get info on how to do this from the TSP site at https://www.tsp.gov/PDF/formspubs/oc05-16w.pdf .

Method 3: Divide current balance (or balance at end of year in question) by sum of total contributions made and EOY balance of previous year
1. Obtain EOY balance from previous year by logging into TSP account and setting "Balance As Of..." date to the last day of December in the previous year. In my case, it would be the balance from 12/31/2012.
2. Obtain YTD/EOY total contributions for year that you are calculating for. In this case, I would use "Balance As Of..." 12/31/2013 and obtain total contributions made from the Contributions tab.
3. Divide EOY balance for 2013 by sum of numbers obtained in steps 1 and 2. --> EOY Bal / (P-EOY Bal + Cont)
4. Subtract 1 from result of step 3
5. Multiply result of step 4 by 100. Using this method I came up with 24.30% for my own account.

So, using the 3 different methods above, I came up with 3 completely different results:
1. Simple Addition = 23.80%
2. Compounded = 26.19%
3. EOY-(P-EOY+CONT) = 24.30%

I believe what userque was alluding to was that Method 2 is technically the more accurate way of calculating the return rate. Perhaps userque can chime in, however, and clarify whether this is indeed the case, or if a method I did not explain above is more "technically correct".

InsaneZane,

Method 2 is an odd Compound Annual Growth Rate that is not annual. It is closer to a Compound Monthly Growth Rate. It is an attempt to incorporate the affect of consistent contributions to the account. Two problems: 1) There is a divisor. The TSP site talks about the nth root, I use the standard deviation, and 2) There is way too much variance (risk or standard deviation) from month to month and you only get two or three contributions during that month. The curve would be way too erratic. I see this when I have Quicken do it monthly.

Method 3 is an Internal Rate of Return. But it is simpler. It is very accurate, but a CAGR is a good approximation when you don't know what you have contributed as long as your contributions are stable. An IRR is (((EOY Balance of 2013 - Contributions) - (EOY Balance as of 2012/12/31)) / (EOY Balance as of 2012/12/31)) - 1. However, rereading Method 3 seems to imply another CAGR computation...

[Cactus]

I thought I replied, but do not see it.
It could very well be that I'm using incorrect numbers. I was using the 12 month PIP that TSP shows every ~3rd day of the month. Should I use something else or calculate a monthly return in a different manner?That is actually your return over the previous 12 months, not the return for the previous month. Right now it is giving you the return for Jan - Dec which is your annual return for 2014.

To get your monthly returns you are going to have to look them up on the AT every month or keep track of it yourself using a tool like the TSP Returns Calculator on this page here: TSP Calculator - Thrift Savings Plan (http://www.tsptalk.com/utilities.html)

You can use that spreadsheet over the whole year to give you the annual return as well. These methods will differ slightly from the 12 month PIP because it includes your contributions while these methods do not.

[chpwolf]

Thanks for the information. I knew it didn't look right - that's why I started with the questions.
Looking at my numbers again, I tried to follow method #3.
A - 12/31/12 EOY balance
B - 12/31/13 EOY balance
C - contributions & match in 2013
D - 12/31/14 EOY balance
E - contributions & match 2014

In this formula:
(((EOY Balance of 2013 - Contributions) - (EOY Balance as of 2012/12/31)) / (EOY Balance as of 2012/12/31)) - 1
What's the 1?

My particular values are:
A - 16,861.93
B - 32,146.34
C - 4,599.50 (*2 for the match)
D - 43,474.92
E - 5,039.04 (*2 for the match)

If I plug in #s for 2013 (without the -1), I get:
((( B - C) - (A)) / (B)) = 0.360896 = 36.09%
TSP reported my annual return for 2013 as 28.46%

If I plug them in for 2014 (without the -1), I get:

((( D - E) - (B)) / (D)) = 0.0389 = 3.89%
TSP reported my 12-month PIP is 3.38%.

Am I still missing something or did I have a spectacular 2013 followed by a crappy 2014? (well, 3.89% beats a stick in the eye...or any loss).

[Cactus]

The annual return & 12 month PIP you got from TSP are what you want here. They give you the annual rate of return on your initial balance and the contributions throughout the year. And, yes, you had a spectacular 2013 followed by a not so hot 2014. But hey, you beat me handsomely both years. :D

The formula I think you are trying to use, (B-C-A)/A, is an approximation that factors out the contribution and calculates the rate of return using only the balance at the start of the year. This is close when the contributions are small in relation to your balance. In your case, though, the contribution is a large percentage of the balance and the returns on the unaccounted for contributions are inflating your return rate. To get a value closer to what TSP is giving you, you would have to account for your contribution going in each pay period and producing earnings/losses from there to the end of the year. It can be done but would be a lot more work.

If you want, you can try another approximation where you add half your annual contribution to the initial balance assuming this balances out the other half not earning anything. That formula would be (B-C-A)/(A+0.5*C). That should give you 28.36% for 2013 which is closer than what you have now.

[Scout333]

chpwolf I have a spreadsheet which provides a couple of simple ROI computations. Take a look.



Hello Fellow TSP'rs, The 2015 version of the Scout TSP Contribution spreadsheet is out. Tom was kind enough to post it in the Utilities section. It is very similar to the 2014 version. There are a couple of very simple return on investment calculators. See the TSP Return and Tips tabs for info. FERS employees receiving matching contributions can input the employee contribution amounts each pay date and the calculator gives you return on investment %s including the matching contributions. I added some additional input lines. Its so easy to mess up a spreadsheet when adding lines in the middle of the year. If you haven't used it before take a look at the Tips tab.

Enjoy the spreadsheet!

http://www.tsptalk.com/utilities/Scouts_Spreadsheet.xls