### Author Topic: How is annual performance calculated?  (Read 2476 times)

#### van59

• Posts: 5
##### How is annual performance calculated?
« on: October 07, 2017, 04:44:11 PM »
I am hoping someone could explain to me how annual performance is calculated. For example when looking at the annual performance of the MSCI ACWI Index it mentions that for 2016 the annual performance was 8.48%. I would like to know how this 8.48% figure was arrived at? I went on MSCI's website and downloaded some data for this index. See attached.

Is this the correct data that can be used to calculate the 8.48% annual return for 2016? How would I calculate it?

Thank you!

#### secondcor521

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##### Re: How is annual performance calculated?
« Reply #1 on: October 07, 2017, 05:50:27 PM »
I don't remember all of the details, but basically you'd want to use the XIRR function in Excel.  There is documentation online about how to use it.

The basic idea is you start at the beginning of the time period (in your example probably 1/1/16) with the initial investment (you can pretend you bought 1 unit at the \$399.xx price).  This is called an inflow.  You would then put in the dividend dates and amounts as outflows.  Then at the end of the period (12/31/16) you would put in an outflow for the 1 share at the 12/31 price (\$421.xx).

(For the XIRR function to work, you need to put inflows in as positive numbers and outflows as negative numbers, or vice versa.)

Then you would put in the XIRR formula and point it to those series of dates and values, and it would figure out the answer for you.  Conceptually, the result is the rate of return that, if you invested your inflow(s) on the date and at the amount given into an imaginary savings account that always continuously earned exactly that rate of return, would return you those outflows (the dividends and the end of year value) exactly.

If that price history and ROI are correct, it looks like there is about 3% worth of dividends missing.  Indexes are not mutual funds and thus don't actually pay dividends, but the companies comprising the indexes do pay dividends, so that 8.x% number probably figures those in.  It would probably be quite a bit of math crunching to know when all of the companies in the index paid a dividend and to figure out how much of a fraction of a share of each company is represented in the index, and then scaling the dividend by that factor.  I don't know how many companies are in this index, but it's probably a few hundred, and companies often pay dividends monthly or quarterly, so that would be a lot of (straightforward) math.

So if this index had 1% of it's assets in General Motors, that would mean \$399 * 1%, or \$3.99 in GM.  GM's stock is at \$44.93, so the index owns 0.0888 shares of GM.  Each share of GM paid 38 cents in dividends on 3/11/16, so the index earned approximately 3.37 cents on that day.  You'd have to do that for the other three dividends GM paid in 2016.  You'd also need to use the actual price of the index, price of the stock, and it's relative weight in the index on each of the dividend dates - not just the initial value and current price and SWAG relative weight I've used in this paragraph.

#### van59

• Posts: 5
##### Re: How is annual performance calculated?
« Reply #2 on: October 07, 2017, 07:30:17 PM »
Thank you secondcor521,

I started reading up on XIRR and trying some examples. Some sites mention that XIRR is used when the cashflow is not periodic and if it is to use IRR. I tried IRR on only the two values, viz., Dec 31, 2015 \$399.362 and Dec 30, 2016 \$421.839

The result is 5.63% which is the same result if I was to use the formula for percent increase. In this case there is a discrepancy of 2.85% when compared to the 8.48% annual performance in the fact sheet.

Is this 2.85% the result of dividends that possibly could be missing from the data I downloaded (as you suggested)?

#### van59

• Posts: 5
##### Re: How is annual performance calculated?
« Reply #3 on: October 07, 2017, 07:50:00 PM »
I noticed on MSCI there is an option across from Index level where I can select Price, Net, Gross, TR (Risk Control), and ER (Risk Control).

I tried Price, Net, and Gross and computed the values in excel (see attached - the negative sign was added by me for the IRR formula).

When Gross is selected as the index level the correct return (8.48%) is computed.

What does Price, Net, and Gross mean when selecting these options across from Index level?

Also the index itself is not traded, so when I see values priced in USD, what do those values actually mean/represent?
« Last Edit: October 07, 2017, 07:52:20 PM by van59 »

#### secondcor521

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##### Re: How is annual performance calculated?
« Reply #4 on: October 07, 2017, 09:07:37 PM »
Is this 2.85% the result of dividends that possibly could be missing from the data I downloaded (as you suggested)?

I don't know this index in particular, but yes, almost certainly the difference is due to dividends.

What does Price, Net, and Gross mean when selecting these options across from Index level?

I have no idea since I don't know which website you're looking at.  Probably something to do with dividends, since as you note, one of the sets of numbers gets you the correct total return, so that set of numbers accounts for dividends.

Also the index itself is not traded, so when I see values priced in USD, what do those values actually mean/represent?

Again, guessing here since I don't know which website you're looking at.  But almost certainly it's the price of one share of a mutual fund, ETF, or unit in a unit investment trust that invests in that index.

As a simple example, let me invent the secondcor521 index, which is 75% Apple stock and 25% General Motors.  It's a stupid index, but let's ignore that for the sake of learning.

Now we create the secondcor521 mutual fund, which invests solely in the secondcor521 index.  Since I have to establish a share price, let me start with a share price of \$100.

You are my first customer and decide to buy 100 shares at \$100, so you send me \$10,000.

I take your \$10,000 and invest according to the index - 75%, or \$7500 into Apple stock, and 25%, or \$2500 into General Motors.  We could do the math and figure out how many shares of each stock that is, but it doesn't really matter.  You can see that, as Apple and GM do well or not so well, the index will do well or not so well, and so will the mutual fund.  If Apple's stock price doubles and GM stock price doubles also, then the \$7,500 becomes \$15,000 worth of Apple stock and the \$2,500 becomes \$5,000 of GM stock.  The ratios are still the same, but the total is now \$20,000.  Since you own 100 shares, each share you own is worth \$20,000 / 100 = \$200.

So the mutual fund or ETF or whatever is selling you units or shares at some price, and if they do a proper job of investing into the stocks in the index at the same ratios as they exist in the index, and keep their overhead costs low, then the investment will track the index pretty well.  If the index goes up 1% on Monday, the investment will also.

Hope that helps.

#### secondcor521

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##### Re: How is annual performance calculated?
« Reply #5 on: October 07, 2017, 09:12:36 PM »
Oh, and yes, XIRR is used if the payments are not periodic, which in this case they wouldn't be, because different stocks pay their dividends on different days and at different frequencies.  IRR is used if the payments are regular, like every month or every 3 months.  I think if you're using IRR you can leave the dates of the payments out and the IRR function will assume that each data point is one period after the previous data point (so you need to have the payments in chronological order to get the correct answer with IRR).

#### NorCal

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##### Re: How is annual performance calculated?
« Reply #6 on: October 07, 2017, 09:33:01 PM »
That looks to be the change in price over the year, which excludes dividends.

The simplest way to calculate returns is to look up ACWI (the ETF that tracks this index) on Yahoo finance, and use the "Adjusted Close" prices under Historical Data.  The adjusted close will get closer, because it includes the impact of dividends and splits.  It can still vary from the index somewhat due to the following:

1. ETF fees (the index doesn't have fees)
2. Tracking error (the ETF won't track the index perfectly)
3. Additional returns from reinvested dividends (some calculations assume dividends are reinvested, others treat them as a simple cash return)

If you want to get advanced, read some articles about the difference between calculating Money Weighted Returns vs. Time Weighted Returns.  To oversimplify a bit, the returns you'll see on your money are almost certainly lower than advertised returns.

#### van59

• Posts: 5
##### Re: How is annual performance calculated?
« Reply #7 on: October 07, 2017, 10:21:55 PM »
Thanks again all for the detailed information.

The website is https://www.msci.com/end-of-day-data-regional
-From there I expand performance on the left
-Then select "End of day data Regional"
-Then on the right select the Market drop down and choose "All Country (DM+EM)" and click "Search"
-On the right I scroll down and select ACWI (flash is required)

When you click on the drop down you have options for Price, Net, Gross, etc..
This section of the website doesn't make any mention of the price representing an ETF/Mutual fund..
Could the price simply represent the value of the components of the index? In that case when the index is first created, is there some initial value that is decided it should start at (e.g. \$1000) and then from that point the price would change depending on how it performs over time?

So the mutual fund or ETF or whatever is selling you units or shares at some price, and if they do a proper job of investing into the stocks in the index at the same ratios as they exist in the index, and keep their overhead costs low, then the investment will track the index pretty well.  If the index goes up 1% on Monday, the investment will also.

I can conceptualize how a mutual fund or ETF would have some price that would represent their underlying components. How does an index have a price (some indexes don't even have a mutal fund or ETF to my understanding) ?
« Last Edit: October 07, 2017, 10:26:15 PM by van59 »

#### secondcor521

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##### Re: How is annual performance calculated?
« Reply #8 on: October 07, 2017, 10:53:43 PM »
Could the price simply represent the value of the components of the index? In that case when the index is first created, is there some initial value that is decided it should start at (e.g. \$1000) and then from that point the price would change depending on how it performs over time?

...

How does an index have a price (some indexes don't even have a mutal fund or ETF to my understanding) ?

You got it almost exactly right with your first paragraph above.  Take my arbitrary secondcor521 index.  If I started my index today and said it was 75% of 1 share of Apple and 25% of 1 share of GM, then you could do the math and find \$116.47 + \$11.23 and my index value would be 127.70.

When they talk about real indices, they leave off the dollar sign (or Euro, or whatever, depending on the index) and refer to the change as points instead of dollars.  So when they talk about the Dow Jones being 22,738 or whatever, it's really \$22,738 worth of a basket of some combination of some amount of shares of 30 stocks.

(Over time, stock splits, spin-offs, acquisitions, and changes in the components of the index all complicate this somewhat, but the basic idea is as above.)

#### Heckler

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##### Re: How is annual performance calculated?
« Reply #9 on: October 07, 2017, 11:39:50 PM »

CCP has many great articles to learn this kind of stuff.  Scroll down to the bottom for his site index and search bar.
« Last Edit: October 07, 2017, 11:42:16 PM by Heckler »

#### Tyler

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##### Re: How is annual performance calculated?
« Reply #10 on: October 08, 2017, 07:15:09 PM »
I noticed on MSCI there is an option across from Index level where I can select Price, Net, Gross, TR (Risk Control), and ER (Risk Control).

I tried Price, Net, and Gross and computed the values in excel (see attached - the negative sign was added by me for the IRR formula).

When Gross is selected as the index level the correct return (8.48%) is computed.

What does Price, Net, and Gross mean when selecting these options across from Index level?

Also the index itself is not traded, so when I see values priced in USD, what do those values actually mean/represent?

You're definitely looking in the right place for good data.  MSCI is the definitive source for all kinds of index information, as they provide the data that companies like Vanguard pay big bucks to track.

In their tool, "Price" is the straight return without the dividends included.  It simply starts at a fixed number and is adjusted based on the daily returns.  The important thing is the percent change, not the number itself.

"Gross" is the total return including both the change in price and the reinvested dividends.

"Net" is the total return including reinvested dividends but less certain international withholding taxes on those dividends.  So Net will always be a little less than Gross, but it also usually understates the true return because the index fund providers are really good at dodging withholding taxes (that's why so many Vanguard funds are domiciled in Ireland).  Note that the Net return really only affects international funds where the money crosses borders.

In general, I prefer to use the Gross numbers.  Once you have those, just look at the MSCI index values at the end of December each year.  The total return (%) for 2016 is simply ((EOY2016/EOY2015)-1)*100.
« Last Edit: October 08, 2017, 07:48:16 PM by Tyler »

#### van59

• Posts: 5
##### Re: How is annual performance calculated?
« Reply #11 on: October 08, 2017, 08:16:28 PM »

CCP has many great articles to learn this kind of stuff.  Scroll down to the bottom for his site index and search bar.

Thanks! I checked out the white paper and it was quite educational. If I've understood correctly I would use the Time-Weighted Rate of Return to see how my investment has performed compared to the underlying indexes rate of return it is attempting to track (without my cashflows impacting the calculation) and I would use the Money-Weighted Rate of Return to see how my investment has actually performed taken into consideration my cashflows.

I was reading the following article: https://www.forbes.com/sites/financialfinesse/2012/06/20/why-your-investment-returns-could-be-lower-than-you-think/#6ebbcf12d0eb

It mentions how the compounded annualized return of the S&P 500 (including dividends) was about 7.8% from 1992-2011. I believe this is the geometric mean. I was surprised to read that "..someone investing systematically from 1992-2011 would only have earned about a 3.2% compounded annualized return compared to the 7.8% return if they invested all at once in 1992"

Since the 3.2% involves cashflow through systematic investment I am assuming this is a Money-Weighted Rate of Return calculation? 3.2% seems pretty low. I was under the impression that if I invested in the S&P 500 and made regular monthly investments (e.g. \$1000) over a 20 year period it would be reasonable to achieve approx. 7% annualized rate of return....

In general, I prefer to use the Gross numbers.  Once you have those, just look at the MSCI index values at the end of December each year.  The total return (%) for 2016 is simply ((EOY2016/EOY2015)-1)*100.

Perfect! I tried this and the numbers match the factsheet.
« Last Edit: October 08, 2017, 08:18:01 PM by van59 »

#### YoungInvestor

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• Posts: 407
##### Re: How is annual performance calculated?
« Reply #12 on: October 09, 2017, 07:02:26 AM »
For all returns, do 1+return in that year, and let's call that  d1,d2,...dlastyear.

(d1 x d2 x d3 x...)^(1/number of years) = 1+ yearly rate of return.

So if there are 3 years, with returns of 10, 0 and 8%, you do:

(1.1x1.0x1.08)^(1/3)= 1+ yearly rate = 1.0591

Yearly rate =5.91%