Calculate monthly returns

Hey,

I don't know whether this question is appropriate here but I don't know where else to go so please help me! ;-(

I have a really important (dumb) question that is driving me creazy. On, for example CNBC, the stock return of ING Group NV is:
5 day return = 6.87%
1 Mo return = 6.17%
3 Mo return = 36.43%

I downloaded the quote prices from finance.yahoo.com (which are below this question) and calculated everything using the methods:
- Arithmetic average return
- Geometric average return
- Continuous compounded return (Ln)
- Etc. etc. etc.

For example for the 1 Mo return I did the following for each method:
Arithmetic = ( Price April 1 / Price March 1) -1
Geometric = (1 + Arithmetic) ^ (1/1) - 1
Continuous = Ln (Price April 1 / Price March 1)

And all other possible combinations --> March 31 instead of April 1, etc.

But no matter what method I use I don’t get the percentages as stated by CNBC. I calculate the 5 day return from the last 5 days. Return from month to month (April to March) but I don’t get the right percentages. I am always of by .4% to 3.5%

Does anybody know how to calculate 1Mo return, 3 Mo return, etc.? How do I calculate the 5 day return, 1 Mo return and 3 Mo return? And what steps do I have to follow?

PS: When I have calculated the monthly returns correctly how do I get the annual returns? What method?

I know that it is f*cking basic arithmetic but its driving me crazy.


DAILY PRICES ING Group N.V.
Date Close
01/04/2011 13.04
31/03/2011 12.71
30/03/2011 12.92
29/03/2011 13.24
28/03/2011 13.13
25/03/2011 13.07

MONTHLY Prices
Date Close
01/04/2011 13.04
01/03/2011 12.71
01/02/2011 12.55
03/01/2011 11.39

 

I know yahoo gives you the adjusted daily closing prices and the unadjusted ones. Which one did you use?

To calculate annual returns, get the starting price of the year and the ending price. And then do arithmetic return.

 

How are you getting those returns from CNBC?

I just got these returns from yahoo's historical prices.

5 day (Mar 25, 2011 to Mar 31, 2011): (12.71-13.07)/13.07= -2.75% 1 month (Mar 1, 2011 to Mar 31, 2011): (12.71-12.22)/12.22= 4.01% 3 months (Jan 3, 2011 to Mar 31, 2011): (12.71-9.90)/9.90= 28.38%

 

The equation simply arithmetic with any dividends reinvested. Since ING does not currently pay a dividend, that is not an issue.

I can't get any of those CNBC numbers to match up to anything in Bloomberg. You can assume CNBC is wrong on this one and move on.

To get the annualized equivalent of the month return (this is how you'd see it in Bloomberg) you'd use this formula :

(close price 3/31)/(close price 2/28)^(365 days/31 days)-1

12.71/12.55^(365/31) = 0.1609

 

Hey guys,

Thanks a lot for your comments. I knew something was wrong. I thought I'd gone crazy. I used everything adjusted/unadjusted. After approximately 2 hours I thought screw it I will ask on wallstreetoasis.

@ jqbuyside: I see that you have an output of 0.1609. I Assume that it is 0.1609% and not 16.09%

The reason I was asking this question is because I have to do academic research on a stock-market related matter. For every company on the AEX I must calculate the monthly returns for every year up to 5 years and than compare it to other firms. For academic purposes I will use the continuously compounding method.

Thnx again y'all for the quick responses. :-)

 

Logically speaking, 72 data points is a much larger sample size than 6, so deviation would be lower.

Think of it this way: the deviation between 1 and 1.5 would be higher than the deviation between 1, 1.1, 1.2, 1.3, 1.4, and 1.5.

Hopefully some monkey will correct my logic in case I just went full retard.

in it 2 win it
 
dannee_:
Hi,

I have returns for 72 months, i.e. 6 years, and I calculated the std deviation using the 72 months of data. To annualize it, I multiplied with the sqr root of 12.

But I also calculated the total return for each of the 6 years using the data, and when I calculated the std deviation for the returns of the 6 years, it was about 10% higher than the other one, am I doing something wrong here? Because I am thinking that they should be almost the same?

No, they will not be the same or not necessarily even that close. You should be happy with that result.
 
dannee_:
ah I understand, thanks. So they are the same but the std deviation for the 72 months is more accurate?
No, it's not more accurate. Neither of these numbers are accurate. You can have a little bit more confidence in the larger number of observations, but it is minimal. Everything is within a range of what you might expect, given random fluctuations.

This all assumes that what you have observed is what is likely to happen in the future. Normally, a big assumption.

 
dannee_:
ah I understand, thanks. So they are the same but the std deviation for the 72 months is more accurate?

Think of it this way: deviation is about measuring average distance between points. The six years' deviation is still accurate, but doesn't give as sharp an illustration of the underlying values. The 72 months' deviation is a lot more granular and accounts for more ponts.

Edit: listen to Trades. My stuff is mostly for you to easily visualize it.

in it 2 win it
 

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