# Finding Annualized Mean and Standard Deviation For Portfolio

Say I'm looking at the monthly investment returns of 3 funds:

``````Date    Index 1     Index 2 Index 3
7/1/2012    0.19%   1.10%   0.26%
8/1/2012    -0.13%  0.22%   0.13%
9/1/2012    -0.11%  -0.12%  0.27%
10/1/2012   -0.25%  -1.31%  0.13%
11/1/2012   0.70%   1.66%   0.63%
12/1/2012   1.09%   1.07%   1.76%
1/1/2013    0.04%   -0.82%  -0.32%
2/1/2013    1.83%   1.41%   0.83%
3/1/2013    0.63%   0.24%   0.47%
4/1/2013    0.45%   0.49%   0.74%
5/1/2013    -0.10%  0.65%   -0.53%
6/1/2013    -0.83%  -0.86%  -0.54%
7/1/2013    1.38%   1.53%   2.06%
8/1/2013    -0.33%  -0.05%  0.05%
9/1/2013    0.27%   -0.14%  0.97%
10/1/2013   -0.63%  -0.35%  0.14%
11/1/2013   -0.14%  -0.75%  -0.74%
12/1/2013   -0.75%  -0.10%  -0.38%
1/1/2014    1.06%   0.33%   8.72%
2/1/2014    0.04%   0.91%   -0.65%
``````

I've put 50% in Index 1, 25% in Index 2 and 25% in Index 3. This is my portfolio. For this portfolio, I want to find the annualized return and the annualized standard deviation for the entire 3 year period here. I'm confused about how exactly to do this.

Do I annualize the returns individually, then take the average of the individual annualized returns, and then use the weighted average to find the portfolio's annualized return? Or is there another way?

Here is an example of what I am trying to implement:

How do I find the annualized standard deviation for the entire portfolio?

Is there a way to see the best 12 month return for the historical data?

The first step is to convert the returns to regular numbers.

e.g. .19% turns into 1.0019. Below the stack of numbers is the product function. "=PRODUCT(D4:D24)" multiplies each cell in that range. The math of compound returns is not addition, it's multiplication. 2 time units of 10% returns result in 1.1 * 1.1 = 1.21 or 21%, not 10% + 10 % = 20%. And, to exaggerate an important point, A return of +50% and then -50% does not average to break-even, 1.5 * .5 = .75 or a 25% loss over the full time, -13.4% per year, compounded.

Now, you don't have 3 years, not even 2. To take 20 months and annualize it, you raise the return to the 12/20 power. I'd say .6 power, but it might not be obvious where that comes from. The 20th root offers a monthly return, then 12th power of that, yearly. 1.0445^.6= 1.0264 or 2.64%/yr CAGR.

You can repeat this and analyze the data as you wish, but, in my opinion, 20 months of data doesn't offer much in the way of a comparison. If my entire investing life saw the same returns as my best 20 month period, I'd be a billionaire.

As far as STDEV goes, that's just another function you can use in the spreadsheet.

• thanks for replying. I am just trying to get a feel for these kinds of calculations so this is sample data - I would be using a much longer period otherwise. So given that these are monthly returns, should I annualize each individual return as (1 + 0.0019)^12 - 1, and then take the average of those annualized returns? I attached a link to a Google spreadsheet to give you an idea of what I mean Aug 16, 2016 at 17:17
• If I understand your question, No. Returns are basically roots/powers. Averaging 12 months' annualized returns will not produce the same result as the method I described above. Aug 16, 2016 at 17:23
• Thank you so much for your help. I think I understand. I followed your approach and changed the google spreadsheet (Total Return sheet). Can you tell me if this looks correct? Aug 16, 2016 at 17:59
• As the saying goes, "I think you've got it". Yes, you got the idea of power/root, and your results look right. The only thing to consider is if/when to rebalance. 2 assets, one growing at 10%, the other, say 2%. Over the the first one will be a huge percent of the portfolio, so depending on your long term plan, you consider rebalancing. Aug 16, 2016 at 18:04