You may know if your portfolio’s average returns are better or worse than your benchmark or other comparison portfolio, but how can you compare the risk? One way to get a better picture would be to compare standard deviations. While the standard deviations of benchmarks and individual mutual funds are easily available, no one provides you with the standard deviation of your own portfolio – so here is an easy method to do just that. (Actually an even easier method is at the end of this post.)
1. The first thing to do is list your calendar year returns, for example:
2000: 8%
2001: -6%
2002: -12%
2003: 3%
2004: 15%
2005: 17%
2006: 17%
2007: 6%
2. Now, calculate the average of these numbers which is simply adding up all the returns and dividing by the number of years in question. The sum of returns is 48 and if you divide by 8 (the number of years) you end up with an average of 6. Remember this number.
3. Now you need to find the sum of the squared deviations. This just means that for every year you subtract the calendar year return from the average you found earlier and then square it. In other words: (Average return – return for that year)2. So for example for 2000 the squared deviation is (6-8)2 which equals -22 which equals 4. The squared deviation for 2001 is just (6-(-6))2 which equals 144. You continue to do this until you have all the squared deviations for all eight years. Then you add up all these numbers together which gives you 804.
4. Divide this number by the number of the years LESS ONE. In this case it is 7 since 8 minus 1 is 7. So in our case we divide 804 by 7 to yield 114.8571
5. Finally, take the square root of this number. In our example this leaves us with 10.71714. And that’s your final answer.
Therefore, this portfolio has an average return of 6.00% and an annual standard deviation of 10.72%.
And if you want to save time, you could just open an excel spreadsheet and enter in the annual returns in a column (for example cells A1 through A8). Then click on a new cell and type: “=stdev(a1:a8)”
Note – don’t include the quotes. Just type everything as shown from the equals sign to the closing parenthesis. You can take the numbers from this example and see if you come up with the same answer.
Hi
1. The first thing to do is list your calendar year returns
A seemingly simple statement but in the messy-real-world is there a consensus on the right way to do that calculation?
q
Excellent point – calculating your annual return is not so simple unless you have a lump sum and no distributions – only capital growth. This is rarely the case. Taxtips.ca has a calculator that can help you out: Click here
Anyone else have any links to some good calculators?
Dear All,
The above article is good one which refreshes my memory & the backend working on the formula of excel as well. I come up to know how to utilize this when doing portfolio analysis
“So for example for 2000 the squared deviation is (6-8)2 which equals -22 which equals 4. The squared deviation for 2001 is just (6-(-12))2 which equals 324”.
Note- 2001 the return rate is -6%, so deviation for 2001 is just (6-(-6))^2= 144
Great article, very helpful!
Fixed – good eye Sarah!