Annualizing Returns and Volatility from Quarterly Portfolio Data
Summary
The document addresses how to compare portfolio performance from quarterly observations over a common sample period. It converts the cumulative return into a per-quarter compounded rate using the number of observations, then annualizes that rate by compounding across four quarters. Another answer describes an equivalent route through a monthly rate, using the sample’s stated duration in months before annualizing across twelve months. It also notes that total return calculations should account for dividends when relevant.
The discussion gives formulas but does not settle every practical detail. The observation count and elapsed time must be aligned with the data’s return convention and endpoint treatment; the answers differ in their intermediate frequency while aiming at annualized compounded returns. Volatility is raised in the question but not answered, so the document provides no volatility calculation or assumptions about estimating it from quarterly returns.
Key ideas
- Convert cumulative performance into a compounded return at the observation frequency before annualizing.
- Quarterly returns are annualized by compounding across four quarters.
- A monthly compounding route is also described using the sample duration in months.
- Include dividends in total return when the data represent a dividend-paying portfolio.
- The document does not explain how to annualize volatility.
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Full text
# Annualised returns and volatility for 3 month data
# Annualised returns and volatility for 3 month data
I have a portofolio with 30 indexes and I want to calculate the annulised returns and volatility because I want to compare it with another portofolio with different number of indexes (but same time period) My data are time series with 3 month frequency from 2009-12-31 to 2020-3-31.
I know that the general formula is: $$annualised \enspace return = (1 + total \enspace returns)^N - 1$$ where $total \enspace returns$ is the last value minus the first divided by the first. $N$ is the period I want to annualised and here is my doubt.
- If I have 3 month frequency data, what is the best value for $N$?
- how to get the volatility after?
## Answer by wanna_be_quant (score 3, accepted)
https://quant.stackexchange.com/a/64261
I think all the previous answers have small mistakes:
Given that you have derived the return over the period of interest, i.e. in your case 2009-2020 we can then:
- Compute the return at the granularity level of your data i.e:
$r_{quarterly}=(1+r_{total_{period}})^{\frac{1}{number_{datapoints}}}-1$
This is then the return of the whole period on a quarterly basis!
- Now we can annualise it accordingly:
$r_{annualised}= (1+r_{quarterly})^4-1$
and this is because we have 4 times those 3 month periods in a year.
I hope this helps.
## Answer by phdstudent (score 0)
https://quant.stackexchange.com/a/55240
If you compute total return as:
$$R_{2009-12-31 \rightarrow 2020-3-31} = \frac{P_{2020-3-31} + D_{2020-3-31}}{P_{2009-12-31}}-1$$
Where $D_{2020-3-31}$ are all the dividend paid in that period. Then you can do the following:
- First note that your sample has $12 \times 10 + 3$ months; I.e. 123 months.
- So the average monthly return is:
$$\bar{r}_{monthly} = (1+R_{2009-12-31 \rightarrow 2020-3-31})^{\frac{1}{123}} -1 $$
- The average annual return will be: $$\bar{r}_{annual} = (1+\bar{r}_{monthly})^{12} -1 $$Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.