Calculating Historical Returns for Mean-Variance Analysis
Summary
The document asks how to turn a stock’s historical open and close prices into returns for mean-variance analysis. Its answer points to the standard rate-of-return definition and gives an example of calculating a period return from the starting and ending prices. This provides a basic way to create a series of historical returns from price observations, such as monthly data, for use in estimating expected returns.
The responses also mention autoregressive integrated moving average as a possible forecasting approach, while cautioning that it may perform poorly as a naive technique. The discussion does not give a worked forecast, assess data quality, or explain how return estimates affect portfolio choices. Historical returns can inform an expected return estimate, but the document does not establish that past performance predicts future returns reliably.
Key ideas
- Calculate a period return by comparing the ending price with the starting price relative to the starting price.
- Use consistently defined periods when forming historical returns for mean-variance analysis.
- The responses mention ARIMA as a possible forecasting method but caution that a naive application may not work well.
- The discussion offers no evidence that historical returns reliably predict future returns.
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# How to calculate expected return based on historical data for Mean Variance Analysis
# How to calculate expected return based on historical data for Mean Variance Analysis
I've recently started reading some books on asset allocation and portfolio theory but I don't work in the field and don't have much knowledge yet.
So I've been reading up on mean-variance analysis and my question is regarding the computation of the expected returns for a particular asset. From what I understand historical data is used to predict future returns. In the book that I'm currently reading, the author provides monthly returns for a particular stock and then we're asked to calculate the expected return for future months.
My question is this, if i have historical open/close data for a particular stock, how do I use this information to calculate the returns? Since the return is based on the share price when the stock was purchased and the price when the it was sold, I'm not sure exactly what the calculation would look like.
## Answer by bill_080 (score 2, accepted)
https://quant.stackexchange.com/a/1418
Try this:
http://en.wikipedia.org/wiki/Rate_of_return
## Answer by RockScience (score 0)
https://quant.stackexchange.com/a/1459
You can have a look at
http://en.wikipedia.org/wiki/Autoregressive_integrated_moving_average
But I doubt you'll have very good results as it is a very naive technique.
## Answer by rtybase (score 0)
https://quant.stackexchange.com/a/2836
http://ci.columbia.edu/ci/premba_test/c0332/s6/s6_3.html contains an example with the percentage returns over the last 10 years (something like $r_{year N}=\frac{P_{end year N} - P_{start year N}}{P_{start year N}} \cdot 100$%).
and here is another link http://academicearth.org/lectures/portfolio-diversification. This is an entire course from Yale University (including this subject).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.