# 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.

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Did your last sentence get cut off? – chrisaycock♦ Jul 7 '11 at 1:36
sorry, i was in mid-sentence when i was interrupted. :) – miggety Jul 7 '11 at 5:55
Even if it is not precisely the question, I think the question raises another issue, which is "Does past returns provide a good estimate of future returns?" These protfolio allocation algos are good but IMO it is a bit easy to assume that we have a good estimate of the returns. If you give me a good estimate of the future return, let me manage your money, its not too hard. Rather than focusing on that, shouldn't we focus on how to forecast returns? – RockScience Jul 8 '11 at 2:42
@RockScience: yes, i've heard the same question asked many times, and have seen in many texts the pitfalls of relying on past returns to estimate future earnings. Although i'm aware of some of these pitfalls, i'm just getting started in this field and so having an understanding of some of the techniques, even if out of fashion, gives me something to cut my teeth on. While we're on the topic though, do you know of any good resources (links, books, etc.) that discuss how to forecast returns? Is that the type of problem time-series analysis would be used for? – miggety Jul 11 '11 at 21:52
@miggety: There is no one best technique to forecast returns. It is the most difficult part of your model. Some take discretionary decisions, others trust machine learning like god. There is a lot of different things to explore. And yes definitely time series analysis is a good basis for this problem. Good luck – RockScience Jul 12 '11 at 0:56
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## 3 Answers

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Thanks Bill, i think that'll get me going in the right direction. – miggety Jul 7 '11 at 19:40

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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).

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Hi rtybase, it may be helpful to summarize what's in those links. You'll notice that the other link-based answers on here didn't get much respect either. – chrisaycock♦ Jan 26 '12 at 21:11
@chrisaycock - fixed! ;) – rtybase Jan 26 '12 at 21:31

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.

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