# Annual rate of return comparison

In the excercise "Calculating the Return of Indices - Solution_CSV.ipynb" I can't explain the graph. It seems that ^ixic is the worst performer, but then the annual return is the best: why?

Hi Davide!

Great to have you in the course and thanks for reaching out!

Please make a distinction between the data we plot on the graph (ind_data, which is the index *data*, i.e. practically *the market value* of the given index on the given days) and the annual_ind_returns, which is the average annual *returns* of the given indices.

In other words, a stock may cost $10,000, but if in a year it costs $10,100, it's simple annual return is 1%, while another stock may cost $5,000 at the beginning of the year, and if its year end value is $10,100, then its simple annual return is greater than 100%! Therefore, a *stock price* and a *return* are two different terms we should be careful about when doing calculations.

Hope this helps.

Best,

Martin

Thanks for the answer, but when we draw the three graphs in the example, we normalized them to 100 so they are all three comparable. I expect whoever is highest to have the highest return. Where am I wrong?

Hi Davide!

We normalized *the prices* of the given indices. Not their average annual returns.

Please feel free to re-watch the video to solidify the difference between the two terms.

Hope this helps but please feel free to get back to us should you need further assistance. Thank you.

Kind regards,

Martin

Thanks for the reply, but I still don't understand, my bad.

If I normalize the prices it means that everyone starts at the same price. So the stock that reaches the highest price after 17 years had the highest return.

The last row of the dataframe is from 12-12-2017 where ^DJI=213.138599 ^GSPC=181.324493 and ^IXIC=168.635954. So compared to the initial price of 100 the return of the ^DJI is 113%, the ^GSPC of 81% and the ^IXIC of 68%. Is my reasoning correct so far?

So what you tell me is that ^ IXIC's average annual return is the best, but the 17-year return is the worst?

Thanks a lot,

Davide.

Hi Davide!

Thank you for getting back to this conversation.

Thank you for explaining your idea in more detail. Your reasoning is absolutely correct, too.

The only discrepancy (that I perceive) is between the results/data used in the video and the data you mention.

In e.g. minute 2:55 from the video, you can see that ^IXIC is the stock that ends with the highest value in 2017 (the orange line), while ^FTSE is the stock that ends with the lowest value in 2017 (the red line).

At the same time, the obtained annual indices returns in minute 3:46 from the video reflect these very same inferences (which also perfectly resonate with the intuition you described), since ^IXIC is the stock with the highest annual index return (0.107043), and ^FTSE - the one with the lowest annual index return (0.042592).

The other two indices also correctly represent the visualization.

Therefore, do you think there might have been some confusion between the data you use and the one from the video? If that's the case, please feel free to apply the dataset as well as the code you use in your reply to this thread and I'd be happy to run the code on my end, if necessary. Thank you.

Hope this helps.

Kind regards,

Martin

Thanks again for your patience, the video of the course is ok, what made me doubt is the file "Section 2 / 11_Calculating the Rate of Return of Indices / Exercises / Calculating the Return of Indices - Solution_CSV.ipynb".

There are exactly those values that I reported in my previous post.

Hi Davide!

Thanks for your reply.

Please accept my apologies for the delayed reply this time.

I do obtain different values from the ones you mention. Therefore, can you please confirm that you are also referring to "Indices_Exercise_Data.csv" (as opposed to Indices_Data_01 or _02)?

It can be found in the link named "Calculating the Rate of Return of Indices - Dataset Exercise Data" just below the video in question.

Hope this helps but please get back to us should you need further assistance. Thank you.

Kind regards,

Martin