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Here is an example of a performance graph of a "motif" on Motif Investing. The motif is a portfolio containing Apple and Microsoft stocks weighted at 50% each. The graph represents the aggregate performance of the 2 stocks over time (the blue line). The green line is the S&P500. The y-axis is measured in percent.

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Given the historical stock prices how would you generate this graph (or something similar to it)?

Enrico Barzetti
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To aggregate two stocks, you have to imagine a portfolio with them in some ratio. The natural thing is $\frac 12$ each by starting dollar value, so you bought the same dollar amount of each on day $1$ and held it throughout. Or maybe you rebalance at the end of each year-selling the one that has gained the most and buying the other so you start each year with the same dollar amount. Maybe you like Apple better than Microsoft, so your portfolio is $\frac 34$ Apple and $\frac 14$ Microsoft. The S & P 500 is essentially this with (about) 500 stocks in a ratio of market capitalization. To create the data, just make a column with the Apple and Microsoft prices each day, then evaluate the value of the portfolio under the rules you choose.

If it sounds like this is more about what you want to plot than how to do it, you are correct. That is the hard part. Whatever you plot, please state clearly what you are plotting.

Ross Millikan
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  • Yes I forgot to mention the weights. This portfolio is 50% Apple and 50% Microsoft. So would it be safe to assume that the graph drawn by Motif assumes some starting amount of money e.g. $10,000? – Enrico Barzetti Nov 16 '13 at 04:17
  • If I understand you correctly you are saying to use the prices of Apple and Microsoft and their respective weights to find the value of the portfolio over time. Then if I make a plot to show the portfolio's performance over time in terms of percent relative to the date when the plot begins I should have something approximating the Motif graph? – Enrico Barzetti Nov 16 '13 at 04:21
  • That is correct. The starting amount of money doesn't matter, because the performance is shown as a percentage. If the portfolio is up 10%, it doesn't matter whether you started with $$1$ or $$1000$. There is a question of how dividends are handled, but they are pretty small here. If you use the stock price without them, you pretend they weren't paid. Otherwise you need to account for the value, maybe reinvesting, maybe collecting some interest rate. – Ross Millikan Nov 16 '13 at 04:27
  • Perhaps the percentage is the percentage of starting capital allocated to each stock (as opposed to a direct weighting of stock prices)? – copper.hat Nov 16 '13 at 04:40
  • @copper.hat: it should be return on the portfolio. If you ignore dividends and don't rebalance, it should be a weighting of the prices. I have no issue with people drawing whatever graph they want as long as they tell us what they are plotting and do it right. My issue is with the conclusions drawn from the graphs, but that is for another day and another website. – Ross Millikan Nov 16 '13 at 04:49
  • @RossMillikan: I agree, I was just commenting that the initial percentage could refer to either a straight percentage of the stock prices at that time or the initial allocation of cash. – copper.hat Nov 16 '13 at 04:58
  • @copper.hat: I think it is the same thing. The percentage of the stock prices is the same as the allocation of cash-you are imagining that you buy that much of each stock on day 1. The questions usually come after that-rebalancing (how often?) and dividends(what do you do with the cash?) – Ross Millikan Nov 16 '13 at 05:03
  • @RossMillikan: Well, I could invest $0.50 in apple and $0.50 in ms on day one (half of my cash in either) or I could invest $ $\frac{S_\text{apple}}{S_\text{apple}+S_\text{ms}}$ in apple and $$\frac{S_\text{ms}}{S_\text{apple}+S_\text{ms}}$ in ms on day one (same number of shares in either). – copper.hat Nov 16 '13 at 05:16
  • @copper.hat you are right. That was the point of my sentence in the original answer that maybe you want a different ratio. One can do whatever one wants in this regard. – Ross Millikan Nov 16 '13 at 05:20