I wonder if what I have in mind exists under some name.

Everyone knows the "performance history" charts that are supplied with virtually any mutual fund. All of them start with "100 imaginary money units invested N years ago", then the chart shows how those 100 units changed value over the course of time.

Every point computed relative to that starting date.

I'd be curious to see the "performance history" according to today's date, not an arbitrary date of the past.

Each point of the chart would answer this question: "had you invested 100 units N days ago, what would be the value of that investment today?". Hence the chart's last point would be 100. Just like the usual performance history chart starts at 100 at a point in the past.

I believe that such a chart would be very, very telling, especially in juxtaposition of the usual performance history charts. E.g. imagine your banker, showing you the typical fund which had a 50% increase 5 years ago, but remained relatively stable, maybe with large drops or highs over the last 4 years. Yet, all of it looks in the positive, since the starting point was very low.

Contrast this with how the chart would look like when the reference point is today rather than 5 years ago: it would be immediately apparent that investors who invested in this fund saw a vastly different performance according to when they entered. Some would be very positive, others would be very negative.

I start to suspect that "performance history" charts with a reference point in the distance past prevailed more due to marketing purposes (to make the average fund look better to the naked eye) rather than usefulness.

The inspiration of all this was from a coworker, who mentioned investing in a certain fund that I had invested to, and that his share was in the negative, while for me I only ever remember seeing it positive. Quite eye-opening.

  • 2
    What is your question? Historical data is not hard to come by, you can chart returns from arbitrary dates using yahoo finance and others...
    – quid
    Jul 29, 2019 at 17:23
  • Is there a name for the chart I'm describing? Does it exist out there and I'm just missing it because I don't know how to look it up? Of course I could compute it from a price timeline but that's too much work! Jul 29, 2019 at 17:30
  • If you imply that Yahoo finance can generate such a chart, then that's an answer right there Jul 29, 2019 at 17:31
  • 1
    Have you actually taken a small amount of sample data, drawn up what you're describing, and compared it to a normal growth chart on the same data? Because if I understand what you're looking for, it sounds like it's going to look exactly the same (or mirrored, depending on which way you do the X axis).
    – glibdud
    Jul 29, 2019 at 17:37
  • 1
    Ok, in that case it may be a vertical mirror image of the growth chart. Still essentially the same shape, though. If you draw up an example that shows that that's not the case, I'd recommend showing it so it's more clear what you're looking for.
    – glibdud
    Jul 29, 2019 at 18:09

2 Answers 2

  1. Make a usual performance chart on a log scale.
  2. Reflect the chart upside down.
  3. Draw a horizontal line at today's price.
  4. Label the vertical (log) scale such that today's price is 100 and other levels are scaled in proportion.

Now, a time in the past when the price was half what it is now will read 200 on the chart, and a time when the price was double what it is now will read 50.

  • What's the point of the log scale? Jul 29, 2019 at 20:12
  • @Dimitris It allows the returns to be "reversed" (a reciprocal operation) with just a rigid flip of the chart -- your yellow curve would be exactly the same shape as the original, just upside down. It's another of the advantages of a log scale where compounded returns appear additive. On a linear scale, you have to replot the data with a nonlinear transformation (as in your own answer).
    – nanoman
    Jul 29, 2019 at 20:51

Ok, so here's what the chart would look like (glibdud was correct in the comments - this is a Y-mirror essentially).

AAPL, weekly over 4 years:


The blue line is the actual closing price. The red is relative to $100 of 4 years ago (the usual performance history chart).

Yellow is relative to $100, invested at any point in time in those 4 years.

Even though this information is the same, it does emphasize a different angle. Red tells a picture of long term growth, and one is bound to ignore the two peaks preceding the current price - it's all positive after all, right? No. It only shows the performance of $100 invested exactly 4 years ago.

Whereas the yellow line shows the performance that investors would see today if they had invested $100 at any point of the 4 years. This makes it obvious (especially if there was a hard horizontal line at Y=100, with a green line on top and a red line at the bottom) that there were periods of time where an investment to this stock would lead to current losses.

I don't know, somehow I find this interesting. E.g. I can tell that all investors between 2015 and 2017 that hold on to this stock, now see a ~+50% in its value, without having to animate the chart, to go through all these reference points. And I can immediately see that there's an unhappy crowd of buyers near the start of 2019.

And some basic instructions of how to plot this, in case it isn't obvious:

A1:A_max are the closing prices, A1 the earliest, Amax the latest (today)

Then, the point Y[n] for a regular performance history chart is:

Y[n] = 100 * A[n] / A_max

The point for Y[n] for the reverse chart is:

Y[n] = 100 * A_max / A[N]

(Would be the inverse of the original, if it hadn't been for the 100 factor)

Here's the underlying sheet: https://docs.google.com/spreadsheets/d/19tYsDESVomjWczykykus7JyPnEVQ8rWDVJ8cnv12Fo8/edit?usp=sharing

  • The chart (and formula) looks wrong. The stock has more than doubled, so the yellow line should start above 200.
    – nanoman
    Jul 29, 2019 at 19:51
  • And I don't really see the relevance of the "if I had made a decision X years ago" is a valuable data point for investment decisions...
    – quid
    Jul 29, 2019 at 19:57
  • quid - the usual performance history chart is always a chart of "if I had made a decision X years ago" - but you only get to see exactly one value for X, then you keep track of that one decision. In this chart, you can see the performance of such a decision at every intermediate date. Not a big difference of course, it's the matter of comparing against 100, vs comparing with today's price relative to X years ago, which is generally a number that is not 100, hence it's harder to make such a comparison. Jul 29, 2019 at 20:07
  • @quid Well, you could say the same about any past-performance statistic/plot. And yet they are very commonly used. Note that algorithmic trading methods are trained on exactly those data points -- "if I had made a decision X years/hours ago, this is what would have happened". Here it's a rather elementary transformation of the data -- there are many other ways to crunch it using indicators and backtesting -- but agreed, if you don't place any value on historical data, this wouldn't be useful.
    – nanoman
    Jul 29, 2019 at 20:09
  • I understand that X% gain over Y time is also looking back, and I would also argue that it's not terribly value; it can be a good tool to start filtering down to specific investments, what sectors have moved in the last X years, what companies in that sector are trailing or beating, etc. This is just a 52-week price range with a variable time aperture. Your chart is "is the price today above or below the price X years ago?" It's neat to have a chart I guess but I don't see the value unless it's for comparison purposes.
    – quid
    Jul 29, 2019 at 20:20

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