Chris P pointed us to the "Financial Comeback" calculator, surely a well-meaning joke from the folks at the Times.Here is how one gets to make a 40% loss back in just six years!
Surely, someone has to tell them about simulation. They have to assume a probability distribution on the annual returns, and show us some sample paths. Using the average annualized historical return in essence wipes out all variability and no wonder it's smooth sailing upwards. Eternal optimist.
Here is Chris' comment:
The bad news is that the range of values it offers does not include the return on the market from last year (-31% to -36%). I guess they are optimistic.
The interactive features of this chart, however, impressed me. The smooth adjustment to the chart as one slides the control, including the automatic choice of appropriate axis labels, is very nice indeed.
Okay, they want to trademark the name of the calculator so perhaps this is serious.
Reference: "Calculate your financial comeback", Jan 6 2009.
Matt H., who authored the previous post, and Charles G. both pointed to a great example of how people like readers here can make a difference. A bad chart got made over!
The Financial Times
published a chart from a JP Morgan report, using ... you guessed it ...
bubbles to illustrate the deep plunge in market capitalization of many
Some readers at the blog were none too happy with the choice of bubble charts. Among other things, the designer made the common mistake of plotting proportional diameters rather than proportional areas. This is clear from looking at JP Morgan's bubble.
This chart exposes the weakness of bubble charts well. Look at the top row of bubbles. Most of them look so similar it is impossible to know, without spending much time studying the circles, which bank was hurt more.
Eventually, a bar chart was produced. Felix Salmon linked to it. I am not sure how the banks were ordered in this chart. It isn't one of the two obvious dimensions, nor is it in alphabetical order.
In fact, neither the bubble nor the bar chart works well for this case. What we need is the Case-Schiller style asset-bubble life cycle chart. In order to interpret these changes in market caps, we need to know how big was the bubble, and then how steep was the consequent decline. Take a look at our discussion of real estate bubble charts here.
Reference: "Bank capitalization chart of the day", Felix Salmon at Portfolio.com and "Bank picture du jour", FT Alphaville, Jan 21 2008.
Message to readers: I have a large backlog of reader suggestions. Please be patient as I slowly get through them. The frequency of posts will remain lower for the time being as I am busy finalizing a draft of a book. More on that in the near future.
Matt H, a reader, sent in the following entry (with minor edits).
I saw a couple of bad charts on money.cnn.com and thought I'd submit them to you.
They're both part of the same
feature on investment bargains caused by the recession.
It seems to me like both charts would have made their points more
eloquently by using a much simpler, more common form, like a bar
In Chart A, cubes are used to display the difference between
treasury bond yields and AAA municipal bond yields at the two-year
horizon and the ten-year horizon. The volume of each cube corresponds
to the yield for the given type of bond in the given period (I think),
which spreads the one dimension being compared (yields) across three
dimensions, making the differences look smaller than they really are. [...] At the two-year horizon, the two yields being compared are 1.16% for
Treasury bonds and 3.01% for AAA municipal bonds. The yield for AAA
municipal bonds in this case is more than 2.5 times larger than the
yield for Treasury bonds, but the difference doesn't look nearly that
big in the chart provided. [...]
Time out. Let me add that the inadvertent reference to an optical illusion concerning foreground and background! The "outline only" cube on the left should have approximately the same volume as the "solid red" cube on the right (3.01% versus 3.30%) and yet the red cube appeared quite a bit larger because our eyes reacted to the solid color more than thin outlines.
In Chart B, [...] Again, the
metric in question is bond yields: ten-year Treasury bond yields
compared to investment-grade corporate bond yields. The 2008 figure
for each is shown alongside the five-year average. This chart uses the
area of a circle to express these yields, spreading the one-dimensional
value across two dimensions. As in Chart A, the result is a chart in
which the difference between values does not appear as large as it
I will also send
a simple bar chart version of each chart -- the bar charts should illustrate the differences in yields more effectively than the charts actually used in this article.
These are his revised charts:
We can do even better to convert the chart on the right to a time-seriesline chart. Instead of the five-year average, it is better to display the gap beween treasury and corporate bonds for each of the five years plus 2008. This should make for a more eye-catching graphic.
Reference: "Investment in the bargain bin", CNN Money.
In the last post, we removed the time dimension in order to clarify certain aspects of the S&P 500 returns. We found that with an investment horizon of five years, there was historically about a 25% chance of losing money and a 25% chance of more than doubling.
Even though we looked at cumulative returns, it was still the case that the data was serially correlated; in other words, it could be that the eventual return was not independent of the starting year of the five-year period. To gauge this, we must return to the time dimension that was previously removed.
The chart on the right plots the five-year returns for all five-year periods starting from 1910. What it shows is that even with longer time frames, timing or luck still plays a key role.
For example, any such investment in the S&P 500 between late 1950s and 1980 did not double in five years no matter which year the investment was made. Then again, if the investment was made in the 40s and 50s, no one lost money in a five-year period, similarly in the 1980s.
So the fact that we saw a 25% chance of doubling (or losing money) over history says much less about what might happen in the next 5 years than the simple number suggests.
In response to a reader's comment - the data series was described as "real total return" so these are inflation-adjusted.
I ran across this hugely successful chart on Dean Foster's home page (and noted that he and his Wharton colleagues have a nice blog picking apart statistical errors committed in public.)
This is a histogram plotting the historical year-on-year returns of the S&P 500 index, binned into 10%-levels. It succeeds on two levels: the innovation of printing the years inside little blocks provides extra information without distracting the overall picture; the key message of this plot, that the negative return of 2008 is a negative outlier in the history of returns, is extremely clear.
This, in my mind, is a superior presentation than the usual time-seriesline chart that we see in every economics publication. For some purposes, it is better to unshackle ourselves from the linear time dimension, and this is a good example.
One question/comment: within each 10% level, the years are arranged in reverse chronological order fro top to bottom. This facilitates searching for a particular year. The obvious alternative is to order by the actual level of return, so that the result is akin to a stem-and-leaf plot.
While I like the graphical aspect of the chart, I feel like it has limited function. This graph appears useful to anyone who has a one-year investment horizon. If I want to predict what next year's S&P 500 return is, I might take a random sample from this distribution. However, as a lazy investor, I never look at a one-year horizon so this creates two problems: if I am looking five years out, I can't take five samples from this distribution because there is serial correlation in this data for sure; even if I could take those five samples, it is difficult to compute the five-year return in my head.
So what I did was to take the data and replicate this histogram for 2-year, 3-year, 5-year, 10-year, etc. returns. The results are as follows. I decided to simplify further and use Tukey's boxplot instead of the histogram. The data are real compounded total returns from S&P 500 from 1910-2008.
The boxplot on the top right shows that there is about a 25% chance that an investment in the S&P 500 will return negative in real terms in any three-year period (below the green line). At the other end, there is a 25% chance of getting earning more than 50% on the principal during those three years.
The next set of boxplots compared 5-year returns to 10-year returns and 10-year returns to 20-year returns. If we have a 10-year horizon, there is still positive chance of reaching the end of the decade and finding the investment under water! The median 10-year return is approximately doubling the principal (about 8% per annum compounded).
In a twenty-year period, there is hardly any chance of not making money on the S&P. There were two positive outliers of over 1000% (about 13% per annum compounded over 20 years).
Jon's comment on the previous post pretty much anticipated this post. The prior post concentrated on graphical matters. However, the biggest issue with that chart is the choice of metrics. If the idea is to explore the potential adverse effect of a sharp decline in endowment investment performance, then it is not clear why one should be comparing the proportion of endowment funds and the proportion of operating revenues paid for by endowment funds. A missing element from these two series is the relative size of the budgets of these different departments.
The next chart shows the proportion of each school's operating costs accounted for by endowment funds together with the total size of its operating costs.
We can turn the ratio around and directly compute how much of the total amount of endowment funds distributed for operating costs is accounted for by each school. This is really the simplest metric that gets to the question.
There are really two possible worries: for the School of Arts and Sciences, who pays for just about $1 billion costs with endowment funds, any significant reduction in distribution will leave a gaping hole; for a department like Radcliffe that pays for over 80% of its operating budget out of endowment funds, obviously a reduction in distribution can cause problems but we are talking about a base of $18 million rather than $1 billion.
Reference: Harvard University Financial Report, 2008; Harvard Fact Book 2007
PS. The first source did not contain any data on operating budgets so the first set of graphs (now replaced) did not show what I intended to show. The new ones used the right data and had the right order of magnitude in terms of budgets ranging from millions to 1 billion. The 2008 data are not available as of yet.
When comparing two time series, one typically wants to discuss the size of the gap as it changes over time. This Business Weekchart, for example, depicted for readers the expanding gap between intra-day high and low prices of the S&P 500 for 2008.
This chart construct is effective at pointing out large changes but lacks precision in conveying smaller differences, or trends. It is always a good idea to plot the gap directly, as we will show below.
More importantly, a better choice of scale can help a lot. By focusing exclusively on variability (extreme values), this chart hides the relevant information of the closing prices of the S&P. A point spread of a 100 points means more when the index is at 800 than at 1200. In order to capture this, we can divide the point spread by the opening price of that day so we say the gap is one-eighth or one-twelfth of the opening price.
The junkart version makes both changes. The top chart fixes the scale, plotting the point spread as a percentage of daily opening prices. Relative to the original chart, the variability in the front part of 2008 was muted because the index was at higher levels back then.
The bottom chart plots the gap sizes (lengths of the high-low lines). It is without doubt that directly plotting the gaps showcases the key message. The current level of volatility is more than double what occurred at the beginning of the year.
If one wants to illuminate the trend as opposed to daily fluctuations, a further improvement will be using moving averages.
For those interested, shown below is a scatter plot that compares the original point spread and the derived point spread, which shows that the change is not trivial.
Reference: "The Market: A Daily Roller Coaster", Business Week, Oct 27 2008.