How fund managers can mislead using investment performance graphs

A picture may be worth a thousand words but a performance graph can be misleading, warns Robert Keavney. He points out ways fund managers and others can create an artificial impression of investment performance.

The marvellous thing about investments is that they are all above average — or so it would seem. Every promoter of any particular investment always manages to produce a graph that purports to show it has beaten its benchmark and its competitors.

To illustrate the sleight of hand behind this, compare Graphs 1 and 2. Graph 1 shows that, over a period of almost a decade (9 years and 2 months) to August 31, 2008, the Dimensional Value Fund (DVF) has produced superior return to Investors Mutual Wholesale Australian Smaller Companies Fund (IMSC).

However, Graph 2 shows that over a period of almost a decade (9 years and 11 months) to the same date, IMSC has produced a superior return to DVF.

Which has done better? Whichever you want!

At this point I should make it clear that my purpose is not to compare these funds — in my view, both are good quality Australian share funds and both have strong track records in excess of their benchmarks over the periods graphed. They are used solely to illustrate how graphs are created to produce a desired impression.

Graphs 1 and 2 differ from each other only in that their starting dates are nine months apart. Graph 1 begins on May 1, 2000, and Graph 2 on August 1, 1999.

Strange though the thought is, let us imagine that I had become a BDM for a fund manager. If I represented Dimensional, you can be sure I would show you Graph 1 but if I represented Investor Mutual, I would show Graph 2.

In either case, I could claim that the graph demonstrates that my fund has produced the better track record.

In both cases, you would be wise to be sceptical about the graph presented to you and to draw no conclusions about relative performance.

This is, in fact, the attitude that planners should take whenever they are shown graphs (or performance tables) by anyone presenting an argument for investing in a particular asset or security.

Before explaining how to create graphs which remove the potential distortions of conventional graphs, let’s focus on the all important part of conventional graphs — near the left-hand edge.

To highlight this, let us consider the proposition that, over periods of greater than 20 years, equities are more volatile than cash but compensate with a higher return.

The case for the affirmative is presented in Graph 3, which shows equities fluctuating around the more steady growth of cash for a few years but, ultimately, delivering a much greater return — over the period from the end of October 1987 to September 1, 2009.

The case for the negative is presented in Graph 4, which shows that equities were far more volatile, yet failed to generate a superior result to the more stable investment in cash since October 1, 1987.

The start date was only one month different, but it was a very significant month. Graph 3 begins shortly after the stock market crash of October 20, 1987, and Graph 4 begins just before it.

This simple example highlights how careful selection of start dates is the key to creating a graph that creates a visual impression supporting whatever case is being argued.

Of course, Graph 4 is less than subtle in its start date selection — the red line plummets almost vertically at the left edge of the graph, revealing starkly that the period was carefully chosen to produce a desired result. But a less extreme version of the same trick was used in Graphs 1 and 2.

At the left edge of Graph 1, the red line races to a lead, straight out of the blocks. In Graph 2, the blue line gets a flying start.

If you scrutinise the left edge of many graphs presented by anyone arguing a given view, you’ll notice this phenomenon — the asset they are promoting quickly gains a lead over its benchmark or competitors. The start date for the graph has been selectively ascertained.

This is an inherent flaw in conventional graphs. Some start date has to be chosen, yet the results which follow may have been quite different with any other date.

It would be more useful if graphs showed how well an investment has performed over all periods of time, from all possible start dates to any end date.

There is an alternative method, which we can call backwards graphs.

Conventional graphs show the compared investments as having a common value of, say, $1,000 at the start date and reflect how the value of the investments have grown over time.

Backwards graphs show the compared investments as having a common end value, and reflect the sums that would have been invested at any point in time to produce a current value of say $1,000.

For example, where a conventional graph might show that over five years $1,000 has grown to $2,000, a backwards graph would show that five years ago $500 would need to have been invested to grow to $1,000. In each case the asset doubled, but was presented differently.

In conventional graphs, the investment which has performed best to a certain point in time will be higher in the graph at the date, whereas in a backwards graph the investment that has performed best since a given date will be lower in the graph on that date.

To explain this, it would have been far better to have turned $80 into $100 over a year than to have only turned $90 into $100.

The smaller initial amount required to produce a common result, the better — thus being lower in the graph at any date reflects a smaller initial investment and hence a stronger return since that period.

Graph 5 is a backwards graph comparing the Dimensional and Investors Mutual funds discussed above.

The red line is lower in the graph over all recent periods of time, reflecting DVF’s stronger performance over all dates since then. However the blue line is lower in the graph in the early years reflecting Investors Mutual’s superior return over longer periods.

However, the graph reveals more than that. As a log scale, the line that slopes more steeply upwards or less steeply downwards, between any two dates, has done better over that period. Looking closer reveals that from mid-2002 to mid-2007 (ie, between the two arrows) the funds ran reasonably parallel.

IMSC was stronger for the three years prior to that — hence the blue line rises continuously, while the red line is flatter and choppier.

However, since mid-2007 DVF has performed better, particularly over the last six months, where the red line rises sharply.

This form of graph removes all start-date bias and allows analysis of relative returns over any time frame.

As a general rule, log scales are far better than normal scales, which produce visual distortions. This is illustrated in Graphs 6 and 7. In Graph 6, it appears that the red line continuously pulls ahead of the blue line over the whole period.

In reality, the red line grows more quickly in year one, but then produces a 1 per cent p.a. lower rate than the blue line for every year after that. Graph 7 shows a realistic representation of this, while the red line is misleading. Only log scales can reflect an accurate picture.

If someone is trying to persuade a planner to recommend a particular fund or strategy using performance graphs as evidence, it is a very useful discipline to ask to be provided the raw data and turn it into a backwards, log-scale graph. This will enable an objective picture of returns over any time frame.

Robert Keavney became a financial planner in 1982, has played many roles since then, and still believes financial planning can be an honourable profession.