<Edited on July 11, 2016 to correct errors, clarify, add fees in addition to capital gains and dividends, and provide another example. Note that although there are slight changes to the numbers, the overall take home message remains the same.>

Stanford Chemist recently published an interesting article about Pet Peeves. His first point was that typical graphs showing the contribution of dividends or fees to total returns was misleading and should be replaced by graphs with an exponential scale. The problem is that when using a nominal scale, it looks like dividends are contributing more to total return than are capital gains, and fees are also more important than capital gains.

My first response was to suggest that percentages and exponential growth are difficult to explain well, that exponential scale graphs are difficult for non-professionals to understand, and that not all issues can be explained well with graphs.

However, on further thought, I realized that this is actually a framing issue. The problem is that in the typical graph, the total percentage of annual dividends and fees are added to capital gains (i.e. 7% capital gains + 2% dividends + 1% fees is graphed as 7%, 9%, and 10% returns, respectively).

Instead, however, the values for capital gains, dividends, and fees should be calculated separately such that:

Annual Total Return = Previous Year Cumulative Total Return Value * Total Return %

Annual Dividends = Previous Year Cumulative Total Return Value * Yield %

Annual Fees = Previous Year Cumulative Total Return Value * Fees %

Total cumulative return values are the sum of the annual values.

For example, assuming an initial investment of $100,000, a total return of *9*%, a dividend of 2%, and a fee of 1%, the values at the end of year 1 would be $7,000 for capital gains, $2,000 for dividends, and $1,000 for fees. At the end of the second year, the cumulative values would be $14,630, $4,180, and $2,090, respectively. This process is continued for the total number of years being analyzed. The data are then graphed as a stacked area plot (other graph types may be used with appropriate modifications to the data).

The original graph below plots a hypothetical 9% total return (7% capital gains; 2% dividend) + 1% fees over 50 years, with a starting value of $100,000. I believe that this graph correctly shows the relationship between dividends, capital gains, and fees.

To show that the same relationship holds with different rates, the original graph below plots a hypothetical 5% total return (3% capital gains; 2% dividend) + 1% fees over 50 years, with a starting value of $100,000.