The debate between index fund investing and active fund investing is decades old. It really isn’t much of a debate, if you ask me. Historical data from Vanguard and S& P Dow Jones Indices shows that index funds have outperformed actively managed funds in every investment category over the long-term. But there’s another measure that isn’t discussed as frequently. It’s the payout.

Most studies comparing index funds to actively managed funds are focused on the percentage of active funds that outperformed or underperformed the index product. While that’s a good start, an equally interesting number is the median excess return generated by the winning active funds versus the median shortfall in return experienced by the losing funds. This is called the payout.

Let’s assume you own a racehorse. You enter the horse in a race against three other horses owned by other people. Assume all four owners put $100 into a hat in a winner-take-all bet. If your horse wins, you’ll collect $400 on your $100 bet. That’s a 4:1 payout ratio.

Let’s assume your horse wins, but you only collect $200 of the $400 in the hat. The other $200 goes to the racetrack for various expenses and their profit margin. It won’t take you long to realize that despite owning a winning racehorse, you couldn’t possibly make money in the long-term because the payout for winning isn’t enough to compensate you for the risk of losing.

Payout is important to the active versus passive debate also. It’s not just the percentage of active funds that win or lose relative to index funds that’s important; the payout earned from winning and the shortfall experienced by losing is equally important.

Figure 1 is a performance payout chart for large-cap U.S. actively managed equity funds compared to the Vanguard Total Stock Market Index Fund (VTSMX). It compares the annualized performance over a 16-year period from 1997 to 2012. The long tails were excluded.

The CRSP Survivor-Bias-Free US Mutual Fund Database served as the foundation for this data. The database was cleaned to exclude B shares, C shares, institutional shares, variable annuities, and does not include sales charges or back-end fees. See this whitepaper by me and Alex Benke CFP®, Betterment for more information on this methodology.

**Figure 1: The relative performance of active large cap U.S. equity funds to VTSMX from 1997-2012**

*Source: Chart: Alex Benke CFP®, Data: CRSP Survivor-Bias-Free US Mutual Fund Database*

Figure 1 shows the relative annualized performance of actively managed large-cap U.S. equity funds to the Vanguard Total Stock Market Index Fund (VTSMX). The X-axis represents the percentage of actively managed funds that outperformed and underperformed. Bars to the left of the intersection are underperforming funds and the bars to the right are outperforming funds. VTSMX outperformed 77.1% of the active funds during the period.

The Y-axis is the annualized percentage difference in return of the active funds less VTSMX. The chart is truncated to better illustrate the spread of these returns. The median underperforming active funds fell short of VTSMX by -2.01% annually while the outperforming funds beat it by 0.97% annually.

Figure 1 gives us better insight into the performance of active funds versus a comparable index fund only looking at the winning percentage probability. With both probability and payout on the chart, we are in a better position to make an informed decision.

Given that the index fund outperformed active funds 77.1% of the time, and given that the median losing active fund fell short of the index fund by -2.01% while the median winning active fund beat the index fund by 0.97%, intuitively, index funds may be a good choice for investors from both perspectives.

Let’s go a step further and ask how much the median winning actively managed fund would have had to earn in excess return in order to make active management a fair payout. First, take the 77.1% losing percentage for actively managed funds and multiply it by the -2.01% median shortfall for those funds. The result is a -1.24% expected downside payout. Second, take the 22.9% winning active funds and multiply it by the 0.97% median excess return. This result is a 0.22% expected upside payout.

Next, calculate how much excess return the median winning active fund would have to earn to make up for the -1.24% expected downside payout. This is done by dividing -1.24% by 22.9% and changing the sign.

The answer is 5.4% annually. This is the amount of excess performance the median active fund would need to achieve for a fair game payout based on the -2.01% median downside risk. In reality, the median winning fund earned only 0.97% in annual excess return — far below the amount needed for a fair game. The flip side of this analysis is to determine what the median losing 77.1% of active funds would have needed to lose by to match the 0.22% expected upside payout. This is done by dividing 0.22% by 77.1%.

The answer is -0.30% annually. This is the amount of shortfall the median losing active fund would need to achieve to create a fair game based on a 0.97% median winning active fund payout. In reality, the median losing fund fell short by -2.01% annually – far worse than the -0.30% annually needed for a fair game.

There are risks when investing in funds or any other product. If you win with active management, you may have to earn enough excess return to compensate you for the probability of loss and the expected size of the loss.

Payout is the other side of the coin in the active versus passive debate. When active fund payouts are analyzed alongside the probability of winning against index funds, actively managed funds look worse than if only the probability was considered. Even when investors win with active management, the payout may not be enough relative to the risk.