The Hidden Cost of Active Management

Investors are well aware of the incremental transaction costs managers incur as they seek to replace securities perceived to be overvalued with those perceived to be undervalued. Moreover, it is no secret that active funds charge much higher fees than passive funds designed to track market indexes. What investors may not be as aware of, however, is that there is a hidden cost associated with most active funds. The typical active fund is more than 90% correlated with the market, yet their relatively high active management fee is applied not only to the fund’s active component, but to its market component as well. Rather than pay active fees on total assets, including those that provide market exposure, an investor could achieve essentially the same result before fees by allocation most of the portfolio to an index fund with the residual allocated to a pure alpha fund that nets out market exposure. The following example illustrates this hidden cost.

Table 1 shows the monthly returns and values of a hypothetical actively managed fund and an index fund, assuming an initial investment of $10 million. The index fund serves as the benchmark for the active fund. In this example, the active fund generates a 2.00% alpha with active risk equal to 3.23% for a respectable information ratio of 0.62. If this performance is consistent with past results, it would not be unreasonable for the fund to charge a fee of 100 basis points, or more.

Table 1: Traditional Active Fund and Index Fund Returns and Values

Sounds pretty standard, right? We might be tempted to hire this talented manager, but let us first consider an alternative. Suppose we instruct the manager to deliver a fund that comprises only the active bets of the portfolio. The manager would do this by first putting the capital to work in a short-term fund. Let’s suppose this fund earns 4.00% annually. The manager then sells short the index fund and uses the proceeds of these short sales to purchase the stocks that are expected to outperform, and levers these exposures 12 to 1. By employing this approach, the manager delivers a pure alpha stream rather than the composite of market returns and alpha that make up the active fund. Table 2 shows the returns of this pure alpha fund (again, assuming an initial investment of $10 million).

Table 2: Pure Alpha Fund Returns and Values

The $10 million investment in the short-term fund compounds at 0.33% per month for a cumulative annual return of 4.00%. The initial exposure to the active fund equals $120 million (12:1 leverage), while the initial exposure to the index fund equals negative $120 million (again, 12:1 leverage). The value of the pure alpha fund each period, therefore, equals the sum of the short term investment fund position and the active fund and index fund positions.

The pure alpha fund produces an annual return of 28.00%, which equals 12 times the active fund’s 2.00% alpha plus 4.00% from the funds invested in the short-term investment fund. The annualized standard deviation of the pure alpha fund is slightly less than 12 times the active fund’s active risk, because it is exposed to the short-term investment fund. Thus the pure alpha fund produces and information ratio of 0.79 compared to an information ratio of 0.62 for the active fund.

Now, let’s consider combining a low cost investment in an index fund with investment in the pure alpha fund, instead of investing in the active fund. Table 3 shows the returns and values of a 90/10 mix of the index fund and the pure alpha fund.

Table 3: 90/10 Mix of Index Fund and Pure Alpha Fund Returns and Values

This peculiar mix of a $9,000,000 initial investment in the index fund, together with an initial investment of $1,000,000 in the pure alpha fund, produces precisely the same return (10.00%) as the active fund, and it achieves this at less risk—17.39% versus 19.29% for the active fund. More importantly, the returns of this strategy are 99.85% correlated with the active fund returns. It is almost a perfect substitute for the active fund. Now, let’s compare the costs of these two strategies.

As stated earlier, the active fund charges 100 basis points, which is applied to the average of the beginning and ending values. Therefore, the cost of the active fund is $105,000, as shown:

(10000000+11000000)2×0.01=105000\frac{\left( 10\,000\,000+11\,000\,000\right)}{2}\times0.01=105\,000

Let’s suppose the index fund charges 20 basis points and the pure alpha fund charges 250 basis points. The premium relative to the active fund compensates for the slight increase in complexity associated with netting out the market exposure to isolate the active bets. With these assumptions, the fee of this combined strategy is substantially lower — only $47,220, as shown:

(9000000+9720000)2×0.02+(1000000+1280000)2×0.025=47220\frac{\left( 9\,000\,000+9\,720\,000\right)}{2}\times0.02+\frac{\left( 1\,000\,000+1\,280\,000\right)}{2}\times0.025=47\,220

The chart below summaries the benefits of combining an index fund with a pure alpha fund. This blended approach delivers 100% of the active fund’s return, incurs only 90% of its risk, and is only 45% as expensive.