Most Popular ArticlesWindham Capital Management, LLC
December 1, 2009
The $10 million investment in the short-term investment 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 an information ratio of 0.79 compared to an information ratio 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.
This particular 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 result at slightly less risk – 17.39% versus 19.29% for the active fund. Moreover, 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:
[(10,000,000 + 11,000,000) ÷ 2] x .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:
[(9,000,000 + 9,720,000) ÷ 2] x .0020 + [(1,000,000 + 1,280,000) ÷ 2] x .025 = 47,220
The chart below summarizes 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.2
Perhaps there is a free lunch after all, or at least a less expensive one!
2 There are several simplifying assumptions that underlie this analysis. We assume, for example, that the income from selling securities short exactly offsets the cost of purchasing securities on margin. In practice, there may be net costs associated with the long/short strategy described in our example. Our example also depends on specific assumptions about return, volatility, interest rates, and fee schedules, which all conspire to produce the specific result you see. Nonetheless, variations in these assumptions will not alter the essence of our argument, which is that it is simple to mimic a typical active fund at a much lower cost by combining an index fund with a pure alpha fund.
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