Portfolio Applications For VIX-Based Instruments

October 26, 2011

Path Of Underlying Price Changes
In addition to demonstrating the effects of the length of the holding period on returns, the examples above also highlight that the return on the daily rebalanced instrument is dependent on the path of the changes in the price of the underlying asset or index. In Exhibit C in Figure 8, the price of the underlying instrument at the end of the third day is the same as the price at the beginning of the first day. Therefore, one might conclude that there would be no change in the value of the daily rebalanced leveraged instrument over that time period, but, as the analysis shows, that is not the case. As a result of the level rising significantly and then falling significantly, the return on the daily rebalanced 2x leveraged instrument was -2.1 percent. Clearly, a trader who did not understand the effects of daily rebalancing would not have expected that outcome.

In certain scenarios, daily rebalancing could work in favor of the trader. If the underlying index consistently moves in one direction, then, as shown in Exhibit B, the daily rebalancing works in the trader’s favor—the daily rebalanced instrument outperforms the nonrebalanced instrument. In a trending market, the daily rebalanced leveraged instrument should outperform the nonrebalanced leveraged position. This relationship holds regardless of the direction of the underlying market. This performance results from the positive convexity of daily rebalanced instruments.

Figure 9 compares the return of a daily resetting inverse position in the index with a nondaily resetting short position in the VIX short-term futures index. The outperformance of the daily resetting index is significant. During the January 2009–August 2011 holding period, the daily resetting position returned 249 percent vs. 90 percent for the nonresetting position. This is due to a combination of factors, such as the convexity of daily resetting products, and that effective exposure of the nonresetting position declines as the level of the index falls—as the trade moves in the desired direction, the effective leverage declines.

Outperformance Of Daily Reset Inverse Vs. Short, 2009–Present

A closed-end formula can be used to calculate the expected return on a daily resetting instrument relative to an underlying index based on the return of the underlying index, the volatility of the underlying index and the holding period.3 The analysis assumes a normal distribution of returns for the underlying index (which, as discussed later, the VIX futures indexes are not). Figure 10 assumes a 60 percent annualized volatility, which is the average volatility of the VIX short-term index since 2005.

As Figure 10 demonstrates, the longer the holding period, the more likely that the daily resetting product will underperform the underlying index. For a 10-day holding period, the daily resetting product is expected to outperform the underlying index if the underlying index’s performance is less than –10 percent or is greater than 10 percent. In effect, it behaves as a long straddle position on excess return: In the event of a large move down or up, the product should outperform the underlying index. However, rather than the cost of the straddle being determined by a fixed option premium, it is determined by the expected decay of a resetting position. The 252-day holding period requires a much larger move to generate a positive expected excess return, approximately a +/-55 percent move in the underlying index.

Expected Total Returns Daily Resetting Products

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