Case Studies: Hedging With Single Inverse**ETFs In Different Market Conditions**

We use case studies to further illustrate hedging with single inverse ETFs, demonstrating the need to rebalance. With case studies representing periods of rising and falling benchmark returns and different volatility environments, we can show how the frequency of rebalancing is linked to market conditions and how the net exposure varies between rebalancing points.

We present two different market scenarios using S&P 500 returns: 1) a period of declining returns (H2 2008); and 2) a rising return period (H2 2009). To simulate the performance objective of an inverse and leveraged ETF, we’ve taken each of the S&P 500’s daily returns and multiplied them by -1 and -2, thus ignoring fees, financing, interest and expenses.^{11} In all of the case studies, we employ a fixed-percentage rebalancing approach to keep the net exposure of the combined long and hedge positions within a fixed-percentage band of +/-10 percent. With a fixed-percentage approach, rebalancing occurs when this range is exceeded in either direction.

Case Study I: Single Inverse Hedge In A Declining Return Environment

Figure 2 shows the risk/return characteristics and net exposure of fully (100 percent) and partially (50 percent) hedged positions in the S&P 500 during the second half of 2008. The table at the bottom of Figure 2 shows the net exposure of the 100 percent hedged position^{12} and the points where rebalances occurred, which are seen where the black line pierces the +10 percent and -10 percent rebalancing bands. Through early August 2008, net exposure would have stayed relatively stable, only breaking out of the band and requiring rebalancing twice between June 30 and the end of August. At that point, the S&P 500 began to decline steeply, with higher volatility through year-end. During this latter period, fluctuations in net exposure increased as the gap between the return of the S&P 500 and the inverse strategy increasingly diverged, prompting the need for more frequent rebalancing. For the six months as a whole, the 10 percent rebalancing band required the hedge to be adjusted, on average, about every 10 days.

As summarized in the table at the bottom of Figure 2, rebalancing helped maintain a consistent hedge during the six-month horizon, and the hedge significantly reduced losses and return volatility over the entire six-month period. A 50 percent hedged position declined by just over 10 percent during this period when the index return was -28.5 percent, and reduced volatility from 54 percent to less than 15 percent.^{13} As hoped, the fully hedged position has close to zero return and zero volatility.^{14}

Case Study II: Single Inverse Hedge In A Rising Return Environment

In our next case study, we looked at the same hedging strategies against S&P 500 exposure but in a period of rising returns, specifically the second half of 2009 when the S&P 500 appreciated by 22.6 percent. Results for this market scenario are shown in Figure 3.

Over this period, the volatility of the S&P 500 index was 17 percent, much less than that experienced during the turbulent second half of 2008. Not surprisingly, the net exposure of the hedging strategies was far less volatile as well. A 10 percent band applied over this particular period prompted rebalancing about every 31 days versus the average of every 10 days in the second half of 2008. All of these rebalances were additions to the size of hedge position, as the inverse position declined relative to the index. This would have required adding additional capital to the hedging strategy over this period. The hedging strategies succeeded in reducing the volatility of S&P 500 exposure and maintaining the desired equity exposures near 0 percent and 50 percent, but at the cost of lower returns.

In both market scenarios, we see that the -1x hedging strategies, using a 10 percent rebalancing band for the hedge, fulfilled the objective of reducing downside return risk significantly, measured both by volatility and maximum drawdown. On balance, it is important to understand that these hedging strategies may significantly reduce upside returns as well.