Understanding Returns Of Leveraged And Inverse Funds

August 25, 2009

 

A Review Of How Compounding Affects Returns For Periods Greater Than One Day

As previously discussed, leveraged and inverse funds are designed to achieve a multiple of index return only on a daily basis. Over periods greater than one day, returns can be greater or less than the one-day target multiple times the index return. This is a result of the effects of compounding as gains or losses compound daily. Compounding affects all investments over time. It is reflected in index returns as well as the total returns of unleveraged mutual funds, stocks and bonds held over time. The magnitude of the compounding effect is related to market conditions that occur during the investment holding period, whether they are upward-trending, downward-trending or volatile.

Figure1

Figure2

Compounding With Unleveraged Investments

In an upward-trending market, compounding can result in longer-term returns that are greater than the sum of the individual daily returns. In Figure 1, the Index Daily Return column shows that an investment strategy that returns 10 percent a day for two consecutive days generates a 21 percent gain over the two-day period. This is greater than the sum of the individual-day returns, or 20 percent. Similarly, in a downward-trending market, compounding can also result in longer-term returns that are less negative than the sum of the individual daily returns. An investment that declines 10 percent a day for two consecutive days would have a -19 percent return, not -20 percent. But in a volatile market scenario, compounding can result in longer-term returns that are less than the sum of the individual daily returns. An investment that rises 10 percent on one day and declines 10 percent the next would have a -1 percent return, which is less than the 0 percent sum of the individual-day returns.

Compounding With Leveraged (2x) Investments: “The Same But More”

Compounding in leveraged funds can result in gains or losses that occur much faster and to a greater degree, as shown in the 2x Fund Daily Return column. In an upward-trending market, compounding can result in longer-term leveraged returns that are greater than 2x the return of the unleveraged investment. A leveraged fund that grows 20 percent a day (2 x 10 percent index gain) for two consecutive days would have a 44 percent gain, not two times the 21 percent compound gain of the index daily return. In a downward-trending market, compounding results in 2x leveraged fund returns that are less negative than two times the return of the unleveraged investment. A 2x leveraged fund that declines 20 percent a day (2 x 10 percent index decline) for two consecutive days would have a -36 percent return. This is less negative than two times the 19 percent compound loss of the unleveraged investment.

In a volatile market, compounding can result in leveraged longer-term returns that are less than two times the return of the unleveraged investment. A 2x leveraged fund that rises 20 percent one day (2 x 10 percent index gain) and declines 20 percent the next (2 x 10 percent index decline) generates a -4 percent return. This is a greater loss than the two times -1 percent compound return of the unleveraged investment.

Extreme Volatility In 2008 Magnified The Compounding Effect

Volatility in financial markets reached unprecedented levels in the fall of 2008. The global economy experienced a severe contraction in credit, a loss of confidence in financial institutions, and uncertainty over the type and degree of government intervention. This sparked the most severe economic crisis and financial market volatility since the Great Depression of the 1930s (Figure 2). As discussed earlier, extremely volatile markets can have a dramatic effect on leveraged and inverse ETFs. Some investors have noticed large differences between the funds’ longer-term returns and that of the index times the funds’ one-day target.

Figure 2 shows the annualized volatility for rolling three-month daily returns of the S&P 500 Index from mid-1928 through mid-2009. From mid-September through December, three-month volatility reached its highest level (72 percent) over this entire time period. (The average volatility over the 81 years was 16 percent.) Similar extreme volatility levels were reached only two other times over this period: during the Great Depression period (1929 to 1932) and in the equity market crash of 1987.

To understand how leveraged and inverse products fit into portfolio strategies, as well as to establish guidelines for their use, it is important to understand how volatility affects longer-term returns. Specifically, investors should consider the extreme volatility environment that has occurred recently, and the volatility environment that is likely to be experienced over their investment horizons. Volatility depends on a number of economic and financial market factors, but there has already been a decline in U.S. equity risk, with an annualized three-month volatility for the S&P 500 of 34.8 percent as of June 30, 2009. In addition, the CBOE Volatility Index (VIX), a measure of the market’s forward-looking view of volatility conditions, was below 26.3 percent as of the same date.

 

 

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