Leveraged and inverse ETFs, 1

29 Jan 2010 by Jim Fickett.

Leveraged and inverse ETFs, which return, each day, a multiple or the inverse of what a stock market index returns, are both useful and dangerous (like the stock market itself). Much has been written about these tools in the last year, and much of it incorrect. This is the first in a short series of posts on these ETFs. Here we deal with definitions and a particular criticism promulgated by the CFA Institute.

The best known of the leveraged and inverse ETFs are those from Proshares. Here is a brief introduction from the Proshares home page:

Short ProShares – Hedge against downturns, or seek profit when markets decline, with the first ETFs designed to go up when indexes go down or down when indexes go up on a daily basis (before fees and expenses).

Ultra ProShares – Get more exposure for your investment dollars with the first ETFs designed to double the daily performance of popular market indexes (before fees and expenses). …

Most ProShares ETFs Target Daily Returns – Each Short or Ultra ProShares ETF seeks a return that is either 300%, 200%, -100%, -200% or -300% of the return of an index or other benchmark (target) for a single day. Due to the compounding of daily returns, ProShares' returns over periods other than one day will likely differ in amount and possibly direction from the target return for the same period.

Over the last year there has been a great deal of fuss about these funds. Here is the core of the reason why. Consider two days in a row, where the S&P 500 goes up by 1% and then down by 2%.

First look at the S&P 500 itself over the two days. Since (1+.01)*(1-.02) = 1-.01-.0002, the result is that the S&P 500 is down after two days by 1.02% (not down by 1% as you might think without reflection).

Next look what happens with Proshares S&P 500 UltraShort, which returns -200% of the S&P 500, on each day. Over the two days, this fund returns (1-.02)*(1+.04) = 1+.02-.0008; so the ultrashort fund is up 1.92%.

The net effect is that over two days the market is down a little more than 1%, while the ultrashort fund is up a little less than 2%. That is, you get -200% each day, but over two days you get something a little different (in this particular case -188%). For small market movements and short time periods, the effect is not too big an issue (presumably you are more pleased/upset about correctly/incorrectly predicting market direction than about the difference between 200% and 188%). For larger market movements and longer time periods the distortion can be quite significant. From a pragmatic point of view, one needs to know what market conditions, over what time periods, lead to major distortions. That will be the subject of later posts.

Before getting on to serious analysis, here is one example of a mistaken criticism from someone who should know better. In a 5 Apr 2009 article in the Financial Times, entitled Volatility is a drag on leveraged funds in the long run, Rodney Sullivan (CFA, and head of publications at the CFA Institute), wrote,

How does volatility affect returns? Volatility erodes compound returns and hence wealth accumulation over time, a fact not commonly understood. The path that returns take has important effects on the total return achieved and thus risk management. For example, consider an investment that loses 50 per cent of its value in one year and gains 50 per cent of its value in the next year. Although the average return is zero, the investor has actually lost 25 per cent of the initial investment for a negative compound return.

The difference between the average return and the impact on compound return is attributable to volatility, which negatively affects how wealth accumulates over time. The higher the volatility, the lower the investor’s wealth accumulation. …

Because leverage amplifies volatility, leveraged funds will tend to underperform the targeted multiple of the underlying index.

It is of course true that if any investment goes down by 50% and then up by 50%, it does not come back to where it started. However this has nothing whatsoever to do with volatility; it is a simple consequence of arithmetic. If your investment of $100 goes down by 50%, you are taking off 50% of $100 and ending up at $50. If your investment now goes up 50%, you are adding 50% of $50, which is $25, and you end up at $75. The fact that 50% of $50 is smaller than 50% of $100 is not very surprising, and certainly not a useful statement about volatility or leverage.

I include this example not to embarrass anyone, but to say that even sophisticated people get confused about the leveraged and inverse ETFs, and you should read anything in this area quite critically.