Tuesday, 3 December 2013

Leveraged ETFs: Volatility Drag And Tracking Error Continue To Be Minimal (Useful)

By: Gary Jakacky, Sep 29 2013, 05:13

seekingalpha.com/article/1719092-leveraged-etfs-volatility-drag-and-tracking-error-continue-to-be-minimal

Just about a year ago, I analyzed some leveraged ETFs and compared their performance to their underlying index. See here .

Leveraged ETFs attempt to double, or even triple, the performance of broad indicators like the Dow Industrials or S&P 500.

I addressed two concerns. One was tracking error. This is a legitimate concern for any ETF owner. Suppose the S&P 500 advances 7 percent in 3 months. Then we would expect the SPDR 500 Index Trust ETF (SPY ) to also go up 7 percent. Furthermore, we would expect it to track the zigs and zags of the broad market quite faithfully.

Look below. You have real sharp vision if you can even distinguish between the S&P500 and SPY on this chart. No tracking error here.

What about the ProShares Ultra S&P500 ETF (SSO )? Their Yahoo profile says the fund is designed to track two times the daily performance of the S&P500 .

Pay attention to the words daily performance. Leveraged ETFs such as SSO rebalance their portfolio each day, using futures, derivatives and stock holdings, in order to achieve this 2x performance. This can lead to losses caused by volatility drag. Let me turn to an illustration of volatility drag, using an extreme example to make the discussion and mathematics brief.

Suppose you bought a stock for $20 a share. The first day it rises to $25; the second, it falls to $15, and the third day it went back up to $20. A buy-and-hold investor has broken even. What happens to an ETF adjusted daily designed to track this one stock?

OOPS! Not so good, especially a double index. On the first day the stock gained 25 percent, doubled this is 50 percent. On the second day it fell 40 percent; doubled, this is an 80 percent loss; and on the third day it rose about 33 percent, for a 66 percent doubled gain. What is your overall result if you rebalance each of the three days? Turning the percentages into decimals, and multiplying we have

• (1.00 + .50) for day 1;
• (1.00 — .80) for day 2; and
• (1.00 + .66) for day 3. The final result is

(1.5)x(.2)x(1.66) or approximately .50.

Returning to percentages (isn’t math fun!) you have 50 percent of your investment remaining. You have lost half your money! Savvy investors can see that since you lost so much on the second day, it was almost impossible for the recovery on day three to make much of a difference.

Now we can look at the data. The chart below compares SSO against the S&P500 for the past twelve months. There seems to be very little problem with tracking error, and as you will see in the calculations beneath it, no volatility drag, either.

Over the last year the S&P500 has gained 18 percent. If you double this, 36 percent, it appears that SSO has overperformed a bit, since it is up almost 40 percent.

This is not quite true. The trick lies in the leveraged ETF mathematics and arithmetic. For very small percentage changes, such as 1 percent or half a percent, typical of day to day fluctuations in the market, you can just double the percentage and you will get SSO performance on that date accurately enough.

For larger percentage changes typical of several months, a year, or longer, you must use a different calculation. You do not double the performance, you square it.

Thus after one year you gained 18 percent, or you had

(1.00 + 0.18) = (1.18)

times your original holdings. For a 2x leveraged ETF, when you square this number, you get

(1.18)*(1.18) = 1.39, or a 39 percent increase in your holdings.

And that is almost exactly how much SOO gained in the last twelve months.

Why has there been no volatility drag?

In the extreme example above, daily fluctuations were very large. For the smaller percentage changes typical of a broad index like the S&P 500 each day the drag is barely noticeable. Mid June’s 1 percent drop in the S&P 500 was the biggest daily change over the past year. On most days changes have been far less than that. So drag is minimal.

We do see a bit of overperformance in the ProShares Ultra Dow 30 ETF (DDM ), though. This ETF is designed to double the returns on the Dow Jones Industrial Average.

The Dow has gained about 14 percent in the last year; using the calculations illustrated above we would expect DDM to gain

(1.14)*(1.14) = 1.30 or thirty percent.

The ETF actually gained 32 percent in the last year. A tad better than expected.

Thus, despite the concern about tracking error and volatility drag for broad index based ETFs over long periods of time, I find little evidence of either.

Readers’ Comments:

1. Gary this is VERY useful. I have owned UYG (Dow Financials double long ETF) for 5 years and have absolutely no complaints about its performance, many doom and gloom articles notwithstanding. It has consistently doubled its index, up and down, and more recently over both 1 and 3 year periods. SSO is a great investment going forward if one believes in the US story (I do) and the fundamental weakness of competitors such as Europe (I also do).

Good stuff, thank you.

2. Author’s Reply:

Thanks. Keep in mind that very volatile periods will see drag for the reasons I mentioned. It took me a while to realise that 2x was good enough for small % changes; but squaring was necessary for larger % ages. and then it all come together.

I also think there is a mathematically adept group of SA followers. And, I use these statistics-based SA articles on my resume, since I am snooping around for a position as a stat guy for investment/analytical firms

By: Gary Jakacky, Oct 22 2012, 15:48

seekingalpha.com/article/939411-proshares-ultra-s-p500-etf-an-amplified-and-interesting-ride

A few weeks ago I evaluated the Proshares Ultrashort S&P500 ETF, (SDS ). That ETF was designed to perform twice the inverse of the popular Standard and Poor’s 500: if the latter gained 10%, you would expect the Ultrashort to fall 20%. The overall conclusion was the SDS performed as expected, with little tracking error and not much evidence of volatility drag. The latter arises from the daily rebalancing of Ultra ETF holdings. I shall give an example in a moment.

This time we shall examine the performance of the ProShares Ultra S&P500 ETF (SSO ). The fund is designed, according to Yahoo Finance, to invest in securities and derivatives that ProShare Advisors believes, in combination, should have similar daily return characteristics as two times (2x) the daily return of the index. In simpler words this ETF tries to double the market return. If the S&P500 rose 1.3% yesterday, you would expect SSO to gain 2.6%, or twice as much. A nice way to rebuild your wealth on short notice, if you can time the market correctly.

Of course, the opposite also is true: If the market dropped 1% yesterday, you would expect SSO to drop 2%.

Let me turn to an illustration of volatility drag first, using an extreme example to make the discussion and mathematics brief. Suppose you bought a stock for $20 a share. The first day it rises to $25; the second, it falls to $15, and the third day it went back up to $20. A buy-and-hold investor has broken even. What happens to an ETF designed to track this one stock?

OOPS! Not so good, especially a double index. On the first day the stock gained 25%, doubled this is 50%. On the second day it fell 40%; doubled, this is an 80% loss; and on the third day it rose about 33%, for a 66% doubled gain. What is your overall result if you rebalance each of the three days? Turning the percentages into decimals, and multiplying we have

• (1.00 + .50) for day 1;
• (1.00 — .80) for day 2; and
• (1.00 + .66) for day 3. The final result is

(1.5)x(.2)x(1.66) or approximately .50.

Returning to percentages (isn’t math fun!) you have 50% of your investment remaining. You have lost half your money!

This example is extreme, but the point is that over a long period of time market volatility acts as a drag (thus the name) on the performance of ETFs which rebalance their portfolios daily.

How does this affect SSO? Let’s see how SSO performs under various market conditions and draw our own conclusions.

Start with advancing markets. Traders would be looking for this when they buy SSO. From March 2009 to May 2010 the S&P500, as measured by the S&P500 Trust Series ETF (SPY ), gained over 70%. And SSO?

The double ETF gained nearly 180%, more than double than the index it was designed to track: twice 70% would be 140%. While you may be tempted to say bully for you, SSO!, remember this technically does mean the fund is not performing as advertised.

This overperformance occurs in other bull market periods as well. Look at the second leg of the current bull market:

Double the 30% gain of the SPY and you get 60%, whereas the SSO shot up nearly 70%.

And in the third leg up, which may have ended last month?

Double the 35% gain in the SPY and you get 70%, whereas SSO gained nearly 78%. The Holy Grail of finance: a consistent overperformer!

Of course, perhaps the SSO is simply more than twice as volatile as the index it is designed to track. A finance professor would say the BETA of this ETF is greater than 2. If that is the case we would expect results to suffer more than we expect, in declining markets. No shortage of examples of those in the last few years. Let see how the SSO performed in the 3 down waves of the great recession.

The first wave, in late 2007.

With a 10% decline in the market, we’d expect a 20% decline in SSO, but the actual fall was 25%. But look at the second wave, a big down move in the market:

The market fell by 37%; a simple 2x analysis would suggest a fall of 74%. The SSO fell less than this. Overperformance? No. Tricky mathematics. though we need not get into the details here. (I will in the comment section for those who wish).

In a nutshell, since SSO is an equity holding, it cannot fall more than 100% in value. For example, suppose the market fell 70%. a nasty day! Could you expect SSO to drop twice that, or 140%? Impossible. It can decline only 100%; after that it has gone to zero. The bigger the drop in the index the ETF is designed to track, the greater this percentage overperformance becomes.

We see this with the final leg of the bear as well. The market dropped 27% in the first three months of 2009. The SSO did not fall 54%, but somewhat less:

about 47%, not the 54% we expected.

Finally, as I discussed in my first article, the real opportunity for tracking error and volatility drag to show themselves are in sideways markets. From February to August of 2010 stocks traded flat. So did the SSO:

Same for a similar period in 2011:

Thus, first we can conclude the Proshares Ultra S&P500 exhibits no significant volatility drag over a periods up to several months. While my extreme example showed such drag, the daily percentage fluctuations typical of broad market indexes such as the S&P500 are much smaller—less than 1% on most days—so the drag is very minor.

Second, SSO appears to more volatile, especially to the upside, than its 2x moniker suggests. Thus for traders confident they can identify periods of rising stock prices, SSO provides opportunity for eye-popping total returns.

Readers’ Comments

1. Beta is not a measure for correlation of return for a long time period. Try plotting the daily return of SSO against SPY, you will get a regression line with a slope very close to 2.

2. Author’s reply:

Correct. it is not simple correlation (which does not imply a causal relationship, and does not allow for a Y intercept, or alpha. which is what this site is all about. )

The slope of that regression line would be the Beta you are referring to.

Beta can be determined over whatever time period the researcher chooses. Daily data, for one year, is the favorite.

Because of the odd mathematics by which the returns of 2x funds (and inverse 2x funds) are determined, the daily beta is very close to two. The beta in bull markets gets greater and greater than 2, as the time period lengthens; and the beta in bear markets gets less and less than 2, as the bear market lengthens.

3. I don’t disagree with you that you can choose any time period. The problem lies with that you just picked a few time periods of variable lengths and presented the result. That does not sound like beta to me. If you have a chart with annual return comparison of the past couple year, that would give a better idea of how the beta looks like if calculated by the year.

Also, as you quoted, Proshares created this ETF so that it should have similar daily return characteristics as two times (2x) the daily return of the index. The keyword is daily. If you want monthly 2x funds, there are some out there. Yearly 2x funds just aren’t here yet.

The returns of 2x funds aren’t odd mathematics, it’s just compounding. You can’t really complain about credit cards compounding interest if the balance is not paid in full.

4. Author’s reply:

You are getting too hung up on a one sentence, off the cuff reference to beta. The article is about volatility drag and whether it was significant in the intermediate term. The answer is a qualified, no. Thus 2x ETFs can be used effectively by position traders as well as day traders.

I chose time periods of variable lengths because the bull market and bear market legs I was examining, also lasted various lengths. If SDS doesn’t perform well during bear stretches, its not likely to EVER perform well. If SSO does not perform well during bull stretches, it is not likely to EVER perform well. Ergo, i chose bull and bear market legs of several months to over a year.

5. if you want to understand why sso and sds are bed investment for long period, just put both on a single graph and check that graph foe 5 years period.

i am short sds and sso since Jan 2010

6. I like your short play on these ETF’s. Are you shorting the ETF or selling options? Selling options looks like a viable play to me. I’m curious as to how you play these ETF’s and what kind of return you are experiencing.

7. Author’s Reply:

Correct. Over 5 years the cumulative effect of volatility drag is incredible. My article dealt with shorter time periods from several months to over a year, because these were rtime periods when the market was either predominantly rising, or falling, and I wanted to see how the ETFs performed over these meaningful and relevant intervals. If the clouds parted and God told you the market was going to fall for the next 5 months, you’d want to own SDS for those 5 months, believe me. Ditto with SSO if a bull market leg was coming. An intermediate trader would not hold SSO or SDS during periods when the he expected prices to move against him.

Posted: Singapore, 4th Dec 2013 @ 12.07pm

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PERFORMANCE FROM 21 MARCH 2013 — 3 JANUARY 2014 (200 DAYS)

PERFORMANCE FROM 2O JUNE 2006 — 3 JANUARY 2014 (1899 DAYS)

PERFORMANCE FROM 26 FEB 2009 — 3 JANUARY 2014 (1233 DAYS)

PAYS TO BUY LEVERAGED ETFs AT MAJOR LOW POINTS