Read the Beforeitsnews.com story here. Advertise at Before It's News here.
Profile image
By Quantum Blog (Reporter)
Contributor profile | More stories
Story Views
Now:
Last hour:
Last 24 hours:
Total:

FAS vs FAZ - inverse etf behavior

% of readers think this story is Fact. Add your two cents.


There has been a lot of talk about leveraged etf (under) performance . In general, these etfs seem to underperform their benchmark. A google search for ‘leveraged etf decay’ will provide a couple of hours worth of reading material, so  I will try to limit information redundancy to a minimum. I’ll limit myself to a single sentence introduction: ‘leveraged and inverse etfs are based on the arithmetic returns of their benchmark, which introduces a negative tracking error’.
If you have little idea about what I’m talking about, take a look here for an explanation of the difference between the arithmetic and geometric returns.
So I’ll continue the examination of inverse etf dynamics from what is already known: underperformance.

Let’s first take a look at the relation between FAS and FAZ. Both are 3x leveraged versions of the same underlying index, FAZ being the inverse one.

Here can be seen clearly that while the etfs move in the opposite directions, FAS in the long run outperforms FAZ.
Their daily arithmetic returns however are performing exactly as advertised:

However, anybody holding a position for longer than one time period (being a day) should be only interested in geometric returns, or log returns.
When log returns of these two are examined, the picture changes:

Instead of following a straight line, the returns are skewed in favor of FAS. The green line here is a theoretical estimation of inverse relation based on algebraic returns.
For example: FAS gains 10% on a given day and FAZ follows with a 10% decline. In log returns this would translate to FAS: log(1.1) = 0.0953   FAZ: log(0.9)=-0.1054.   The log returns are not equal (duh!) but skewed in favor of FAS . When the position is held for a longer time and the pair moves 10% every day (no matter in which direction), we loose approx 0.5% per day of the total position.
Please take a note that this ‘skew’ is not about leverage, but inverse algebraic relationship. Leverage only provides more daily movement, exaggerating the skew.
A handy chart below shows the under performance of inverse etf as a function of its underlying daily change. One can see that the error is relatively small for <1% moves, but increases rapidly with bigger moves.

The difference between geometric and algebraic returns has been explained by E.Chan on his blog (and in his book) . However, he made a mistake in the calculation of average loss per time period stating it to be -0.5%.
When we have a 50/50 chance of winning or loosing 1% , in fact the expected return per minute is exp(0.5*log(1.01)+0.5*log(0.99)), which translates to -.005 % per minute, which is equivalent to -7%  in 24 hours ;-) .

There are a couple of very interesting strategies that can be derived from this asymmetry, if one can handle the  math and rebalancing logic.


Source: http://www.matlabtrading.com/2011/05/fas-vs-faz-inverse-etf-behavior.html



Before It’s News® is a community of individuals who report on what’s going on around them, from all around the world.

Anyone can join.
Anyone can contribute.
Anyone can become informed about their world.

"United We Stand" Click Here To Create Your Personal Citizen Journalist Account Today, Be Sure To Invite Your Friends.

Before It’s News® is a community of individuals who report on what’s going on around them, from all around the world. Anyone can join. Anyone can contribute. Anyone can become informed about their world. "United We Stand" Click Here To Create Your Personal Citizen Journalist Account Today, Be Sure To Invite Your Friends.


LION'S MANE PRODUCT


Try Our Lion’s Mane WHOLE MIND Nootropic Blend 60 Capsules


Mushrooms are having a moment. One fabulous fungus in particular, lion’s mane, may help improve memory, depression and anxiety symptoms. They are also an excellent source of nutrients that show promise as a therapy for dementia, and other neurodegenerative diseases. If you’re living with anxiety or depression, you may be curious about all the therapy options out there — including the natural ones.Our Lion’s Mane WHOLE MIND Nootropic Blend has been formulated to utilize the potency of Lion’s mane but also include the benefits of four other Highly Beneficial Mushrooms. Synergistically, they work together to Build your health through improving cognitive function and immunity regardless of your age. Our Nootropic not only improves your Cognitive Function and Activates your Immune System, but it benefits growth of Essential Gut Flora, further enhancing your Vitality.



Our Formula includes: Lion’s Mane Mushrooms which Increase Brain Power through nerve growth, lessen anxiety, reduce depression, and improve concentration. Its an excellent adaptogen, promotes sleep and improves immunity. Shiitake Mushrooms which Fight cancer cells and infectious disease, boost the immune system, promotes brain function, and serves as a source of B vitamins. Maitake Mushrooms which regulate blood sugar levels of diabetics, reduce hypertension and boosts the immune system. Reishi Mushrooms which Fight inflammation, liver disease, fatigue, tumor growth and cancer. They Improve skin disorders and soothes digestive problems, stomach ulcers and leaky gut syndrome. Chaga Mushrooms which have anti-aging effects, boost immune function, improve stamina and athletic performance, even act as a natural aphrodisiac, fighting diabetes and improving liver function. Try Our Lion’s Mane WHOLE MIND Nootropic Blend 60 Capsules Today. Be 100% Satisfied or Receive a Full Money Back Guarantee. Order Yours Today by Following This Link.


Report abuse

    Comments

    Your Comments
    Question   Razz  Sad   Evil  Exclaim  Smile  Redface  Biggrin  Surprised  Eek   Confused   Cool  LOL   Mad   Twisted  Rolleyes   Wink  Idea  Arrow  Neutral  Cry   Mr. Green

    MOST RECENT
    Load more ...

    SignUp

    Login

    Newsletter

    Email this story
    Email this story

    If you really want to ban this commenter, please write down the reason:

    If you really want to disable all recommended stories, click on OK button. After that, you will be redirect to your options page.