http://tinyurl.com/gks...

40% XIV, 60% TMF, rebalanced weekly.]]>

http://tinyurl.com/gks...

40% XIV, 60% TMF, rebalanced weekly.]]>

I am so sorry that I have not been able to be more helpful with your mathematical confusion.

It is actually a well known phenomenon in the literature known as correlation decay.

Put simply, the greater the underlying volatility, the greater the path dependent negative convexity in the instruments.

This negative convexity causes both the bullish and inverse instruments in a pair such as UGAZ and DGAZ to drift lower over time. Literally, a common cause (underlying volatility), causes both the bullish and bearish levered ETFs to go to zero in the long term.

That's what makes both instruments drift downwards and exhibit a longer term correlation. Empirically, and mathematically, the literature proves definitively that as we increase the time period observed, that the correlations between the instruments increases from something approaching -1 in the short term to more and correlated over greater and greater time periods as volatility decay (path dependent negative convexity) takes hold.

Hope this clears it up. There is a common cause of the downward drift of two levered bullish and inverse instruments. It's volatility in the underlying that causes correlation decay.

As an interesting aside, shorting two levered bullish/inverse pairs such as ugaz/dgaz is actually an interesting way to be long gamma as a costless synthetic call option on volatility if borrow/margin/slippage... costs were zero.

@TMD hope this helps clear up your problems with basic convexity concepts. You insist on focusing on 20 day correlations, entirely missing the point of correlation drift longer term due to volatility in the underlying. It must be hard being so confused all the time, I really feel for you. As you get out to periods well beyond a year, you can really measure the correlation decay due to volatility in the underlying.

If you would like to go through both the empirical evidence and calculus starting on page 13 of the paper (section on Correlation Decay), I would be super pleased to get on a call with you to walk you through the math. Before I thought you were joking, but now I understand that you are genuinely confused about some basic concepts that are well known in the literature.

http://tinyurl.com/hu9...

@TMD Please let me know if I can be of further assistance in helping you understand this important issue. I want to help you clear up any confusion you may have with basic concepts.

This way, we can both move forward in an evidence-based manner, rather than the notion that your opinions create reality.]]>

I am so sorry that I have not been able to be more helpful with your mathematical confusion.

It is actually a well known phenomenon in the literature known as correlation decay.

Put simply, the greater the underlying volatility, the greater the path dependent negative convexity in the instruments.

This negative convexity causes both the bullish and inverse instruments in a pair such as UGAZ and DGAZ to drift lower over time. Literally, a common cause (underlying volatility), causes both the bullish and bearish levered ETFs to go to zero in the long term.

That's what makes both instruments drift downwards and exhibit a longer term correlation. Empirically, and mathematically, the literature proves definitively that as we increase the time period observed, that the correlations between the instruments increases from something approaching -1 in the short term to more and correlated over greater and greater time periods as volatility decay (path dependent negative convexity) takes hold.

Hope this clears it up. There is a common cause of the downward drift of two levered bullish and inverse instruments. It's volatility in the underlying that causes correlation decay.

As an interesting aside, shorting two levered bullish/inverse pairs such as ugaz/dgaz is actually an interesting way to be long gamma as a costless synthetic call option on volatility if borrow/margin/slippage... costs were zero.

@TMD hope this helps clear up your problems with basic convexity concepts. You insist on focusing on 20 day correlations, entirely missing the point of correlation drift longer term due to volatility in the underlying. It must be hard being so confused all the time, I really feel for you. As you get out to periods well beyond a year, you can really measure the correlation decay due to volatility in the underlying.

If you would like to go through both the empirical evidence and calculus starting on page 13 of the paper (section on Correlation Decay), I would be super pleased to get on a call with you to walk you through the math. Before I thought you were joking, but now I understand that you are genuinely confused about some basic concepts that are well known in the literature.

http://tinyurl.com/hu9...

@TMD Please let me know if I can be of further assistance in helping you understand this important issue. I want to help you clear up any confusion you may have with basic concepts.

This way, we can both move forward in an evidence-based manner, rather than the notion that your opinions create reality.]]>

Easy, no problem. As you requested: "an example of a periodically balanced portfolio of two negatively correlated leveraged assets (with similar levels of leverage) which is adversely affected by volatility decay"

http://seekingalpha.co...]]>

Easy, no problem. As you requested: "an example of a periodically balanced portfolio of two negatively correlated leveraged assets (with similar levels of leverage) which is adversely affected by volatility decay"

http://seekingalpha.co...]]>

The symbols given were concrete, this graphic is concrete, try to understand the point:

http://seekingalpha.co...]]>

The symbols given were concrete, this graphic is concrete, try to understand the point:

http://seekingalpha.co...]]>

WRONG AGAIN. You keep getting confused between the short term and the long term, which is why you keep getting the wrong answer.

I keep explaining to you that the short term correlation is going to give you the wrong answer. And you refuse to understand. Hope this helps:

http://seekingalpha.co...]]>

WRONG AGAIN. You keep getting confused between the short term and the long term, which is why you keep getting the wrong answer.

I keep explaining to you that the short term correlation is going to give you the wrong answer. And you refuse to understand. Hope this helps:

http://seekingalpha.co...]]>

Again, your obtuse thinking on this matter is a source of continued frustration to me. This graphic will correct your statistical mistakes:

http://seekingalpha.co...]]>

Again, your obtuse thinking on this matter is a source of continued frustration to me. This graphic will correct your statistical mistakes:

http://seekingalpha.co...]]>

Everyone should read RV's insightful comments. I have personally been witness to the brilliance of this thinking. I can promise you all, he's like an iceberg, he is only showing a tiny sliver of his capability, the rest he privately benefits from.

http://seekingalpha.co...]]>

Everyone should read RV's insightful comments. I have personally been witness to the brilliance of this thinking. I can promise you all, he's like an iceberg, he is only showing a tiny sliver of his capability, the rest he privately benefits from.

http://seekingalpha.co...]]>

This is getting tiresome. Look at the graphic!

http://seekingalpha.co...]]>

This is getting tiresome. Look at the graphic!

http://seekingalpha.co...]]>

As promised, this is why your focus on the short term correlation is a mistake. As illustrated, longer term, leveraged instruments can be correlated due to path dependent negative convexity while being negatively cointegrated (mirroring while drifting downwards).

Can you see the phenomenon in this graphic which clearly shows the difference between the shorter and longer term? Do you see why I vehemently disagreed with your myopic focus on 20 day correlation which misses the entire point? You're completely wrong. Be intellectually rigorous and admit it.

http://seekingalpha.co...]]>

As promised, this is why your focus on the short term correlation is a mistake. As illustrated, longer term, leveraged instruments can be correlated due to path dependent negative convexity while being negatively cointegrated (mirroring while drifting downwards).

Can you see the phenomenon in this graphic which clearly shows the difference between the shorter and longer term? Do you see why I vehemently disagreed with your myopic focus on 20 day correlation which misses the entire point? You're completely wrong. Be intellectually rigorous and admit it.

http://seekingalpha.co...]]>

As promised, a graphic:

http://seekingalpha.co...]]>

As promised, a graphic:

http://seekingalpha.co...]]>

http://seekingalpha.co...]]>

http://seekingalpha.co...]]>

Sounds like you're agreeing that longer term two instruments can be correlated, but shorter term be inversely correlated.

In any case, your agreement or disagreement is irrelevant. I will post an link to a graphic on my instablog that will prove the point.]]>

Sounds like you're agreeing that longer term two instruments can be correlated, but shorter term be inversely correlated.

In any case, your agreement or disagreement is irrelevant. I will post an link to a graphic on my instablog that will prove the point.]]>

I have stated why LONG TERM, UGAZ and DGAZ are correlated, with both drifting downwards. I've stated it MANY TIMES on this thread.

It's because of path dependent negative convexity.]]>

I have stated why LONG TERM, UGAZ and DGAZ are correlated, with both drifting downwards. I've stated it MANY TIMES on this thread.

It's because of path dependent negative convexity.]]>

I keep saying that longer term, both are somewhat correlated, and you keep responding with the 20 day coefficient. You're not getting it.]]>

I keep saying that longer term, both are somewhat correlated, and you keep responding with the 20 day coefficient. You're not getting it.]]>

Inverse instruments can make money if both drift down over time. In that way, LONG TERM, both are somewhat correlated, but because they are mirrors, are negatively cointegrated.

It is a common mathematical error you are making.

I will post a graphic that illustrates this, since many people are not getting it.]]>

Inverse instruments can make money if both drift down over time. In that way, LONG TERM, both are somewhat correlated, but because they are mirrors, are negatively cointegrated.

It is a common mathematical error you are making.

I will post a graphic that illustrates this, since many people are not getting it.]]>

With respect, that's not what I am saying.

I am saying, and have said repeatedly, that both sides had a point.

There is path dependent negative convexity, but the correlation attributes (really negative cointegration more recently), more than made up for it.]]>

With respect, that's not what I am saying.

I am saying, and have said repeatedly, that both sides had a point.

There is path dependent negative convexity, but the correlation attributes (really negative cointegration more recently), more than made up for it.]]>

Exactly, longer term they both drift down, correlated because of path dependent negative convexity. However, they are negatively cointegrated.

Imagine a downward sloping ellipse, where both halves of the ellipse are mirrors, but are tilted downwards.

That's the visual, if you can see that in your mind's eye.

That's the visual, if you can see that in your mind's eye.]]>

Exactly, longer term they both drift down, correlated because of path dependent negative convexity. However, they are negatively cointegrated.

Imagine a downward sloping ellipse, where both halves of the ellipse are mirrors, but are tilted downwards.

That's the visual, if you can see that in your mind's eye.

That's the visual, if you can see that in your mind's eye.]]>

You asked for an example of two instruments that were positively correlated while being negatively cointegrated.

So, I gave you the example of DGAZ/UGAZ. You are NOW MAKING ANOTHER FACTUAL ERROR. Whether or not you short DGAZ/UGAZ does not change the fact that they are positively correlated while being negatively cointegrated.

Amazing. Your record is almost perfect--wrong 3 times in a row.]]>

You asked for an example of two instruments that were positively correlated while being negatively cointegrated.

So, I gave you the example of DGAZ/UGAZ. You are NOW MAKING ANOTHER FACTUAL ERROR. Whether or not you short DGAZ/UGAZ does not change the fact that they are positively correlated while being negatively cointegrated.

Amazing. Your record is almost perfect--wrong 3 times in a row.]]>

6 cents from an all time high on the stock. Randall Rocks.]]>

6 cents from an all time high on the stock. Randall Rocks.]]>

I am going to try this again:

1. There is path dependent negative convexity.

2. However, the negative cointegration between SPXL/TMF has provided a benefit which more than compensates for the negative convexity.

3. Going forward, we do not know what the cointegration between SPXL/TMF will be.

4. You made a sloppy mistake with your SPY/SH example, because you did not understand the difference between correlation and cointegration.

5. Your further demonstrated your lack of basic understanding by making factually incorrect statements about UGAZ/DGAZ.

6. After ALL of your points and examples were proven wrong, you then pretended that it was about your interest level, rather than your absurdly incorrect logic which is public for all to see.

7. Now that you've learned the difference between correlation and cointegration, and have seen that it's important, just thank me for helping you, and stop making lame excuses for faulty logic and incorrect reasoning.]]>

I am going to try this again:

1. There is path dependent negative convexity.

2. However, the negative cointegration between SPXL/TMF has provided a benefit which more than compensates for the negative convexity.

3. Going forward, we do not know what the cointegration between SPXL/TMF will be.

4. You made a sloppy mistake with your SPY/SH example, because you did not understand the difference between correlation and cointegration.

5. Your further demonstrated your lack of basic understanding by making factually incorrect statements about UGAZ/DGAZ.

6. After ALL of your points and examples were proven wrong, you then pretended that it was about your interest level, rather than your absurdly incorrect logic which is public for all to see.

7. Now that you've learned the difference between correlation and cointegration, and have seen that it's important, just thank me for helping you, and stop making lame excuses for faulty logic and incorrect reasoning.]]>

You are now totally changing your argument. You now understand that UGAZ/DGAZ both drift down over time (long term correlation) due to path dependent negative convexity, but are negatively cointegrated.

However, rather than recognizing your error, you are using the excuse that shorting does not "interest you". Truly hilarious. Glad to see that you recognize that shorting both does work PRECISELY BECAUSE OF VOLATILITY DECAY.

Stay evidence-based Varan. You can have your own opinions, but not your own "facts". Glad to see that you learned something today. Your interest level has nothing to do with the facts.]]>

You are now totally changing your argument. You now understand that UGAZ/DGAZ both drift down over time (long term correlation) due to path dependent negative convexity, but are negatively cointegrated.

However, rather than recognizing your error, you are using the excuse that shorting does not "interest you". Truly hilarious. Glad to see that you recognize that shorting both does work PRECISELY BECAUSE OF VOLATILITY DECAY.

Stay evidence-based Varan. You can have your own opinions, but not your own "facts". Glad to see that you learned something today. Your interest level has nothing to do with the facts.]]>

It does work, you short both. This is simple stuff. We did a whole piece on it.]]>

It does work, you short both. This is simple stuff. We did a whole piece on it.]]>

Thank you as always for your kind words my friend.]]>

Thank you as always for your kind words my friend.]]>

You are literally completely wrong! I will do a special article to explain this for people like you who are similarly confused about the difference between correlation and cointegration. Perhaps I should start the article by quoting your comment, since it would be instructive to others.

Both instruments, DGAZ and UGAZ, drift down over time, so they are correlated, however, shorting both provides an excellent hedge, because they are NEGATIVELY COINTEGRATED! This is simple stuff. Stop whining Varan.]]>

You are literally completely wrong! I will do a special article to explain this for people like you who are similarly confused about the difference between correlation and cointegration. Perhaps I should start the article by quoting your comment, since it would be instructive to others.

Both instruments, DGAZ and UGAZ, drift down over time, so they are correlated, however, shorting both provides an excellent hedge, because they are NEGATIVELY COINTEGRATED! This is simple stuff. Stop whining Varan.]]>

I did give a concrete example, DGAZ/UGAZ, right there in the thread. It's a concrete example. You just didn't recognize it as such, because you don't understand the difference between correlation and cointegration, as proven by your attempt to use SPY and SH as an example. Check the message thread, it's all there.

And this IS NOT UNIQUE KNOWLEDGE. Google cointegration vs correlation or consult a textbook. It's just knowledge you don't have. Definitely not unique to me.

If we are going to have a rational discussion centered on facts, you need to understand the statistical difference, otherwise you will continue to get the wrong answer. Isn't that obvious?]]>

I did give a concrete example, DGAZ/UGAZ, right there in the thread. It's a concrete example. You just didn't recognize it as such, because you don't understand the difference between correlation and cointegration, as proven by your attempt to use SPY and SH as an example. Check the message thread, it's all there.

And this IS NOT UNIQUE KNOWLEDGE. Google cointegration vs correlation or consult a textbook. It's just knowledge you don't have. Definitely not unique to me.

If we are going to have a rational discussion centered on facts, you need to understand the statistical difference, otherwise you will continue to get the wrong answer. Isn't that obvious?]]>

You are confused about the difference between correlation and cointegration. The best of all world is POSITIVE correlation with negative cointegration.

One you understand this important difference, you will understand what I am saying.]]>

You are confused about the difference between correlation and cointegration. The best of all world is POSITIVE correlation with negative cointegration.

One you understand this important difference, you will understand what I am saying.]]>

If you are referring to positively correlated and negatively cointegrated pairs, such as DGAZ/UGAZ, path dependent negative convexity does cause the positive correlation between them.

But my major point is that the negative cointegration benefits of SPXL and TMF have far outstripped the negative effects of negative convexity.

It's not that either party is right or wrong, it's about the positive attributes of the pair vs the negative attributes. So far, the positive attributes have outweighed the negative. Going forward, we would only know the answer if a priori, we knew the cointegration.]]>

If you are referring to positively correlated and negatively cointegrated pairs, such as DGAZ/UGAZ, path dependent negative convexity does cause the positive correlation between them.

But my major point is that the negative cointegration benefits of SPXL and TMF have far outstripped the negative effects of negative convexity.

It's not that either party is right or wrong, it's about the positive attributes of the pair vs the negative attributes. So far, the positive attributes have outweighed the negative. Going forward, we would only know the answer if a priori, we knew the cointegration.]]>

Or as I call beta: relying upon the kindness of strangers.]]>

Or as I call beta: relying upon the kindness of strangers.]]>