Michael Bommarito

Capitalization Coupling: Major Indices at Correlation Highs

These are all from June 2001 to yesterday, and significant to at least p=0.025 again.

Capitalization Coupling: Major Indices at Correlation Highs

Middle of exams here so I don't have time for any stochastic volatility or adaptive models, but feel free to provide any results you find doing so. Here are some more extensive results just under this simple model with non-parametrics for comparison.

Colums:
Pearson/Sign Pearson/Spearman Rank/Sign Spearman Rank

Rows:
1st: Pearson correlation between return & each correlation
2nd: Spearman rank correlation between return & each correlation

Results:

0-Day (no lag)
ans =
-0.0279 -0.0283 -0.0377 -0.0268
-0.0006 -0.0555 -0.0439 -0.0555

1-Day
ans =
0.0115 0.0147 0.0236 0.0145
0.0261 0.0224 0.0368 0.0269

2-Day
ans =
0.0010 0.0035 0.0004 0.0029
0.0015 0.0074 -0.0087 0.0057

Capitalization Coupling: Major Indices at Correlation Highs

Yes, I accept that my suggestion about the trend was not significant under this model, but what I meant to show in my reply was that the opposite was not true either, as you argued. My p-values were all significant at least to the 0.025 level, though I did not record them.

I would also note that your samples were contained strictly within the local phenomenon that I am trying to explain, and thus not only do they have no chance of demonstrating a difference from prior relationships, but you have an N smaller than mine by an order of magnitude wrt power.

Capitalization Coupling: Major Indices at Correlation Highs

By the way, I'd appreciate links to studies or your own analysis in the future instead of suggestions about tea leaves.

Capitalization Coupling: Major Indices at Correlation Highs

Rudi, are you talking about correlations between assets *within* an index or correlation *between* these specific capitalization-oriente... indexes?

Both rank and Pearson-product correlations indicate that:
i) daily R^2 between the average correlation change and return is -1%
ii) weekly R^2 between the average correlation change and return is 2%
iii) monthly R^2 between the average correlation change and return is 4%
iv) quarterly R^2 between the average correlation change and return is 6%

Which seems to contradict your statement.

ProShares Ultra and UltraShort Sector ETFs: Does 2 = 2?

Also, in response to User 170913, I've used adjusted close values for these calculations, so the dividends are already incorporated.

ProShares Ultra and UltraShort Sector ETFs: Does 2 = 2?

All numbers I use in calculations are cumulative log-returns, so Ben and Cato's comments are not relevant. The bar charts are endpoint cumulative log-return comparisons converted to standard %-return.

ProShares Ultra and UltraShort Sector ETFs: Does 2 = 2?

Roger & 2TallTurk, note that I'm not talking about whether these funds return twice their underlying index's price return. I point readers to the ProShares article on the difference between daily NAV tracking and cumulative price return...

What I *am* investigating is why the daily NAV return for these fund pairs do not match. That is, the daily NAV return of UYG should be the negative of the daily NAV return of SKF.

2TallTurk, note that I readily accept tracking error from portfolio construction. These ProShares funds have done well considering that the difficulty of matching the magnitude of returns lately. I was merely investigating alternative reasons for the imbalance.

Building a Long-Volatility ETF Portfolio

There's a typo/word omission in there - you should *hold* equal amounts of SDS and SSO, though you should hold SDS long and SSO short.

hillcrest, I almost always calculate log-return, and so the left-scale is cumulative log-return. Log-return is nearly identical to standard return for small values, but diverges for larger returns. A 100% increase is log(1+1) = log(2) = 0.6931 in log-return, whereas this would simply be 1.0 for price return. The difference has to do with the utility of returns, and although there isn't a strictly correct answer, many sophisticated calculations are much cleaner in log-return.

Morgan Stanley: VaR Datapoint of the Day

Hey Felix, just a few caveats...
i) The probability of exceeding a given loss has nothing to with the amount that loss will be exceeded by.
ii) If jck's statement of their 95% VaR level is correct, then you would precisely expect 1 out of 20 days to exceed such a loss. Over a 56-day quarter, this translates into 2.8 expected days of such loss.
iii) If the market factors that caused these MS losses were predictable, then tails in the market itself should have been predictable, and no one should have really lost money. Tails are what make financial markets so profitable and so risky, and without them, no one would care too much about markets at all.

Moment and Omega Rankings of Index ETFs

Hello Susan, the double accounting is for two reasons - firstly, to confirm the ranking of the first four moments, and secondly, as you mention, to include the higher order moments.

Also, if you'd like an example of a distribution with negative mean and positive skewness, take December 31, 2001 to March 15th, 2003, and you should get just such a distribution. For reference, I calculate a log-return mean of -0.0011 and skewness of 0.4057. Make sure you're not using excess moments either.

ETFs With a 50% Correlation To the VIX

If you want some kind of hedge for volatility through a long-only ETF strategy, here's your list. If you want to fit this into a pre-existing allocation strategy or want to actually hold more than one of these assets, pick ones that have a low correlation with each other.

If you have other questions, feel free to ask. Your favorite search engine is also a great resource if you're ever confused about something.

Best, Worst ETF and CEF Year-to-Date Returns

Hello TheLasko,
These returns are calculated with the dividend factored in, so it seems they have not been much of a bargain even after the yield is factored in. We'll see if the chance for falling rates helps push up these funds, assuming as you mention that they can sustain these dividend rates.

Update On Oil ETFs and Contango

Hello ETF Investor,
Yes, I discuss the difference in these funds for traders vs. investors in the link mentioned in the article. I understand that these funds are not all technically designed to track the same price, but as USO was for a long while the only liquid proxy to oil, many still hold and treat it as such.

Sector Correlations With S&P 500 On the Rise

I just wanted to note that I've responded to a few caveats I have with this methodologoy here - www.etf-central.com/re...