## Paper: R. Werpachowski. Arbitrage-Free Rate Interpolation Scheme for Libor Market Model with Smooth Volatility Term Structure

Interesting paper released by R. Wepachowski from Markit, well-known for their credit risk indices.

Abstract:The Libor Market Model describes the evolution of a discrete subset of all interest rates quoted in the market. Generation of the complete yield curve from a simulated set of rates (the so-called “Libor rate interpolation”) is one of the basic challenges which are faced by a practical user of LMM. Incorrect implementation can lead to arbitrage in the model and render generated prices invalid. In this paper, we present a rate interpolation scheme which not only is arbitrage-free, but also generates a natural-looking, smooth term structure of interpolated rates’ volatilities. It is conceptually simple and computationally efficient.

R. Werpachowski. Arbitrage-Free Rate Interpolation Scheme for Libor Market Model with Smooth Volatility Term Structure. http://ssrn.com/abstract=1729828

## Paper: J. Brogaard. High Frequency Trading and its Impact on Market Quality

I saw that this paper on SSRN, High Frequency Trading and its Impact on Market Quality, was updated a week or so ago (courtesy of Alea) and I thought it would be worth posting.   The abstract of the paper below:

The results shouldn't be too surprising.  The pack is led by leveraged funds that track technology, Treasury, and commodities.  TYP, TYH, and SQQQ all correspond to triple-leverage Nasdaq or broad tech funds; of these, TYH and SQQQ were much more heavily traded this week.  Treasury funds hold their own as well, with the triple 20-year (TMF) and the triple short 30-year (TMV) showing large ranges this week.   ZSL is a double-leverage short silver fund, and CZM/CZI are triple-leveraged long/short China funds; much of the move in both Chinese and commodity markets this week was driven by the dollar.  Of all these funds, the triple-leverage financial ETF (FAS) clearly saw the most trading action, churning more than $4B this week. With plenty of housing, job, and industrial data out next week, look for these funds to continue to expand on their recent price ranges. ## FaithShares fund inflows “Faith-based” investing, a close cousin of “socially responsible” investing, has received an increasing amount of attention over the past decade. Though both of these trends have been adversely affected by the recent downturn, I thought we’d check in to see how the family of funds issued by FaithShares Advisors, LLC has fared year-to-date. FaithShares offers funds for five “different” faiths – Catholic, Lutheran, Methodist, Christian, and Baptist values. The first figure belows shows the upper bound on fund inflows since January 15th. The upper bound logic is based on the following two tricks. First, I’ve calculated dollars traded based on each day’s price high. Second, if you assume that every share traded represents an inflow and not an outflow, then the number of dollars traded represents the maximum possible inflow. The first figure below shows that this upper bound is just under$22 million dollars.

The second figure shows this upper bound on inflows by each faith.  The broad, Christian based fund appears to have attracted the most interest with an upper bound of $7.78M. The Catholic and Methodist funds follow far behind with upper bounds of$5.35M and $4.30M respectively. The Baptist and Lutheran funds round out the pack with a respective$2.49M and \$1.96M.

To put this into perspective, more dollars are usually traded in SPY in the first 10 seconds after 9:30AM.  If you’re interested in more of the details on the internal management of these funds and FaithShares Advisors, LLC, please refer to their last Certified Shareholder Report on EDGAR.

## New Revision: Intraday Correlation Patterns Between the S&P 500 and Sector Indices

I’ve just released a new revision of my working paper, Intraday Correlation Patterns Between the S&P 500 and Sector Indices, which you can download by clicking the link.  Here are a few of the improvements in the new revision:

• I’ve updated the paper to include minutely data from August 23rd to October 1st.  This has effectively doubled the size of the dataset.  Furthermore, the sample now includes both up and down weeks.
• I’ve added two-sample K-S and Wilcoxon rank-sum tests to show more rigorously that the patterns observed in return and volume correlation are significant at the \alpha=0.001 level.
• The paper now includes many more references to relevant existing literature.  If you think I’ve missed a paper that should be included, please let me know!

You can cite the paper in its current form as:

Bommarito, Michael James, Intraday Correlation Patterns between the S&P 500 and Sector Indices (September 16, 2010). Available at SSRN: http://ssrn.com/abstract=1677915

## New Paper: Intraday Correlation Patterns between the S&P 500 and Sector Indices

Kristina Peterson’s article in the WSJ last week on intraday patterns got me thinking and the result is this brief research paper.  There’s a significant amount of work I’d like to put into the paper, especially the preliminary analysis on volume correlation, but the results are interesting enough that I decided to publish a draft.  You can read the abstract below and download the paper here.

In this brief research note, I explore recent patterns in intraday return and volume correlation between the S\&P 500 and sector indices, as represented by minutely data from Aug. 23 to Sep. 10 for the SPDR exchange-traded funds. Notably, there appears to be evidence of two previously unreported patterns in intraday correlation. First, there is a “U-shaped” trend in return correlation, characterized by higher correlation at open and close and lower correlation during mid-day hours. Second, volume correlation is marked by lower values in the morning and increasing values in the afternoon. In some cases, this trend even takes the infamous “hockey-stick” shape, exhibiting stable values in the morning but sharply increasing values in the late afternoon. To ensure that these patterns are not a function of the choice of correlation window size, I confirm that these patterns are qualitatively stable over correlation windows ranging from 10 minutes to 90 minutes. These findings indicate that non-time-stationary patterns exist not only for volume and volatility, as previously reported, but also for the correlation of return and volume between the market and sector indices. These results have possible implications for intraday market efficiency and for trading strategies that rely on intraday time-stationarity of return or volume correlation.

Bommarito, Michael James, Intraday Correlation Patterns between the S&P 500 and Sector Indices (September 16, 2010). Available at SSRN: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1677915

## ProShares Ultra ETFs Benefit From Market Volatility

This post was originally published on February 3rd, 2008. It has been slightly modified from a previous version of the site.

As volatility has increased over the past months, the ProShares Ultra ETFs have seen a dramatic increase in average dollar liquidity.  There are exactly 50 of these leveraged instruments at the moment, and they are listed below, sorted by age.

 ETF Age (sessions) ProShares Ultra Dow30 407 ProShares Ultra MidCap400 407 ProShares Ultra S&P500 407 ProShares Ultra QQQ 406 ProShares UltraShort Dow30 392 ProShares UltraShort MidCap400 392 ProShares UltraShort QQQ 392 ProShares UltraShort S&P500 392 ProShares Ultra SmallCap600 258 ProShares UltraShort SmallCap600 258 ProShares UltraShort Russell2000 258 ProShares Ultra Russell2000 258 ProShares Ultra Oil & Gas 253 ProShares UltraShort Oil & Gas 253 ProShares Ultra Technology 253 ProShares UltraShort Health Care 253 ProShares Ultra Health Care 253 ProShares UltraShort Industrials 253 ProShares UltraShort Financials 253 ProShares UltraShort Real Estate 253 ProShares UltraShort Semiconductors 253 ProShares UltraShort Consumer Goods 253 ProShares Ultra Consumer Goods 253 ProShares Ultra Utilities 253 ProShares Ultra Semiconductors 253 ProShares Ultra Financials 253 ProShares UltraShort Technology 252 ProShares UltraShort Consumer Services 252 ProShares UltraShort Basic Materials 252 ProShares Ultra Consumer Services 252 ProShares Ultra Real Estate 252 ProShares Ultra Industrials 252 ProShares Ultra Russell1000 Growth 239 ProShares Ultra Russell2000 Growth 239 ProShares Ultra Russell MidCap Growth 239 ProShares UltraShort Utilities 225 ProShares UltraShort Russell1000 Value 208 ProShares UltraShort Russell MidCap Growth 201 ProShares UltraShort Russell2000 Value 201 ProShares UltraShort Russell MidCap Value 201 ProShares UltraShort Russell2000 Growth 201 ProShares Ultra Russell1000 Value 201 ProShares Ultra Russell2000 Value 201 ProShares Ultra Russell MidCap Value 201 ProShares Ultra Basic Materials 201 ProShares UltraShort Russell1000 Growth 198 ProShares UltraShort MSCI EAFE 68 ProShares UltraShort MSCI Emerging Market 63 ProShares UltraShort MSCI Japan 58 ProShares UltraShort FTSE/Xinhua China 58

I’ve taken the product of the close and the volume for the 46 funds that have traded at least 150 sessions and averaged their daily cross-section.  The following is a chart of this average dollar liquidity over the past  150 sessions in blue, with a 20-session moving average in red.  The trend quite clearly indicates that not all market volatility is bad for ETFs.