The Secrets of Skewness

A question came up the other day regarding how to think about skewness in the volatility surface of equity options.

Thinking of volatility skew as approximated by the relative slope of the volatility surface for a given time to expiry, the skew can be a valuable indicator that shows option traders' biases towards a particular stock or index. Expensive options are a strong indicator of pending changes in a stock's price. The measure of expensiveness is the options implied volatility.

The ATM or vega-weighted implied volatility measure tells only whether the overall stock volatility is high, but doesn't yield any information about the markets sentiment of the stock's impending directional movement.

Under a Black-Scholes framework, options of the same maturity should in theory have the same implied volatility across strikes. However, in reality this is not the case. Supply-demand dynamics for individual option contracts can distort the price (and thus implied vol) at different points across the volatility surface's term structure and strike range.

The disparity of implied volatility between calls / puts indicates the position of traders in aggregate (volume alone does not imply net buying or selling). For instance, if OTM call ivol is higher than same strike/expiry put ivol, it may imply that traders favor an increase in the underlying.

To really understand the implications of volatility skew for impending price movements, one needs to analyze the volume of individual option contracts. Here is where volume can add color:

• High volume and low volatility may indicate that option contracts are being sold.
• High volume and high volatility may indicate that option contracts are being purchased.
  
  Additionally, it is important to consider Time Skew vs. Strike Skew:

• Time Skew: measures the spread between option ivol for contracts with same strike but different time to expiry.
• Strike skew: measure of spread in ivol for contracts with different strikes, but same time to expiry

Together, combining Implied Volatility and Volume, we can infer the following relationships:

• Higher ivols in NTM / ITM calls vs. puts may indicate a majority of call buyers, which can be viewed as bullish.
• An abundance of volume in the OTM call, coupled with low ivol, can indicate OTM call sellers. While this is a relatively neutral indicator of direction, it may suggest that traders aren't anticipating the stock rising beyond the OTM call's strike price.

So, what does this all mean in practice, what is the skew of the S&P 500 (SPX) telling us now, and are options "fairly" priced today?

While, except for a brief respite in mid-November, equity index options have not been this fairly valued in nearly a year (measuring IVOL/30D HVOL), meaning that realized volatility has more closely matched the volatility implied by options prices (see chart at right).

From a distribution standpoint, the ratio is relatively middle of the road, at a 44th-percentile relative to the past year (see histogram at right).


I constructed an equal-weighted index that looks at 80%, 90%, 95%, 105%, 110% and 120% strike options' implied volatility relative to the ATM implied volatility. The index captures the degree of slope, or skew, in the ivol term structure on any given day.

In looking at the past year's distribution of this index, we see that today the degree of skew in the SPX is incredibly high, or a 5th-percentile event (see charts at right). This high-degree of skew has persisted well over the past month.

However, SPX skew is the highest among global indices, despite extensive focus on the deteriorating macros of Europe and concerns over China. Furthermore, an important implication is that SPX correlation has nearly doubled, which can be seen to indicate the degree to which the market has focused more exclusively on the macro. This coupled with a flattening of the VIX term structure (at right) due to upward pressure on spot/near-term contracts may be indicative of market expectations for higher volatility due to an impending pull-back.

The sovereign macro risks seem to be inherently driving the market...

Superior Well Services (SWSI) - GARP?

Thesis: The bullish thesis for SWSI is predicated upon increased demand for their services related to the ongoing recovery from a capacity bubble within the pressure pumping market. Increased demand for SWSI's hydro fracing is due to greater per-well intensity in the Marcellus Shale, where growth is expected to be sustained even despite a lousy gas price environment. The market does not fully appreciate the magnitude of this dynamic's impact on SWSI's top-line, and still has some concern over the firm's financial leverage (The bulk of principal payments are not due until 2013 ($207.1mm))

Company Profile: $570mm Market Cap, $785mm Enterprise Value. SWSI provides well-site solutions to oil and natural gas companies. The company offers technical pumping services and down-hole surveying services. Its technical pumping services include stimulation services, such as fracturing and acidizing, which are designed to improve the flow of oil and natural gas from producing zones; It serves regional, independent oil and natural gas companies in the Appalachian, Mid-Continent, Rocky Mountain, and southeast and southwest regions of the United States. The company operates service centers in Pennsylvania, West Virginia, Oklahoma, Mississippi, Alabama, Michigan, Arkansas, Utah, Texas, Virginia, New Mexico, Louisiana, Ohio, Kansas, North Dakota, Colorado, and Wyoming. As of December 31, 2008, Superior Well Services, Inc. owned a fleet of 1,628 commercial vehicles and 116 logging and perforating trucks and cranes. The company was founded in 1997 and is based in Indiana, Pennsylvania.

The Story: Once near the brink of bankruptcy, SWSI stock has surged ~170% over last the 6 months to become one of the top performing oilfield service stocks in the sector. The company has a strong presence in the Marcellus Shale, providing over 30% of the horsepower to operators in the region (SWSI also has good exposure to plays in the Haynesville, Barnett and Bakken as well).

The Marcellus in particular possesses good economics and is expected to grow, even despite the current tepid natural gas price environment. SWSI’s large exposure to the Marcellus relative to its size makes the company an excellent pure-play to capitalize on the growth of that region.

Valuation: A 6.3-6.5x EV/EBITDA multiple on 2011 is a reasonable target, given SWSI's size and the valuation history of its comps (RES, BJS and KEG), implying a $20-20.6 per share price target.

Disclosure: I have been Long SWSI since Jan 4th, 2010 at an average fill of $15.10.

What is the Optimal Inflation Hedge?

Yesterday's FT noted the rising demand amongst investors for inflation-safe debt. The UK on Monday saw the second best tender, or mini-auction, for inflation-protected bonds since October 2008. Notably, inflation expectations have risen sharply in the U.S., particularly because of the credit-easing policies and record low nominal rates. Last week, there was strong investor demand for a $10bn 10-year US inflation-linked bond. Its bid-to-cover ratio was 2.65 (versus the average of 2.14 for the past five new sales).

Using the break-even rate, which is the difference between conventional U.S. treasury bond yields and inflation-linked bond yields, we can see that current inflation expectations are roughly in line with pre-Lehman levels. Worth note, since last Friday's disappointing employment report, 5Y and 20Y expectations tightened by nearly 10bps through today.

It is important to put this in context. Looking at a histogram of implied inflation expectation levels since Jan-08, we appear to be back near median forecast levels (histogram at right). It is also important to notice the modest correlation that these expectations have on the price level of both gold and oil (see regressions at right).


This begs a few very important questions for mitigating risk to our portfolios in the future; namely, what are the levels of inflation that we can anticipate in the future, when, and how best can we hedge ourselves for the long run?

I am a believer in Mauldin's view that we can expect to see a "statistical recovery", the statistics (i.e., GDP, etc.) are positive but it certainly doesn't "feel" like a recovery. First, year-over-year comparisons are looking better, since 2008 was horrific. Second, inventory levels are about as low as they will go. In the way GDP is figured, a reduction in inventory reduces GDP (perhaps GDI is an even better barometer...). That was a negative figure for most of this recession. Simply because inventories not falling any more, it is easier to get a positive GDP. Lastly, the onetime benefits for GDP from the fiscal stimulus are coming due (toughly 90% of the 2.2% growth in GDP in the third quarter was attributable to the stimulus), and we can already see the effects of federally-sponsored growth (auto sales fell in Dec-09 0.8% after a 1.2% Nov-09 gain, slumping in Sep-09 after the "cash-for-clunkers" plan expired).

I am always skeptical of outliers and when the momentum of the herd moves to quickly. Looking at how quickly inflation expectations have resumed to pre-crisis levels, despite a tremendously negative macro, gives me great pause in the bubble taking place in commodities like gold and oil. This has been a shift away from my more tactical-oriented momentum-based trading of options on the GLD in recent months. I am cautious with how quickly risky assets and inflation-sensitive commodities like gold have risen in recent months. Granted the past is not indicative of future performance, but if you look at past recessions, it is not all that unusual (8 out of 11 times) for there to be positive GDP quarters in the midst of an ongoing recession.

Getting Back to Business!

After a much needed respite from exams, it's time to get back to business.

Let's start the New Year by discussing updates to the portfolio over the past four weeks.

The Gold Trade:
It looks like the violent interruption in gold's strong trend during early December was likely just a reversion to the mean. It was during that correction that GLD options appeared to be reasonably priced relative to the past several months (see Chart #1, at right). However, it looks like the short-term will be characterized by turbulent trading, with a skew toward the upside (see Chart #2, at right).

The fundamental rationale for being long-gold (ideally not in USD-terms) still seems intact. As highlighted in today's Gartman Letter, the logic behind the problematic nature of the EUR as a reserve currency strengthens the notion of owning gold, not in US dollar terms but in terms of the EUR, Sterling and the Yen (particularly in light of recent comments made by Naoto Kan, the newly appointed Finance Minister in Japan). Gold is now being seen by more and more governments as reserve currency. More so, with a weakened EuroZone, which is increasingly threatened by the weighing divergence from member nations' (i.e., the PIIGs), it would seem reasonable that capital, which may have been earmarked for euro-denominated assets, on the margin, may more likely be allocated to gold denominated in euro terms.

Energy - Fundamental Book: XTO Bought up by XOM
On Dec-14, ExxonMobil (XOM) announced that it had reached an agreement to buy XTO Energy in an all-stock transaction valued at $41 billion, including approximately $10 billion of XTO debt. The deal implies a ~25% premium for XTO shareholders based on Dec-11 prices.

I first recommended getting long XTO's equity and neutral on CDS in early Mar-09. The thesis was that XTO was more highly levered than peers, and the market was uncertain that they could successfully digest their mammoth acquisitions of 2008 and develop the acquired resources successfully.

However, from a technicals standpoint, XTO initially underperformed relative to key peer Anadarko (APC) by nearly 22% over the subsequent 5 weeks due to crude's nearly 25% rally. After some humbling analysis, I discovered the reason was related to XTO's tighter correlation to natural gas prices and greater hedging toward crude. However, this exercise validated that the underlying fundamental thesis was still intact: because of XTO's best-in-class hedging program and strong management expertise, they would likely maintain the flexibility to successfully development acquired resources on schedule in 2009 while reducing debt through stronger-than-expected operating cash flows. The market had not appreciated their strong CF position via hedging and operational expertise.

XTO's strategic move to acquire promising, high-profile shale assets in 2008 (45 Tcfe resource base and 14 Tcfe of proved reserves at YE08) has paid off. The transaction price comes out to about $0.90 / Mcfe of 3P (proved, probable and possible) reserves and ~$2.88/Mcfe of proved reserves.

In the end, gross of hedging costs (which detracted approximately 950 bps from performance; Jun-09 38 strike ATM puts bought in advance of May 6, 2009 earnings call), the trade returned approximately 48% cumulative, or 78% annualized.

Looking at the bigger picture, the deal meaningfully expands Exxon’s exposure to North America natural gas prices and unconventional natural gas resources. North America unconventional gas has been dominated by the E&P companies, most notably XTO and CHK amongst many others. Now, Exxon will need to demonstrate that it can develop XTO’s resources at an even lower all-in cost than XTO. I would not be surprised if this is the catalyst which sets off massive M&A activity in the shale space, particularly as the Majors look to secure a longer-term energy outlook amidst record low NG prices.

Technical Options Trade: Short Brazil via EWZ Puts
The long Brazilian Jan-10 80 strike ATM EWZ put position, recommended on Dec-2 was closed on Dec-8 when the +/- 40% PnL threshold was reached (this is my internal trading guideline for 1M ATM options where time to expiry is greater than 20 days). Again, I failed to participate in even further upside due, perhaps, to too conservative risk limits and return thresholds; had I held on to the position until Dec-21 (theoretically assuming perfect market timing), the position would have generated twice the return, with 79.6% cumulatively over a three week period. As I get more experience under my belt, I will come back to re-evaluate these guidelines, but in the meantime, the over-arching credo is that the market can remain irrational far longer than I can remain solvent... so, I'll stick to the side of prudence in the meantime.

The Nature of Natural Gas: EIA-914 - Shut-ins or natural declines?

Yesterday the Department of Energy,'s EIA released their EIA-914 Monthly Natural Gas Gross Production report. Fist a little background: prior to Jan-05, the EIA had published estimates of natural gas production based on data supplied by or collected from individual State agencies and the Minerals Management Service. Because these production estimates were not considered sufficiently timely nor accurate to meet customer needs the EIA instituted this monthly survey, which collects production data directly from well operators.

This month's 914 report was modestly bullish, showing continental U.S. gas production to be approximately -1.4 bcf per day (a negative number is bad, positive is good for gas prices) out of balance (in from nearly -3.5bcfpd during massive Aug-09 production builds)

However, it is unclear whether the sequential decline is driven by either production shut-ins (operators such as CHK and ECA stated their voluntary shut-in volumes, and it is likely that others followed suit as spot gas prices declined to sub $2/mcfe in early Sep-09, and only gradually improved to ~$3.5/mcfe by the end of the month) or natural declines in production capacity (TPH had estimated 0.5 bcf/day of natural wellhead declines back in late Nov-09).

Net-net, the 914 data seems inconclusive and ~1.5 bcf/day of production shut-ins seems statistically unrealistic based upon historical trends. Additionally, the latent winter weather is not helping to clarify the demand side of the situation - I will be watching the weekly storage data tomorrow morning for implied supply-demand, which will no longer be disguised by full storage effects.

Trade Update: "Going for the Gold" - Part II

Well, I left money on the table. What can I say. I exited the directionally long GLD and long GLD Gamma trade a day too early, and missed out on an additional 1.35 of upside today alone.

While I am thrilled with how well the trade worked out already, my naivete reminds me of Lefevre's old adage to follow the path of least resistance; I had been to caught up in the short-term horizon of this trade, that I forgot to acknowledge the influence of the longer-term momentum.

It is bitter sweet to have closed out of the position. This has been my largest trade to date, on a risk-weighted basis, comprising ~12% of portfolio 20-day VaR / PML - the upper threshold of my internal trading guidelines. Now without another week of sleepless nights, I can re-focus my efforts back to my core strategies.

While I still believe there are reasonable fundamentals underlying the demand for Gold, I do believe there is a non-negligible probability of jump risk given that this rally seems to be catalyzed by a crowded USD-carry trade and the potential for a strengthening dollar (Friday's job report will be key). A short squeeze on the Short Dollar-Long Risk trade, as talked about in Mauldin, seems inevitable but not imminent. If the U.S. economy begins to mend itself ahead of schedule, the potential for rate increases will be dollar positive-gold negative; again, the unemployment rate will serve as our barometer for indications of FOMC posturing. Now that I have reduced risk, I am thinking about ways to quantitatively express my fundamental views on this jump risk, particularly in E.M., perhaps via deep OTM puts and long-vol expressions on E.M. ETFs? Brazilian puts (EWZ) or short Chinese Real Estate (TAO) anyone? I also want to re-shift my focus back onto natural gas as we get into the winter draw season. More to come...

Trade Update:"Going for the Gold"

The Wednesday 11/25 rally in Gold caused the Dec 115 GLD Calls (GCZ-LG) to be exited on 3/4 of the positions risk capital (I have established internal +/- 40% option guidelines for 1M ATM options where time to expiry is greater than 20 days and Gamma is between 5-15).

As discussed in a prior post, we have seen a sharp technical pullback catalyzed by the fear of Dubai's debt dilemmas, which gave way to a pronounced pullback from nearly all risky assets on the 27th. Managers have finally been reminded that the crisis is not over, and that risk premiums exist for a reason. Fortunately, the systematic trading style has been advantageous in uncertain times like these: the flight-to-quality led resulted in a strong appreciation of the dollar and a nice consolidation on the GLD.

I am still looking for directionally net long exposure to GLD. I am rebuilding an entry back into the Dec and Jan ATM calls. However, Skew is still biased to the downside and 5% OTM strangles are still too expensive to capture long-vol, based upon historical volatility cone analysis.

So far, profit on the trade has been 38.8% in 3 days net of transaction costs and with vol of 49%, leading to a Sharpe of 0.79 over the trade's duration.