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**HyperVolatility End of the Year Report 2014**

**HyperVolatility End of the Year Report 2014 (PRINT)**

The 1^{st} part examines the performances of the following asset classes throughout the 2014:

**Equity Indices:** Mini S&P500, DAX 30

**Treasury Bonds: **German Bund, US 10–year Treasury Bonds

**Currencies: **Euro, Japanese Yen, British Pound Sterling

**Commodities: **WTI Crude, Brent Crude, Gold

**Volatility Indices:** VIX Index

The 2^{nd} part analyzes the macroeconomic scenario in USA, Europe, Australia, Japan and BRICS economies (Brazil, Russia, India, China and South Africa). The economic indicators that have been considered for the study are the following:

**GDP Growth Rate**

**Unemployment Rate **

**Inflation Rate**

** Debt–to–GDP Ratio**

**Credit Rating**

Please, email all your questions at **info@hypervolatility.com**

The above reported table shows, in the first column, January’s lognormal returns calculated for the S&P500 while the second one lists the total return for each year. The right hand side of the table provides the same calculations but based on the NASDAQ Composite index. First of all, it is worth noting that, over the last 11 years, the average return for the S&P500 index has been +4.89% while the NASDAQ Composite yielded an average of +6.78%. Secondly, both equity indices have experienced similar fluctuations during the crises but the NASDAQ has consistently outperformed the S&P500 since the 2012 so far. The following chart plots the success/failure rates of the January Barometer theory applied to the aforementioned asset classes over the last 11 years:

The success rate for both S&P500 and NASDAQ Composite is 54.5% while the failure rate is 45.5%. These numbers simply mean that the JB theory held true for 6 years but it unsuccessfully predicted yearly returns in 5 occasions. Nevertheless, the 54.5% success rate definitely does not fall within the category “reliable strategies” but different results could potentially come from different markets. The next table presents the results of our analyses on the German DAX30 and the British FTSE100:

The tables evidently show that during the financial crises in 2008, the selected European markets performed as poorly as their American counterparties (although the British FTSE100 did not violate the –40% threshold). The last 3 years have gone quite well as far as returns are concerned although in the 2014 the British FTSE100 (–2.62%) underperformed the DAX30 (+3.06%). On average, the German index, over the last 11 years, has yielded a +7.26% return while long term investors in the British market managed to gain only +2.34%. The next graph plots the success/failure rates of the January Barometer theory applied on the aforementioned European asset classes:

The results are very different from the ones observed for the overseas equity indices. First of all, the JB theory applied to the DAX30 has higher failures (54.5%) than successes (45.5%). In particular, the January Barometer strategy has successfully predicted future returns 5 times but it has failed 6 times implying that even in this market it led to poor results. On the other hand, the JB applied to the British FTSE100 shows a 63.6% winning chance while the losing probability is only 36.4%. In this case, the returns registered in the first month of the year since 2004 proved to be good forecasters for yearly returns. Numerically, the JB strategy would have been profitable in 7 cases while it would have failed only in 4 occasions. The next table lists the historical returns for the AustralAsian region:

The equity indices that have been used as a proxy for the AustralAsian geographic region are the Japanese Nikkei225 and the Australian ASX200. The 2008 was a very negative year also in AustrlAsia, in fact, both yearly returns are very close to the –50% threshold. However, also the European credit crisis in 2011 has dramatically influenced the aforementioned indices: –20.58% for the Nikkei225 and –13.16% for the ASX200. The data for the average returns, calculated over the last 11 years, show that the Nikkei225 yielded a +2.89% while the Australian equity index returned an average of +3.57% to potential long term investors. Did the January Barometer strategy provide any extra gains? The next chart will attempt to answer this question:

The Japanese index displays the usual 54.5% / 45.5% split between success and failure rates implying that the JB strategy proved profitable only 6 times and failed in 5 cases. Conversely, the success rate for the ASX200 is 63.6% (7 successes) while the failure rate is only 36.4% (4 failures) implying that the JB strategy was definitely more profitable when applied to the Australian index than to its Japanese equivalent. The last table of the present research focuses on the past performances of a geo–economic, rather than merely geographic, area: emerging markets.

The equity indices that have been selected for this section are the Hang Seng (Hong Kong), the Bovespa (Brazil) and the BSE Sensex (India). The first thing to notice is that during the crisis the losses incurred by these markets have been larger than the ones observed for the indices we have mentioned so far. In fact during the credit crunch, with the exclusion of the Brazilian Bovespa that in 2008 had a negative return of “only” 46.25%, the Hang Seng yielded a –55.43% while the Indian return for the same year was a remarkable –70.64%. However, the scenario considerably changes if the 2011–2014 time interval is taken into account. In fact, the Indian equity index, even including the drop in the 2011, has consistently outperformed the other two. As far as long term average returns are concerned, since the 2004 so far, the Hong Kong’s Hang Seng yielded a +5.43%, the Brazilian Bovespa returned a +5.81% while the Indian BSE Sensex averaged an impressive +13.68%. Emerging markets average returns are clearly very high but the BSE managed to outperform all other equity indices considered in the present research (the German DAX30 ranks second with a +7.26% and it is immediately followed by the NASDAQ Composite index that yielded an average return of +6.78%). The next chart plots the success/failure rates obtained by running the January Barometer strategy on the Hang Seng, Bovespa and BSE Sensex:

The success rates for the BSE Sensex (54.5%) and Bovespa (45.5%) do not really seem to provide a hedge (although the strategy proved more profitable on the Indian equity index than on the Brazilian one). The most significant information that can be extracted from this analysis is the high failure rate on the Hong Kong’s index (63.6%). In particular, the January Barometer strategy has consistently failed to predict yearly returns on the Hang Seng index for 7 years while it proved successful only in 4 cases.

All in all, the analyses just conducted on the 9 equity indices considered in the study seems to point out that the JB strategy does not to provide any particular hedge for investors. Nevertheless while wrangling data some interesting patterns have emerged. The patterns that have been detected can be grouped in two categories: the winning pattern and the losing pattern.

*Winning Pattern*

The January Barometer strategy can only yield two mutually exclusive outcomes: it is either profitable or not (there is a chance that the yearly return could eventually be 0% but the associated probability, over 252 trading days, is so low that we have voluntarily excluded it from the scenario analysis). The winning pattern has been extracted by simply running a frequency analysis on the times the JB strategy proved to be profitable. The JB strategy basically states that January’s return should match the yearly one, however, it makes no difference between negative or positive returns. Consequentially, as stated at the beginning of the research, a positive January’s return in a positive year would be counted as a success but a negative January’s return in a negative year would be also counted as a success. The most important thing for the strategy to work is a match between returns. The questions this section is trying to give an answer to are: is there a pattern among success cases? Do success cases have anything in common? Do bullish success cases outnumber bearish ones or vice versa? Before showing the results, it is worth reminding that 11 years worth of data on 9 different asset classes have been filtered implying a total of 99 observations. 52 out of 99 observations fall into the winning pattern category while the remaining 47 are axiomatically assigned into the losing pattern one. The following pie chart attempts to summarize the results obtained from data mining the data associated to the first pattern:

The success cases, for the combination January’s positive return in a positive yielding year (green area called BULL), are 34 while the success cases, for the combination January’s negative return in a bearish year (red area called BEAR), are only 18. Clearly, the outcome of this frequency analysis is a consequence of the overall trend in each year but it seems that the JB strategy, when profitable, works best in positive performing years rather than in negative ones (winning pattern). In order to understand why this is the cases we have to proceed and mine the data for failure cases.

*Losing Pattern*

In the previous section it has been observed that, numerically speaking, the majority of success cases happened during the combination January’s positive return in a positive yielding year. It has also been stated that the JB strategy “works best in positive performing years rather than in negative ones”. However, in order to understand why this is case, the present section will analyze all failure cases. If the JB strategy did not work, it axiomatically implies that January’s return did not match the sign of the yearly one. Consequentially, there are only two scenarios to consider when analyzing failure cases: the return in January was positive but the yearly one turned out to be negative or the year started by yielding a negative return in January but it ended with a positive performance. The next pie chart plots all the failure cases and groups them into two categories: BEAR TO BULL (negative return in January but positive on a yearly basis) and BULL TO BEAR (positive return in January but negative on a yearly basis):

The above reported chart is evidently displaying that, among failures, there is a very frequent pattern: the vast majority of failures in the JB strategy are due to years starting out with a negative return but that subsequently yield a positive one (losing pattern). Numerically speaking, the BEAR TO BULL cases counted 39 observations while the BULL TO BEAR ones are only 8.

*Conclusion*

- The January Barometer strategy does not seem to provide consistent profits at least for the considered asset classes and the selected time frame
- The January Barometer strategy successfully predicted yearly returns in 52 cases (52.5% of the total observations)
- 34 of the 52 success cases come from the combination January’s positive return in a positive yielding year while only 18 come from the combination January’s negative return in a negative yielding year
- The January Barometer strategy failed to predict yearly returns in 47 cases (47.5% of the total observations)
- 39 of the 47 failure cases fall within the BEAR TO BULL category where January yielded a negative return but the year ended up with a positive performance
- Only 8 failure cases fall within the BULL TO BEAR category where January yielded a positive return but the year ended up with a negative performance

The present research can be expanded in many ways. In fact, potential research developments could come from increasing the datasets in order to allow 20 or 30 years worth of observations, from including more equity indices or by expanding the analysis to different types of asset classes such as treasury bonds, commodities and currencies.

]]>Gold is currently a bad, short term investment. It may remain in the range of $1,100 – $1,200 in the first two quarters of 2015 because of a very strong dollar.

Despite this, however, gold remains a necessary investment for investors who believe in its power during hyper inflation. Long-term investors of gold can take advantage of the precious yellow metal’s current price levels. Short-term investors, on the other hand, would need to wait for better levels and for its correction to happen in the coming months.

**Factors that weigh gold prices down**

Gold and the USD are inversely correlated and the following chart, which plots the monthly correlation between the aforementioned asset classes since the beginning of January so far, helps proving this point:

The coefficient, if we exclude the very last part, has always been negative and, over the last 12 months, it averaged -0.82

The Euro and gold relationship, however, doesn’t work the same way. The Euro zone may do a huge monetary easing (probably something similar to what the U.S. did until The Fed’s easing a few months back) and this will weaken the Euro against the dollar. A weak euro means weak gold, since it will cost European investors more to buy the dollar-denominated metal.

The current strength of the U.S. economy will guarantee that investors will put their assets more into stocks even if the Euro-zone and China are not very attractive investments. Stocks will likely outperform gold until the latter bottoms out.

Gold prices are also being undermined by the looming interest rates hike in 2015. Short-term investors are taking their money out of gold because it doesn’t yield high interests. While most investors see an interest rates hike next year, some remain skeptical about the matter. Precious metal pundits believe that The Fed will not raise interest rates because when it does, the government would have to pay more interest on its debt. This would be very difficult, given all the money it has printed.

**Gold’s possible turnaround**

There is reason to believe that gold may shine brighter next year. Wall Street thought that gold would sharply decline below the $1,000 mark before the year ends, but it has increased to $1,200 partly due to China and Europe’s stimulus. This rally is just the beginning, as what most supporters of the precious yellow metal believe.

There’s also huge physical buying particularly in Asian countries, as well as several central banks around the world. In addition, demand for gold in China, despite the price slump of the precious metal, remains high. The precious yellow metal’s prices also spiked in the first two weeks of November because of worsening political turmoil between Russia and Ukraine. In November 7th, gold went up by 3.15% and 2.3% on November 14th. Gold’s gains in the aforementioned dates haven’t been upturned since then.

Jordan Roy-Byrne, editor and publisher of The Daily Gold Premium, is convinced that gold will skyrocket after it bottoms out. According to his interview with The Gold Report, gold may have an inflation-adjusted price of around $3,000 per ounce by 2017. Investors may read his interview with The Gold Report here.

Gold’s battle isn’t over yet when long-term output is considered. However, from a short-term perspective, it would be better to place investments in paper securities until gold reaches its bottom.

]]>Commodity traders and portfolio managers are no strangers to the concept of spread trading. In fact, many commodities are powerfully linked by common factors such as fundamentals, demand/supply dynamics, extraction/production procedures, import/export processes, shipping/transportation routes, geographical availability, geopolitical variables and so forth. There are many types of spreads within the commodity sector (natural gas vs power, copper vs aluminium, gold vs silver, platinum vs palladium) and all of them are based on some of the above mentioned common factors. The crack spread, the focus of the present research, is built using WTI Crude oil, RBOB gasoline and diesel prices. Nevertheless, it is worth mentioning that the term “crack spread” can also refer to another spread combination which involves WTI, RBOB and heating oil or to the less popular, but still frequently traded, European crack spread (Brent Crude vs European Gasoil).

The crack spread provides a fairly good approximation of the margin earned by refiners and this is precisely why this strategy is at the core of the oil industry. In fact, it simply expresses the relative value of the cost of crude oil with respect to refined products (gasoline and diesel). Refiners can enter a simple 1:1 crack spread (crude oil vs gasoline or crude oil vs diesel), however, in a typical refinery the gasoline output is usually two times larger than that of distillate fuel oils (diesel, heating oil, jet fuel oil, bunker oil, etc). Consequentially, it would be more appropriate to trade diversified crack spread constructions like a 3:2:1 spread or a 5:3:2 spread. The present analysis will focus on the 3:2:1 crack spread which is the most popular and useful construction because it meets the needs of many refiners. The formula for calculating the price of a crack spread is the following:

[(2 * RBOB $/bb + 1 * ULSD $/bb) – (3 * WTI $/bb)] / 3

The calculation is simple. However, RBOB and ULSD prices (or RBOB and heating oil prices) are expressed in $ per gallon and not in $ per barrel. Hence, they have to be multiplied by 42 (1 barrel contains 42 gallons) in order to express them in barrel terms. For example, on the 9^{th} of June 2014, RBOB and NY Harbor Diesel closed at $3.049 and $2.886 per gallon respectively, hence, their “per–barrel prices” would automatically be ($3.049 *42) = $128.058 for RBOB and ($2.886*42) = $121.21 for ULSD.

Refiners are naturally long the crack because they have to purchase crude oil, refine it and then sell the products. Hence, the profit margin comes from the relation between crude prices and product prices while the biggest concerns for refiners come from any unwanted changes in such relation. Refiners predominantly fear increases in crude oil prices and drops in product prices because in this case their profit margin would shrink. The refiner, in order to lock in the price, will therefore cover its physical position on the financial market. Let’s assume a refiner decides to lock in the current margin because he fears an increase in the price of crude oil with respect to product prices. The best strategy he can implement involves selling a crack spread so that the long crude position will offset potential augments in oil prices while the short positions on products will counterbalance losses coming from potential plunges in diesel and/or gasoline prices. WTI is trading at $100.52, RBOB gasoline trades at $2.905 per gallon while NY Harbor diesel is at $2.927 per gallon. Consequently, RBOB gasoline and NY Harbor diesel in barrel terms are priced at ($2.905*42) =$122.01 and ($2.927*42) = $122.93. The 3:2:1 crack spread can now be constructed, so the refiner will purchase 3 WTI crude contracts at $100.52 and simultaneously sell 2 gasoline futures at $122.01 and 1 diesel futures at $122.93. The margin from the financial crack spread is equivalent to:

[(2 * $122.01 + 1 * $122.93) – (3 * $100.52)] / 3 = $21.79

The refiner has now locked in a $21.79 margin and it has secured its transaction. In fact, any potential rises in crude oil prices will be counterbalanced by a larger profit on the long WTI futures position while any potential plunges in gasoline or diesel prices will be offset by the gains on the financial short positions. Clearly, refiners tend to hedge looking forward so the contracts that will be used can expire in 1, 2 or 3 months from the implementation time depending on the delivery date. On the other hand, there are times where refiners are forced to sell crude oil and buy products. Consequentially, in order to hedge such exposure, they need to implement a reverse crack spread (also known as crack spread hedge). The reverse crack spread is just the opposite of a regular crack, in fact, it involves taking a short futures position on WTI crude oil and long positions on gasoline and diesel futures. Why would a refiner sell crude and buy products? Isn’t that counterproductive? Refineries work at full capacity to satisfy the demand for oil derivatives, however, forced shutdowns, due to machine breakdowns or unexpected technical problems, can happen. Contractual agreements must always be honoured, therefore, in the unfortunate event of a technical breakdown, refiners have to purchase products from someone else and deliver it to their clients as per contract. Furthermore, refiners tend to buy crude oil 2–3 months in advance so a breakdown would obligate them to sell the amount already delivered, or about to be delivered, because a technical “crash” would not allow them to refine it. These situations can easily happen, not that frequently, but they do happen. Hence, the best way to protect the business is to enter a reverse crack spread where crude oil is shorted and products are bought. The final margin is the difference between the operations on the physical market (selling WTI barrels and purchasing barrels of products) and the ones on the financial market (selling WTI futures while purchasing gasoline and diesel futures). Let’s assume that on the physical market the refiner faces a loss of $22.52 because he is forced to buy many thousands of barrels of products at a higher price due to the unexpected breakdown. On the other hand, thanks to the reverse crack strategy, he manages to lock in a $23.46 profit. The final margin would be $23.46 – $22.52 = $0.94.

Again, refiners do not usually buy products and sell crude unless obligated to do so, hence, the crack spread hedge is implemented only in particular occasions.

It is also worth mentioning that many refiners may want to enter different types of crack spread in order to cover the so–called energy basis risk. The basis risk is the difference in price between the same product delivered or traded in 2 different locations. The price difference between US Gulf Coast Ultra Low Sulphur Diesel and New York Harbor Ultra Low Sulphur Diesel is an example of basis risk. A refiner that uses only NY Harbour diesel will build a crack spread using NY Harbor ULSD futures while another one may want to take simultaneous positions on Gulf Coast and NY Harbor diesel because he refines them both.

The following section of the present research will quantitatively analyze the crack spread and it will separate each component of the strategy to study its behaviour and fluctuations. The first chart displays the price oscillations of the 3:2:1 crack spread that has been synthetically replicated using WTI crude, RBOB gasoline and NY Harbor diesel futures prices ranging from June 2006 to June 2014:

It is evident that the margin earned by refiners has remarkably fluctuated over the past years and it is safe to say that geopolitical factors have strongly impacted its performance. The chart shows that the price of the crack spread has predominantly oscillated within $10 and $40 with occasional deviations from such channel. The price drop in 2008 and the violent spike in 2012 are clear examples of what happens to the margin when crude oil and products prices diverge in relative terms: crude oil goes up while products prices plunge or vice versa. The following graph summarizes the performance of the crack spread on a yearly basis:

The figures reported in each bubble represent the average price for the crack spread in that year. The graph shows rather eloquently that, in the time interval 2006–2010, the price action moved between $13.3 and $17.3. However, the trend observed during the aforementioned 5 years was clearly bearish and the refiners’ margins decreased by $2–$3. The second part of the chart, instead, displays a diametrically opposite scenario. In fact, the data for the interval 2011–2014 show a violent explosion of the price action and a consequential widening of the margins. The highest average price was achieved in 2012 ($34.05) while 2013 and the first half of 2014 registered lower average prices ($25.55 and $23.77 respectively). It is interesting to notice that the price gap between 2010 and 2011 is as high as $15.94. Once again, the price jump was due to a divergence between the price of WTI, which at the beginning of 2011 dropped below $90 in several occasions, and the price of gasoline and diesel that, contrarily, remained constant. The initial imbalance between crude oil and products, however, persisted throughout the rest of the year even if the WTI recovered and moved back in the $100 area. It is important to point out that in November 2011 the Seaway pipeline project, which reversed the flow of crude oil, allowing its transportation from the Cushing to Houston’s vast refining area, got started. This project, which was completed on May 2012, has without a doubt contributed to increase the margin for refiners.

The next chart displays the fluctuations of the realized volatility for each component of the crack spread: WTI Crude Oil, RBOB gasoline and Ultra Low Sulphur diesel:

At a first glance, it is clear that the most volatile component is RBOB gasoline because the spikes in volatility are usually more violent in this market than in all the others. The second component, as far as volatility fluctuations are concerned, is WTI Crude Oil because its realized volatility is rather close to the RBOB one but slightly lower. The least volatile component of the entire crack spread is the diesel. In fact, it is evident that diesel realized volatility is well below the RBOB one and it is lower than the volatility curve observed for crude prices. The next graph, in order to provide a more accurate and quantitative approach, plots the distribution of the realized volatilities for each component and it ranks them:

The above reported chart eloquently confirms that RBOB is the asset class with the highest average volatility (37.73%), followed by WTI (27.97%) and ULSD (26.32%). It is important to point out that we are dealing with commodities and therefore it is not surprising to observe average volatilities well higher than the ones usually obtained by filtering equity indices data. The RBOB market is so volatile that its Low range values oscillate around 30.28% while WTI and diesel experience Low values fluctuating around 21.16% and 19.76% respectively. The same scenario can be easily noticed in the High segment of the distribution because, even in this case, the RBOB has the highest figure (46.61%) while WTI (35.76%) and ULSD (34.07%) rank lower. The examination of the extreme values, Minimum and Maximum, shows rather similar results. In particular, the Minimum segment has the identical ranking seen so far: RBOB is still the most volatile (16.68%), WTI is the second most volatile (11.15%) while diesel remains the third most volatile component (8.55%). The analysis of the Maximum segment, instead, provides some interesting evidence. Firstly, realized volatility spikes within energy markets can be rather violent and aggressive, therefore, it is not surprising to see values well beyond 100% for both RBOB gasoline (125.46%) and WTI Crude Oil (122.63%) while ULSD ranks again 3^{rd} (81.26%).Secondly, it is very interesting to notice that in the Maximum segment, WTI values are very close to RBOB ones implying that extreme realized volatility explosions in the American crude oil market can be tremendously violent. Numerically speaking, a realized volatility explosion, that would cause the volatility to shift from the Medium segment to the High segment, would mean a 232.5% increase for RBOB gasoline but, in the case of WTI, it would imply an increment of 365.9%. It means that WTI extreme volatility explosions can be up to 57.3% more aggressive than the ones on RBOB which is, on average, the most volatile component of the crack.

So far, the concepts that have been discussed and expanded are:

1) The fundamental reasons behind the crack spread

2) How to construct a crack spread

3) Utilization of the crack spread for hedging purposes

4) Analysis of the crack spread price

5) Volatility analysis of the components

The last section of the present research will conclude the investigation on the components of the crack spread. The previous study showed that RBOB gasoline is the most volatile component of the strategy but, in order to quantitatively define which of the 3 asset classes influence crack spread prices the most, it is necessary to run a correlation analysis:

The correlation matrix is divided into 2 groups. The first group consists of 3 sets of bars containing the distribution of the correlation coefficients calculated by running the analysis between one component against the other: RBOB vs ULSD, WTI vs RBOB and WTI vs ULSD. The second group, instead, presents the distribution of the overall numerical relationships between each component and the crack spread itself: WTI vs Crack Spread, RBOB vs Crack Spread and ULSD vs Crack Spread. Medium correlation bars will be used as a proxy for long term correlation because they provide an assessment of the average connection among the variables under examination. The chart suggests that all components are well linked to each other, in fact, the RBOB/ULSD correlation is +0.70 while the WTI/RBOB rapport is +0.67. The strongest coefficient is observed for the WTI/ULSD pair and in this case the figure is as high as +0.86. The crack spread strategy, instead, displays a robust relationship with RBOB gasoline (+0.78), a very weak one with respect to diesel (+0.30) and an almost non–existent link to WTI (–0.09). The high correlation coefficient between gasoline and crack spread is due to the high volatile nature of the RBOB market. The high volatility in gasoline prices, in fact, is likely to produce sudden and more frequent changes to the price of the crack spread. It is important to mention that the strong linear relationship detected by the correlation analysis, between RBOB and crack spread , has been confirmed also by the regression analysis. In fact, the adjusted–R squared values obtained by regressing every single component against the crack spread concluded that RBOB gasoline is indeed the asset class that influences the price of the crack the most. Numerically speaking, the computed adjusted–R squared for the WTI/Crack Spread regression was 6.75% and it confirms the extremely low linear relationship between WTI and crack prices. The adjusted–R squared for the ULSD/Crack Spread regression was 24.65% and, even in this case, the weak connection is confirmed. The adjusted–R squared for the RBOB/Crack Spread regression was 45.5% and it robustly confirms the relevant linear relationship between gasoline prices and the price of the crack spread.

]]>1) **Handysize Ships:** they account for approximately 34% of the global fleet and can carry 15,000–35,000 dead weight tons of cargo

2) **Supramax Ships:** they account for approximately 37% of the global fleet and can carry 45,000–59,000 dead weight tons of cargo

3) **Panamax Ships:** they account for approximately 19% of the global fleet and can carry 60,000–80,000 dead weight tons of cargo. Panamax ships are the largest ships allowed through the Panama Canal

4) **Capemax Ships:** they account for approximately 10% of the global fleet and can carry more than 100,000 dead weight tons of cargo and they are too big to pass through the Panama Canal

As previously mentioned, every index is specifically created to keep track of the commercial activity connected to the 4 most important type of ship and this is precisely why the BDI is built upon them. Mathematically, the Baltic Dry Index is calculated using the following formula:

BDI = ((CapesizeTCavg + PanamaxTCavg + SupramaxTCavg + HandysizeTCavg) / 4 ) * 0.113473601)

The 0.113473601 is the multiplier introduced to standardize the calculation while the TCavg refers to the Time Charter average. Time Chartering is simply one of the ways to charter a tramp ship. Specifically, the charter will “book” the ship that best fits the size of the cargo for a specific period of time and for a pre–defined route. The hiring fees are expressed on a “per–ton” basis because they are structured on the amount of dead weight tons that are transported each month. It is important to point out that the transactional costs (bunker fuel and storage), on time chartering, are covered by the charterer itself. Consequentially, the TCavg is simply a quantification of the average cost for shipping raw materials on a established route on one the four dry bulk carriers.

The Baltic Dry Index is a very important leading indicator for worldwide business sentiment for several reasons:

1) It is difficult to modify because it is based on pure demand/supply changes which are, in turn, calculated on real orders

2) It is considered to be a leading indicator because orders are usually booked many months in advance (at least 2-3 months because of high intensity traffic in canals and potential port congestions. Think about the ship traffic concentration in the Panama and Suez canals)

3) It is a reliable index because business activities underlying the calculation are all legally certified, financed and paid upfront (none would hire a Panamax ship without having a paid order in place and none would place an order without actually needing raw materials and commodities)

4) It is a very good macroeconomic indicator, as far as shipping raw materials is concerned, because building a dry bulk carrier (whether it is a Handysize, a Supramax, a Panamax or a Capemax ship is irrelevant) takes many years. Therefore, their limited availability makes the tracking easier and more reliable because it means that the largest quantities of shipped raw materials have to necessarily be transported on one of those ships and, consequently, they are being accounted for in the calculation

The Baltic Dry Index is fairly straightforward to understand. In fact, higher or lower fluctuations simply imply a net increase or decrease in the demand for commodities and raw materials. Furthermore, the BDI is an efficient way to measure commodities’ demand because, given the fact that ships are limited and takes years to build, the amount of cargo that needs to be shipped will largely influence the oscillations of the index. The first chart of the present research displays the performance of the Baltic Dry Index since the 30^{th} of June 2009 until the 27^{th} of December 2013:

The above reported graph shows that the blue line (the actual BDI) has never fully recovered since the peak touched in November 2001 (4,661 points) while the lowest level ever touched was in February 2012 (647 points). It is evident that the 2011–2012 time interval has been rather flat in terms of shipping activity and demand for raw materials because both the quarterly and semi–annual trend lines oscillated laterally for many consecutive months. Nevertheless, the second half of the 2013 (from June onwards) showed an increased number of business activity but the recovery was far from being robust implying that the shipping of raw materials is still lower than it was before the credit crunch. The next chart will attempt to provide clue regarding the volatility of the index on different time perspectives:

First of all, it is important to mention that the Baltic Dry Index has a mean reverting volatility which tends to be confined within the 20%–40% thresholds. Also, the above reported graph suggests that the divergence between the volatility in the mid–term (red curve) and the volatility in the long–term (white curve) tends to be lower than the difference between short–term and medium–term volatilities. Volatility analysis is crucial in order to understand the fluctuations of the BDI which is why the next chart has been specifically created to show the volatility distribution of the volatility spectrum over the time period June 2009 – December 2013:

The above reported chart displays the distribution of the volatility of the Baltic Dry Index in the short–term (ST VOL), medium–term (MT VOL) and long–term (LT VOL). The High, Mid–High, Medium, Mid–Low and Low sections correspond to the different volatility segments in the volatility spectrum. The sections will be now examined one at the time:

**High**: The ST volatility touched its highest point at 63.51% while MT and LT volatilities reached their respective tops at 62.41% and 54.20%

**Mid–High**: Mid–High volatilities are higher in the LT and MT than in the ST. In fact, mid–high volatility is 37.64% in the LT, equals 36.45% in the MT and it is approximately 35.05% in the ST

**Medium**: Medium volatility is higher in the long period than in the short one. Specifically, LT medium volatility is 32.25%, MT medium volatility is 30.36% and ST medium volatility is 27.12%

**Mid–Low**: Mid–Low volatilities are, even in this case, higher in the LT than in the ST. Specifically, LT mid–low volatility fluctuates around 25.51%, MT medium–low volatility is usually 24.31% while ST’s one is 19.19%

**Low**: LT volatility touched its lowest point at 13.83%, MT volatility minimum point was reached at 10.67% while in the ST the volatility has never got lower than 6.45%

The distribution analysis of the volatility spectrum has indeed provided very useful information. In fact, the calculation shows that mid–term and long–term volatilities, if we exclude the High segment, tend to systematically be more elevated than short–term volatility. Conversely, the highest spike in volatility was actually achieved in the short–term, although this volatility segment proved to be the least volatile of all. Why is that? What does this entail? The reason behind such phenomenon is the following: long and medium term volatilities are higher than the short term one as a consequence of the fact that the mean reverting pressure is lower in the LT and MT than in the ST. Specifically, such phenomenon implies that long–term and medium–term volatility explosions are more persistent and more ample, in terms of magnitude, and consequentially need more time to be “reabsorbed”. Besides, the fact that the highest volatility point ever reached by the Baltic Dry Index (63.51%) was actually achieved in the short–term implies that, in this segment, volatility explosions can be immediate and rather large although they tend to mean revert quickly. The strong persistency in medium and long term volatility explosions and the higher propensity to a quicker mean reverting process in the short–term volatility can be better understood by looking at the following serial correlation plot:

The chart shows 4 blocks. Each parallelepiped indicates the serial correlation amongst BDI data. The first on the left displays daily serial correlation, the second one from the left refers to weekly serial correlation, the third one from the left shows the monthly serial correlation while the last one refers to quarterly serial correlation. The interpretation of the above reported chart is fairly simple: the data from Baltic Dry Index tends to have a stronger bond in the very short term, a weak link on a weekly basis and they seem to have no relationship as far as monthly and quarterly data are concerned. The significant spread, between the first and the last two parallelepipeds, proves the point that short term volatility explosions tend to mean revert rather quickly and that actual data do not have any strong relationship in the long–term. The serial correlation plot also gives insights about the nature of the Baltic Dry Index itself: poor serial correlation in the long–term is a clear reflection of an ever–changing demand level for commodities and raw materials. The final chart highlights any inter–market relationship between the Baltic Dry Index and the most important asset classes in the world:

The correlation matrix emphasizes the rapport with 3 markets in particular: Euro, American Treasury Bonds and German Bunds. The correlation between the Baltic Dry Index and Euro futures, over the 2009–2013 period, is without a doubt, the most robust (+0.47). The strong bond with the Single currency is predominantly due to the fact that approximately the 40% of the shipping transactional costs are due to bunker fuel. Bunker fuel (also known as fuel oil) is priced in US dollar but, since Euro is the largest currency component of the Dollar Index, every fluctuation in the European coinage will cause significant changes in the hiring fees charged to ship raw materials around the world. Consequently, the Baltic Dry Index, which accounts for the hiring fees charged for Handysize, Supramax, Panamax and Capemax ships, will be inevitably influenced by such variable. The remaining asset classes that display a good, although negative, correlation to the BDI are the 2 government debt world benchmarks: American T–Bonds and German Bunds. The reason American (-0.43) and German (-0.38) sovereign debt securities have an inverse link to the BDI is probably: hedging. In fact, the risk caused by taking positions on Baltic Dry Index futures and options contracts, traded through the Baltic Exchange, is usually counterbalanced via stable government bonds. The low correlation among the BDI and the so–called risky assets (DAX, WTI Crude Oil and Mini S&P500) is predominantly due to business cycles and commercial demand (commercials need to place their orders for raw materials 2–3 months ahead in order to account for production time, manage risk and ensure a continuous flow of commodity supply). On the other hand, the fact that Japanese Yen and Gold do not have a strong relationship with the BDI implies that fund managers, commercials and commodity traders prefer hedging their BDI market exposure using the aforementioned treasury markets.

HyperVolatility Researches related to the present one:

Oil Fundamentals: Upstream, Midstream, Downstream & Geopolitics

Oil Fundamentals: Reserves and Import/Export Dynamics

Oil Fundamentals: Crude Oil Grades and Refining Process

The Oil Arbitrage: Brent vs WTI

The **HyperVolatility Forecast Service** enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at **info@hypervolatility.com**** **with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial

The report has an interactive Table of Contents, therefore, you can simply click on the asset class you are interested in and jump straight to the analysis.

The first copy is read–only while the second file is a printer–friendly version of the research.

The **HyperVolatility End of the Year Report 2013** can be downloaded FOR FREE at the following link (no registration required):

**HyperVolatility End of the Year Report 2013**

**HyperVolatility End of the Year Report 2013 (PRINT) **

The 1^{st} part of the report examines the performances of the most important asset classes in the world (equities, currencies, bonds and commodities) in 2013.

The asset classes that have been object of our annual research are the following

**Equity futures:** DAX, E–Mini S&P500, FTSE/MIB

**Treasury Bonds futures: **German Bund, American Treasury Bonds

**Currency futures: **Euro, Japanese Yen

**Commodity futures: **WTI Crude Oil, Gold

**Volatility Indices:** VIX ** **

The 2^{nd} part, instead, presents the macroeconomic scenario in USA, Europe and BRICS economies (Brazil, Russia, India, China and South Africa). The analysis focuses on important indicators such as GDP growth, inflation, Debt–to–GDP ratio, unemployment rate, inflation rate and credit rating.

A Chinese and an Italian version of the aforementioned research will be uploaded in the upcoming hours.

]]>In this research, we will assume that the implied volatilityσis not stochastic, which means that volatility is neither a function of time nor a function of the underlying price. As a practical matter, this is not true, since volatility constantly change over time and can hardly be explicitly forecasted. However, doing researches under the static–volatility framework, namely, the Generalized Black–Scholes–Merton (GBSM) framework, we can easily grasp the basic theories and then naturally extend them to stochastic volatility models.

Recall that the Generalized Black–Scholes–Merton formula for pricing European options is:

*C = Se ^{(b-r)T} N(d_{1}) – Xe ^{-rT} N(d_{2})*

*P = Xe ^{-rT} N(–d_{2}) – Se ^{(b-r)T} N(–d_{1})*

Where

And *N (* *)* is the cumulative distribution function of the univariate standard normal distribution. *C* = Call Price, *P* = Put Price, *S *= Underlying Price, *X* = Strike Price, *T* = Time to Maturity, *r* = Risk–free Interest Rate, *b *= Cost of Carry Rate, σ= Implied Volatility.

Accordingly, first order GBSM option Greeks can be defined as sensitivities of the option price to one unit change in the input variables. Consequentially, second or third–order Greeks are the sensitivities of first or second–order Greeks to unit movements in various inputs. They can also be treated as various dimensions of risk exposures in an option position.

**1. Risk Exposures**

Differently from other papers on volatility trading, we will initially look at the Vega exposure of an option position.

**1.1 Vega Exposure**

Some of the variables in the option pricing formula, including the underlying price *S,* risk–free interest rate *r* and cost of carry rate *b*, can be directly collected from market sources. Strike price *X* and time to maturity *T* are agreed with the counterparties. However, the implied volatility σ, which is the market expectation towards the magnitude of the future underlying price fluctuations, cannot be explicitly derived from any market source. Hence, a number of trading opportunities arise. Likewise directional trading, if a trader believes that the future volatility will rise she should buy it while, if she has a downward bias on future volatility, she should sell it. How can a trader buy or sell volatility?

We already know that Vega measures option’s sensitivity to small movements in the implied volatility and it is identical and positive for both call and put options, therefore, a rise in volatility will lead to an increase in the option value and *vice versa*. As a result, options on the same underlying asset with the same strike price and expiry date may be priced differently by each trader since everyone can input her own implied volatility into the BSM pricing formula. Therefore, trading volatility could be, for simplicity, achieved by simply buying under–priced or selling over–priced options. For finding out if your implied volatility is higher or lower than the market one, you can refer to **this research ** that we previously posted.

Let’s assume an option trader is holding a so–called ‘naked’ short option position, where she has sold 1,000 out–of–the–money (OTM) call options priced with *S*=$90, *X*=$100, *T*=30 days, *r*=0.5%, *b*=0, σ=30%, which is currently valued at $434.3. Suppose the market agreed implied volatility decreases to 20%, other things being equal, the option position is now valued at $70.6. Clearly, there is a mark–to–market profit of $363.7 (434.3-70.6) for this trader. This is a typical example of Vega exposure.

*Figure 1* shows the Vega exposure of above the option position. It can be easily observed that the Vega exposure may augment or erode the position value in a non–linear manner:

**(Figure 1. Source:** **HyperVolatility Option Tool – Box) **

A trader can achieve a given Vega exposure by buying or selling options and can make a profit from a better volatility forecast. However, the value of an option is not affected solely by the implied volatility because when exposed to Vega risk, the trader will simultaneously be exposed to other types of risks.

**1.2 Theta Exposure**

Theta is the change in option price with respect to the passage of time. It is also called ‘time decay’ because Theta is considered to be ‘always’ negative for long option positions. Given that all other variables are constants, option value declines over time, so Theta can be generally referred to as the ‘price’ one has to pay when buying options or the ‘reward’ one receives from selling options. However, this is not always true. It is worth noting that** **some researchers have reported that Theta can be positive for deep ITM put options on non–dividend–paying stocks. Nevertheless, according to our research, which is displayed in *Figure 2*, where *X*=$100, *T*=30 days, *r*=0.5%, *b*=0, σ =30%, the condition for positive Theta is not that rigorous:

**(Figure 2. Source:** **HyperVolatility Option Tool – Box)**

For deep in–the–money (ITM) options (with no other restrictions) Theta can be slightly greater than 0. In this case, Theta cannot be called ‘time decay’ any longer because the time passage, instead, adds value to bought options. This could be thought of as the compensation for option buyers who decide to ‘give up’ the opportunity to invest the premiums in risk–free assets.

Regarding the aforementioned instance, if an option trader has sold 1,000 OTM call options priced with *S*=$90, *X*=$100, *T*=30 days, *r*=0.5%, *b*=0, σ=30%, the Theta exposure of her option position will be shaped like in *Figure 3*:

**(Figure 3. Source:** **HyperVolatility Option Tool – Box)**

In the real world, none can stop time from elapsing so Theta risk is foreseeable and can hardly be neutralized. We should take Theta exposure into account but do not need to hedge it.

**1.3 Interest Rate/Cost of Carry Exposure (Rho/Cost of Carry Rho)**

The cost of carry rate *b* is equal to 0 for options on commodity futures and equals *r–q* for options on other underlying assets (for currency options, *r *is the risk–free interest rate of the domestic currency while *q *is the foreign currency’s interest rate; for stock options, *r *is the risk–free interest rate and *q *is the proportional dividend rate). The existence of *r*, *q* and *b* does have an influence on the value of the option. However, these variables are relatively determinated in a given period of time and their change in value has rather insignificant effects on the option price. Consequently, we will not go too deep into these parameters.

**1.4 ****Delta Exposure**

Delta is the sensitivity of the option price with regard to changes in the underlying price. If we recall the aforementioned scenario (where a trader has sold 1,000 OTM call options priced with *S*=$90, *X*=$100, *T*=30 days, *r*=0.5%, *b*=0, σ =30%, valued at $434.3) if the underlying price moves downwards, the position can still be able to make profits because the options will have no intrinsic value and the seller can keep the premiums. However, if the underlying asset is traded at, say, $105, all other things being equal, the option value becomes $6,563.7, which leads to a notable mark–to–market loss of $6,129.4 (6,563.7-434.3) for the option writer. This is a typical example of Delta risk one has to face when trading volatility. *Figure 4* depicts the Delta exposure of the above mentioned option position, where we can see that the change in the underlying asset price has significant influences on the value of an option position:

**(Figure 4. Source:** **HyperVolatility Option Tool – Box)**

Compared to Theta, Rho and cost of carry exposures, Delta risk is definitely much more dominating in volatility trading and it should be hedged in order to isolate volatility exposure. Consequentially, the rest of this paper will focus on the introduction to various approaches for hedging the risk with respect to the movements of the underlying price.

**2. Hedging Methods**

At the beginning of this section, we should clearly define two confusable terms: hedging costs and transaction costs. Generally, hedging costs could consist of transaction costs and the losses caused by ‘buy high’ and ‘sell low’ transactions. Transaction costs can be broken down into commissions (paid to brokers, *etc.*) and the bid/ask spread. These two terms are usually confounded because both of them have positive relationships with hedging frequency. Mixing these two terms up may be acceptable, but we should keep them clear in mind.

**2.1 ‘Covered’ Positions**

A ‘covered’ position is a static hedging method. To illustrate it, let us assume that an option trader has sold 1,000 OTM call options priced with *S*=$90, *X*=$100, *T*=30 days, *r*=0.5%, *b*=0, σ=30%, and has gained $434.3 premium. Compared to the ‘naked’ position, this time, these options are sold simultaneously with some purchased underlying assets, say, 1,000 stocks at $90. In this case, if the stock price increases to a value above strike price (*e.g.* $105) at maturity, the counterparty will have the motivation to exercise these options at $100. Since the option writer has enough amount of stocks on hand to meet the exercise demand, ignoring any commission, she can still get a net profit of 1,000*(100-90) + 434.3= $10,434.3. On the contrary, if the stock price stays under the strike price (*e.g.* $85) upon expiry date, the seller’s premium is safe but has to suffer a loss in stock position which in total makes the trader a negative ‘profit’ of 1,000*(85-90) + 434.4=-$4565.7. The ‘covered’ position can offer some degrees of protection but also induces extra risks in the meantime. Thus, it is not a desirable hedging method.

**2.2 ‘Stop-Loss’ Strategy**

To avoid the risks incurred by stock prices’ downward trends in the previous instance the option seller could defer the purchase of stocks and monitor the movements of the stock market. If the stock price is higher than the strike price, 1,000 stocks will be bought as soon as possible and the trader will keep this position until the stock price will fall below the strike. This strategy seems like a combination of a ‘covered’ position and a ‘naked’ position, where the trader is ‘naked’ when the position is safe and he is ‘covered’ when the position is risky.

The ‘stop-loss’ strategy provides some degrees of guarantee for the trader to make profits from option position, regardless of the movements of the stock price. However, in reality, since this strategy involves ‘buy high’ and ‘sell low’ types of transactions, it can induce considerable hedging costs if the stock price fluctuates around the strike.

**2.3 Delta–Hedging**

A smarter method to hedge the risks from the movements of the underlying price is to directly link the amount of bought (sold) underlying asset to the Delta value of the option position in order to form a Delta– neutral portfolio. This approach is referred to as Delta hedging. How to set up a Delta–neutral position?

Again, if a trader has sold 1,000 call options priced with *S*=$90, *X*=$100, *T*=30 days, *r*=0.5%, *b*=0, σ=30% the Delta of her position will be -$119 (-1,000*0.119), which means that if the underlying increases by $1, the value of this position will accordingly decrease by $119. In order to offset this loss, the trader can buy 119 units of underlying, say, stocks. This stock position will give the trader $119 profit if the underlying increases by $1. On the other hand, if the stock price decreases by $1, the loss on the stock position will then be covered by the gain in the option position. This combined position seems to make the trader immunized to the movements of the underlying price.

However, in the case the underlying trades at $91, we can estimate that the new position Delta will be -$146. Obviously, 119 units of stocks can no longer offer full protection to the option position. As a result, the trader should rebalance her position by buying 27 more stocks to make it Delta–neutral again.

By doing this continuously, the trader can have her option position well protected and will enjoy the profit deriving from an improved volatility forecasting. Nevertheless, it should be noted that Delta–hedging also involves ‘buy high’ and ‘sell low’ operations which could cause a loss for every transaction related to the stock position. If the price of the underlying is considerably volatile, the Delta of the option position would change frequently, meaning the option trader has to adjust her stock position accordingly with a very high frequency. As a result, the cumulative hedging costs can reach an unaffordable level within a short period of time.

The aforementioned instance show that increasing hedge frequency is effective for eliminating Delta exposure but counterproductive as long as hedging costs are concerned. To reach a compromise between hedge frequency and hedging costs, the following strategies can be taken into considerations.

**2.4 ****Delta–Gamma Hedging**

In the last section, we have found that Delta hedging needs to be rebalanced along with the movements of the underlying. In fact, if we can make our Delta immune to changes in the underlying price, we would not need to re–hedge. Gamma hedging techniques can help us accomplishing this goal (recall that Gamma is the speed at which the Delta changes with respect to movements in the underlying price).

The previously reported example, where a trader has sold 1,000 call options priced with S=$90,X=$100,T=30days,r=0.5%,b=0** , **

σ** ** =30% had a position Delta equal to -$119 and a Gamma of -$26. In order to make this position Gamma–neutral, the trader needs to buy some options that can offer a Gamma of $26. This can be easily done by buying 1,000 call or put options priced with the same parameters as the sold options. However, buying 1,000 call options would erode all the premiums the trader has gained while buying 1,000 put options would cost the trader more, since put options would be much more expensive in this instance. A positive net premium can be achieved by finding some cheaper options.

Let us assume that the trader has decided to choose, as a hedging tool, the call option priced with *S*=$90, *X*=$110, *T*=30 days, *r*=0.5%, *b*=0, σ=30%, with 0.011 Delta and 0.00374 Gamma. To offset his sold Gamma, the trader needs to buy 26/0.00374 = 6,952 units of this option which cost him $197.3 which leads to an extra Delta of 6,952*0.011=$76. At this point, the trader has a Gamma–neutral position with a net premium of $237 (434.3-197.3) and a new Delta of -$43(-119+76). Therefore, buying 43 units of underlying will provide the trader with Delta neutrality. Now, let’s suppose that the underlying trades at $91, the Delta of this position would become -$32 but since the trader had already purchased 43 units of stocks, she only needs to sell 12 units to make this position Delta–neutral. This is definitely a better practice than buying 27 units of stocks as explained in section 2.3 where the trader had only Delta neutralized but was still running a non–zero Gamma position.

However, Delta–Gamma Hedging is not as good as we expected. In order to explain this, let us look at* Figure-5* which shows the Gamma curve for an option with *S*=$90, *X*=$110, *T*=30 days, *r*=0.5%, *b*=0, σ=30%:

**(Figure 5. Source:** **HyperVolatility Option Tool – Box)**

We can see that Gamma is also changing along with the underlying. As the underlying comes closer to $91, Gamma increases to 0.01531 (it was 0.00374 when the underlying was at $90) which means that, at this point, the trader would need $107 (6,954*0.01531) Gamma and not $26 to offset her Gamma risk. Hence, she would have to buy more options. In other words, Gamma–hedging needs to be rebalanced as much as delta – hedging.

Delta–Gamma Hedging cannot offer full protection to the option position, but it can be deemed as a correction of the Delta–hedging error because it can reduce the size of each re–hedge and thus minimize costs.

From section 2.3 and 2.4, we can conclude that if Gamma is very small, we can solely use Delta hedging,** **or else we could adopt Delta–Gamma hedging. However, we should bear in mind that Delta–Gamma hedging is good only when Speed is small. Speed is the curvature of Gamma in terms of underlying price, which is shown in Figure – 6:

**(Figure 6. Source:** **HyperVolatility Option Tool – Box)**

Using the basic knowledge of Calculus or Taylor’s Series Expansion, we can prove that:

*Δ **Option Value **≈ **Delta * **Δ**S + ½ Gamma * **ΔS + 1/6 Speed * ΔS*

We can see that Delta hedging is good if Gamma and Speed are negligible while Delta–Gamma hedging is better when Speed is small enough. If any of the last two terms is significant, we should seek to find other hedging methods.

**2.5 Hedging Based on Underlying Price Changes / Regular Time Intervals**

To avoid infinite hedging costs, a trader can rebalance her Delta after the underlying price has moved by a certain amount. This method is based on the knowledge that the Delta risk in an option position is due to the underlying movements.

Another alternative to avoid over–frequent Delta hedging is to hedge at regular time intervals, where hedging frequency is reduced to a fixed level. This approach is sometimes employed by large financial institutions that may have option positions in several hundred underlying assets.

However, both the suitable ‘underlying price changes’ and ‘regular time intervals’ are relatively arbitrary. We know that choosing good values for these two parameters is important but so far we have not found any good method to find them.

**2.6 Hedging by a Delta Band**

There exist more advanced strategies involving hedging strategies based on Delta bands. They are effective for finding the best trade–off between risks and costs. Among those strategies, the Zakamouline band is the most feasible one. The Zakamouline band hedging rule is quite simple: when the Delta of our position moves outside of the band, we need to re–hedge and just pull it back to the edge of the band. However, the theory behind it and the derivation of it are not simple. We are going to address these issues in the next research report.

*Figure-7* provides an example of the Zakamouline bands for hedging a short position consisting of 1,000 European call options priced with *S*=$90, *X*=$110, *T*=30 days, r=0.5%, *b*=0, σ=30%:

**(Figure 7. Source:** **HyperVolatility Option Tool – Box)**

In the next report, we will see how the Zakamouline band is derived, how to implement it, and will also see the comparison of Zakamouline band to other Delta bands in a quantitative manner.

The **HyperVolatility Forecast Service** enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at **info@hypervolatility.com**** **with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial

Nevertheless, the demand for refined products is still very high and each oil derivative has its own market and its own price driver. A perfect example of divergence in price drivers for refined products comes for Europe. In the 90s many European governments guaranteed tax incentives to all the drivers who would have bought diesel–powered cars because diesel fuel emits less greenhouse gases than gasoline. Needless to say that such policy provoked a sharp augment in diesel prices but not in other oil derivatives.

Let’s now have a look at the oil industry as a whole.

First of all, it is worth mentioning that the oil industry is subdivided into 3 subsectors: upstream, midstream and downstream. The upstream involves the exploration and the extraction of crude oil, the midstream sector consists of transportation and storage while the downstream segment refers to the refining industry, marketing and distribution of refined products.

**Upstream** – The supply chain falls within the upstream segment. Here, the most important thing to determine is the capacity of the on–shore or off–shore site because this measurement identifies how big the oil well is and, consequently, the extraction rate. It is worth noting that major companies tend to retain a certain amount of unused capacity in order to face unexpected or sudden explosion in demand (usually caused by geopolitical issues).

**Midstream** – Once the extraction process is over, the oil “enters” the second segment: the midstream. This sector has to do, predominantly, with the transportation of the extracted petroleum liquids towards the refining centers. The transition can be processed using pipelines, trucks, barges or rail.

**Downstream** – Downstream operations are strongly connected with the refining industry because it is in this segment of the production chain that diesel, kerosene, jet fuel oil and all the other petroleum liquids get synthesized. Now, refining capacity is often closely related to demand for obvious reasons but not all refineries can deal with a broad range of crude oils so there are certain production boundaries. Nevertheless, the business is straightforward: refineries buy crude oil, they refine it and then sell the synthesized outputs. The income generated by refineries is measured with the so–called “crack spread” (there will be another study entirely focused on this product).

The cost of crude oil is not solely influenced by upstream, midstream and downstream operations. In fact, exogenous variables or unexpected events such as natural disasters, political turbulences and quality reduction of a specific oil well can push market players to increase their inventories. Consequentially, an augment in the short term demand and forward delivery would increase the cost of storage and, in turn, the cost of carry.

Amongst all of the exogenous factors that can alter oil prices, the geopolitical ones are certainly the most dangerous.

Conflicts and political instability in the Middle East have always had a remarkable impact on oil prices. Besides, African or Latin American countries, such as Nigeria and Venezuela, have often “hosted” violent riots that have increased the buying pressure on the oil market. Geopolitical issues create nervousness among market players and increase prices because internal riots, civil wars, unstable or corrupted governments could jeopardize the supply and limit the amount of oil available. Also, extreme forms of governments (fascism, communism, military controlled countries, etc) are not well seen by oil importing countries because dictators and/or non–democratically elected governments could threaten to limit the extraction or the export of oil.

The next chart provides a better clue on the relationship between geopolitical factors and oil prices:

The chart shows the fluctuations of WTI Crude Oil futures prices since July 1986 so far. The graph does not really need any comment because the arrows are self explanatory. Wars, civil wars, political turmoil, crises and cuts in the extraction rate have always added a significant pressure on crude prices which have been inevitably pushed higher. The only 3 big events, worth mentioning, that have depressed oil prices have been the Asian Economic Crisis in the mid 90s, the terroristic attack to the Twin Towers in September 2001and the Credit Crunch in 2008–2009.

Clearly, the Middle East is a vital geographical area for oil so any turbulence in this zone is strongly felt by market participants. Likewise, the other OPEC members do not always enjoy a great deal of political and civil stability (the OPEC members are Algeria, Indonesia, Islamic Republic of Iran, Iraq, Kuwait, Libya, Nigeria, Qatar, Saudi Arabia, United Arab Emirates, Venezuela). The following chart shows the weight of each OPEC member in terms of number of daily extracted barrels:

As previously mentioned, the chart displays the weight of each country expressed as a percentage of the total OPEC daily barrel production (the data are recent and they refer to the period January–June 2013). Saudi Arabia (29.68%), Iran (11.6%), Iraq (9.43%), Kuwait (9.17%) United Arab Emirates (8.78%) and Venezuela (8.63%) are the top 6 largest OPEC members. The fact that 5 out of 6 among the largest OPEC members are all located in the Middle East explains very clearly why this world region is so closely monitored by oil importing countries like United States, China, Japan, India and Germany.

If you are interested in trading oil or oil derivatives markets you might want to read the following **HyperVolatility **researches:

1) **Oil Fundamentals: Reserves and Import/Export Dynamics**

2) **Oil Fundamentals: Crude Oil Grades and Refining Process**

3) **The Oil Arbitrage: Brent vs WTI**

The **HyperVolatility Forecast Service** enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at **info@hypervolatility.com** with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial**.**

**(1)**

Where

=

**T** = Time to expiration

**F** = Forward Index price (the ATM strike price)

**K _{0}**= First strike price below the Forward price

**K_{i}**= Strike of the

**ΔK*** _{i}* = it is the midpoint between the strike prices. Specifically, the strikes used will be on both the sides of

**R** = Risk free interest rate (the interest rate used is usually the Treasury Bond yield that more closely matches the option expiration date)

**Q (K_{i}) **= The midpoint of the spread between bid price and ask price for each option with a strike

This is the formula that it is currently employed to calculate the most famous risk management index in the world. Before we provide any real example it is necessary to clarify some points. First of all, the VIX index is calculated using 2 expirations: the front month and the second front month contracts. In our study we will be using S&P500 option prices recorded on the 10^{th} of October 2013 and therefore the front month options will be those expiring on the 18^{th} of October 2013 (which will provide us with information about the volatility in the near term) while the second front month options will expire on the 15^{th} of November 2013 and they will provide us with information about the volatility in the medium term. It is important to point out that near term options must have at least 7 days to expiration and when this criteria is no longer met the model automatically rolls to the next available contract. Let’s give an example, our front month options expire on the 18^{th} of October while the medium term options will expire on the 15^{th} of November, hence, on Friday the 12^{th} the VIX will mechanically roll. At this point, the front month options used will be the ones expiring on the 15^{th} of November while the second front month options employed in the calculation will become those expiring in December. This measure has to be adopted in order to avoid mispricing issues that commonly happen when options are about to expire. Another important detail to mention is that **T** (time to expiration) is calculated in minutes using calendar days, consequently, the time to expiration will be given by

**(2)**

**M _{current day}**= minutes remaining until midnight of the same day

**M** ** _{settlement day}**= minutes remaining from midnight until 08:30 am on SPX settlement day

**M** ** _{other days}**= total minutes in the days between current day and settlement day

If we assume that the data have been recorded exactly at 08:30 am on the 10^{th} of October and that options will expire at 08:30 am of the 18^{th} of October:

Needless to say that **T _{1}** and

We now need to determine the F price of the index and in order to do so we take the strike price at which puts and calls have the smallest difference in absolute terms. The below reported table displays call and put prices with their absolute differential:

The red back–grounded figures are the strike prices at which calls and puts have the lowest difference, however, the two expiration dates have 2 different strike prices: ATM for October options is at 1,650 while ATM for November options is 1,655. In order to simplify calculations, and given the fact that the difference is extremely small, we will take 1,650 as F price because it is the front month contract. We can calculate F using the following formula:

** (3)**

Obviously, there will be two forward index values, F_{1} and F_{2 }, the first for near term and the second one for medium term options respectively:

Now we have both **F _{1}** and

The next step is to select all put options whose strike is lower than **K _{0 }**and all call options whose strike is higher than

The above reported table explains very well what stated before. In the month of October the lowest puts are at 790 and 795 but the two red back–grounded options cannot be accepted in our calculation because there are two consecutive 0 in their bid prices and therefore they are our stopping point. In other words, no option with a lower than 800 strike price will be considered into the calculation of the VIX. The same principle applies to calls and in fact 2,095 and 2,100 are the highest call option strike prices that will be considered. The same procedure will be applied to November options. It is important to point out that the option chains will rarely have the same amount of strikes available because according to volatility fluctuations the number of strikes that will be priced by market makers will vary. It goes without saying that high volatility explosions will obligate market makers to price even Far–Away–From–The–Money options on both sides because the demand for these instruments will rise. Consequentially, the number of strikes that will be used for the purpose of calculating the VIX will vary according to volatility fluctuations and swings in S&P500 futures. The following table lists the options that will be used for calculating the volatility index:

The ATM strike is highlighted in blue. The put options in the near term contract that will be used start from strike 800 until strike 1,645 while the call options range from strike 1,655 until strike 2,100. The medium term strikes, instead, goes from 985 until 1,645 for put options and from strike 1,655 until strike 2,100 for calls. We now calculate the specific weight that every single strike will have in the calculation by using the following formula and we will take the 800 put as an example:

**(4)**

Please bear in mind that **Q** is the midpoint between bid and ask while **ΔK** is the difference between the last option’s strike and the closest next strike, hence, in our case **ΔK** is (805 – 800) = 5. Let’s proceed with the calculation:

The next table summarizes the contribution of each option strike to the overall computation of the VIX Index:

Now, the weights need to be added up and multiplied by **2/T _{1}**

The equation **(1)** that we presented at the beginning of this study is almost completed, in fact, the final part is the only one yet to be estimated. Let’s proceed:

We can now complete the calculation by subtracting the two members of equation **(1)**:

Near Term **σ ^{2}_{1}** : 0.074319519775 – 0.000016423 = 0.074303096

Medium Term **σ ^{2}_{2}** : 0.041553088 – 0.000021750 = 0.041531338

The final VIX computation is given by the following formula:

The second term of the equation is nothing but the computation of the square root of the 30 day average of **σ ^{2}_{1}** and

**N _{T1}**= minutes left before the settlement of near – term options

**N _{T2}**= minutes left before the settlement of medium – term options

**N _{30}**= number of minutes in 30 days

**N _{365}**= number of minutes in a year composed by 365 days

If we plug in the numbers we have the following outcome:

This leads to the very last step: VIX = 100 x 0.209736087 = 20.9%

Now, the number we came out with is fairly accurate but it is limited to the moment in which the option prices have been “frozen”. Consequentially, the aforementioned procedure and calculation, in order to be precise, has to be automated and repeated every instant because any changes in option premiums will inevitable affect the final assessment of the VIX.

**HyperVolatility Forecast Service** enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at **info@hypervolatility.com** with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial**.**

**(Source: HyperVolatility Option Toolbox)**

As we can see from the above reported graph, the curve is higher at the extremes but rather low in the middle (bear in mind that the At–the–Money strike was $107.5). This is the typical shape for a front month implied volatility curve where the high demand for ITM calls and OTM puts as well as for ITM puts and OTM calls drives the volatility higher. In many cases, you will hear that the volatility for Out–of–the–Money options is higher but such statement is clearly incorrect because without further specification it implies that only OTM puts and calls experience such high volatility. The chart evidently shows that the volatility for ITM and OTM options is higher but, for obvious reasons, the volatility for the strike where a call option is In–the–Money will be almost as high as the volatility for the Out–of–the–Money put option and vice versa. Consequentially, saying that Away–from–the–Money options (both calls and puts) have a higher implied volatility than At–the–Money options is without a doubt the most correct statement. The most natural questions at this point would be: Why? What does a smile–shaped curve tell us?

The most obvious thing to say is that the volatility on AFTM options is higher because investors tend to trade them more often and they consequently push the volatility on the upside. The reason why investors buy wings is that ITM options have more intrinsic value than the ATM ones while OTM options have more extrinsic value than an option struck At–the–Money. Consequentially, the presence of an implied volatility smile–shaped curve is typical of more speculative markets. The smile suggests that, when large volatility shifts happen, many market players rush to buy OTM options for speculative reasons while ITM options are primarily purchased to stabilize portfolio gains. The next chart shows how the curve moves:

**(Source: HyperVolatility Option Toolbox)**

Many researches on implied volatility curve dynamics showed that the 75% of volatility changes can be defined by a total shift, up or down, of the entire curve as you can see from the chart. A further 15% of the movements consist of curve twisting (the right hand side of the curve goes deeper down while the left side gets pulled on the right or vice versa) while the remaining 10% is the product of a change in convexity (wings getting wider or tighter).

Smile–shaped curves are frequently found in equity index options, stock options and popular commodities / currencies (Euro, WTI, Gold, etc). Nevertheless, it is worth noting that the shape of the curve can even evolve over time. This concept can be better explained by looking at the following chart:

**(Source: HyperVolatility Option Toolbox)**

The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility. This phenomenon is commonly found in equity markets and risky assets. In this simulation the ATM strike is 116 and its volatility is 13.1% but OTM puts and ITM calls are much more expensive because they are trading above the 70% level. As previously mentioned, the implied volatility curve can change and evolve and a volatility smile can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened. Smirks are simply telling us that lower strikes are more traded than higher strikes and OTM puts as well as ITM calls are being heavily traded. If the market is heading south, a smile would easily evolve into a smirk because of the great buying pressure generated by market players rushing to buy OTM puts to protect their portfolios. The purchase of ITM calls, even during market crashes, makes sense because ITM call options have already an established intrinsic value and they have the highest probability to expire In–the–Money; in other words they are safer. However, in the event of market downtrends the evolution of a volatility smile into a smirk would predominantly be caused by the large buying volume on OTM puts.

The Volatility smile, nevertheless, can go through another metamorphosis whose final output is the so–called forward skew:

**(Source: HyperVolatility Option Toolbox)**

The forward skew is nothing but a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls. This type of curve is more frequently found in commodity markets, particularly agricultural products, than equity indices or stock options. Even in this case the increase in volatility is provoked by an augment in demand for these options. However, the strong buying pressure concentrated on OTM calls is often the main cause of such shape. Let us break it down. Many players in commodity markets are commercials (mining and energy companies, grain / wheat / sugar / coffee producers) and therefore a disruption in the supply chain of a particular commodity can generate serious problems. A shortage in oil supply due to geopolitical variables, a disappointing crop due to a frost or to challenging meteorological conditions, continuous strikes in a particularly large mine are all factors that would force companies to buy as quickly as possible the commodity they need in order to lock in the order. Consequentially, the remarkable buying pressure on OTM calls would inevitably drive their price up and that is why the implied volatility of higher strikes is more elevated than others.

Let us now summarize the main concepts in order to avoid confusion:

1) An implied volatility smile means that Away–from–the–Money options have a higher implied volatility than At–the–Money options

2) Implied volatility smile–shaped curves are typical of highly speculative markets

3) Many researches on implied volatility curve dynamics showed that the 75% of all volatility changes consist of a shift, up or down, of the entire curve

4) Smile–shaped curves are frequently found in equity index options, stock options and the most popular commodities / currencies

5) The smirk is a particular volatility profile where ITM calls and OTM puts are priced with a much higher implied volatility

6) Volatility smile curves can turn into a smirk if investors, traders and market players are expecting a market crash or if the plunge in price has already happened

7) The forward skew is a reversed form of smirk, in fact, the volatility here tends to become higher for ITM puts and OTM calls

8) The forward skew curve is more frequently found in commodity markets (particularly in agricultural products)

9) The formation of a forward skew curve is often the consequence of a shortage in the supply chain due to transportation issues, geopolitical problems, adverse meteorological conditions, etc

**HyperVolatility Forecast Service** enables you to receive statistical analysis and projections for 3 asset classes of your choice on a weekly basis. Every member can select up to 3 markets from the following list: E-Mini S&P500 futures, WTI Crude Oil futures, Euro futures, VIX Index, Gold futures, DAX futures, Treasury Bond futures, German Bund futures, Japanese Yen futures and FTSE/MIB futures.

Send us an email at **info@hypervolatility.com** with the list of the 3 asset classes you would like to receive the projections for and we will guarantee you a 14 day trial**.**