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I recommend Steven Pinker’s book (Amazon affiliate link) Rationality: What It Is, Why It Seems Scarce, Why It Matters and give it a five-star rating.

I am going to create a fictional medical situation and ask you to estimate the odds of a person being truly sick.

Let us assume for a moment that there is a new disease where 0.5 percent of the population is afflicted with the disease. If a random person not exhibiting any symptoms tested positive using a blood test, what are the odds that that person is truly sick knowing that the blood test has the following attributes:

  • 98 percent of the sick people being identified as sick (true positive reading)
  • 2 percent of the sick are falsely identified as okay (false negative reading)
  • 95 percent of the healthy people identified as healthy (true negative reading)
  • 5 percent of the healthy people being identified as sick (false positive reading)

Remember, this test is 98 percent accurate in identifying those that are sick as being sick. The answer of how many are truly sick may surprise you: it is about 9 percent.

To determine the 9 percent answer, we need to calculate the true positive readings and the total number of positive readings, which is false positive plus true positive readings.

For illustrative purposes, let us assume a total sample population of a million people.

False positive readings are calculated as follows: total sample population times percent healthy times false positive readings or 1,000,000 times 0.995 times 0.05 = 49,750 people.

Similarly, true positive readings are calculated as follows: total sample population times percent sick times true positive reading or 1,000,000 times 0.005 times 0.98 = 4,900 people.

Total positive reading = 4,900 + 49,750 = 54,650 readings.

Then, true positive readings are divided by total positive readings or 4,900 / 54,650 to get about 9 percent.

Probability tree

Figure 1: Probability Tree

Please see figure 1. To enlarge the figure, click on it.

If this Bayesian theory example piqued your interest, then Rationality will be an interesting book for you to read. It discusses Bayesian theory and other similar statistical topics.

At the end of the book, Steven Pinker tells us why rationality matters. In short, if we want to progress as a society, we need to make rational choices.

I have always enjoyed these types of topics and therefore enjoyed this book and recommend it to those of you who enjoy similar topics.

As an aside, on his blog, David Epstein wrote an excellent article “Here’s How to Understand What a ‘95% Accurate’ Test Is Actually Telling You.” There, he references two good sources: one, the New York Times article “When They Warn of Rare Disorders, These Prenatal Tests Are Usually Wrong”; and two, JAMA Internal Medicine article “Medicine’s Uncomfortable Relationship With Math: Calculating Positive Predictive Value.” What is surprising is that the medical field itself has challenges with understanding Bayesian theory.

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The Molecule of More

Books written about our brains tend to be complex and hard to understand. The Molecule of More: How a Single Chemical in Your Brain Drives Love, Sex, and Creativity–and Will Determine the Fate of the Human Race is different. It is easy to understand, entertaining, and informative. Those two qualities make this book (Amazon affiliate link) an outstanding read.

The main focus of the book is on one of the brain’s chemicals: dopamine.

Dopamine is a chemical that our brain uses when we want more of something now or focus more on abstract goals, needs, wants, or desires in the future.

As soon as we want something, our dopamine brain circuit kicks in and starts pumping dopamine, a feel-good drug. Dopamine remains as long as we are in pursuit of that something, but once we have obtained our goal, dopamine drops off and we need find something new to pursue to keep that dopamine high. If we are fortunate, though, our brains transition from dopamine to the Here and Now molecules.

Dopamine is one of the instigators of love, the source of the spark that sets off all that follows. But for love to continue beyond that stage, the nature of the love relationship has to change because the chemical symphony behind it changes. Dopamine isn’t the pleasure molecule, after all. It’s the anticipation molecule. To enjoy the things we have, as opposed to the things that are only possible, our brains must transition from future-oriented dopamine to present-oriented chemicals, a collection of neurotransmitters we call the Here and Now molecules, or the H&Ns. Most people have heard of the H&Ns. They include serotonin, oxytocin, endorphins (your brain’s version of morphine), and a class of chemicals called endocannabinoids (your brain’s version of marijuana). As opposed to the pleasure of anticipation via dopamine, these chemicals give us pleasure from sensation and emotion. In fact, one of the endocannabinoid molecules is called anandamide, named after a Sanskrit word that means joy, bliss, and delight.

According to anthropologist Helen Fisher, early or “passionate” love lasts only twelve to eighteen months. After that, for a couple to remain attached to one another, they need to develop a different sort of love called companionate love. Companionate love is mediated by the H&Ns because it involves experiences that are happening right here, right now—you’re with the one you love, so enjoy it.1

Addictions, such as alcohol and drugs, trigger a dopamine release. The faster dopamine release, the more addictive the drug. Different drugs, of course, have different strengths and absorption rates. The addiction is caused by a chemical cultivation of desire or wanting. Whether this wanting is good or bad is irrelevant. And addiction should not be viewed through a moral lens of weak character or lack of willpower. Instead, it is a chemical addiction that is difficult from which to break.

Dopamine can make people act in strange ways. For example, although dopamine causes people to want more of everything, including power and domination, people can put aside their immediate desires for longer-range goals. By being more pleasant, people can often get more cooperation and work from others over the longer term.

Creative and mental illness often require abstract ideas, needs, wants, or goals. Dopamine figures prominently in both. And not surprising, mental illness afflicts a high percent of creative people compared to the general population. Various medications for mental illness seek to control the way dopamine works within the brain.

Scientists and artists have more in common than many believe.

The fine arts and the hard sciences have more in common than most people believe, because both are driven by dopamine. The poet composing lines about a hopeless lover is not so different from the physicist scribbling formulas about excited electrons. They both require the ability to look beyond the world of the senses into a deeper, more profound world of abstract ideas. Elite societies of scientists are filled with artistic souls. Members of the U.S. National Academy of Sciences are one and a half times more likely to have an artistic hobby compared to the rest of us. Members of the U.K. Royal Society are about twice as likely, and Nobel Prize winners are almost three times as likely. The better you are at managing the most complex, abstract ideas, the more likely you are to be an artist.2

I found the discussion on politics interesting and complex, but I will let you, my kind reader, find out for yourself.

Not surprisingly, dopamine is also helpful for adventurers because they are not satisfied with the status quo of their current environment. The authors discuss how people migrated from Africa to across the globe and what role dopamine played.

In the last chapter, we learn that to be happy, people need to focus on the here and now, not the future. Therefore, to lead a happier life, we need to temper our insatiable hunger for more and learn to appreciate what we have now. In reality, we need both the drive and ambition that comes from dopamine to make progress, and we need to enjoy and appreciate what we have accomplished.

To reiterate, I thoroughly enjoyed this book and highly recommend it.

1Daniel Z. Lieberman and Michael E. Long, The Molecule of More: How a Single Chemical in Your Brain Drives Love, Sex, and Creativity–and Will Determine the Fate of the Human Race, Kindle Edition, (BenBella Books, 2018), 16

2Lieberman and Long, The Molecule of More, 134-135

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Book Reviews

One of my goals for the New Year is to read at least thirty books and write a brief book review afterward.

My reviews will typically only be a paragraph or two. To write longer, a more detailed book review requires a lot more effort. Once I have finished a book, I want to move on to the next one, not spend several hours writing a review.

Furthermore, I expect most of my ratings will be five stars. When reading, I am not looking for perfection or riveting information on every page. Instead, if I can come away with one good idea, something that I never knew before, or am forced to reevaluate a current belief or bias, then I will consider my time reading well spent. I got this idea of what constitutes success from Alex Honnold in a Harvard Business Review article “Life’s Work: An Interview with Alex Honnold.” Alex Honnold is the free solo climber who conquered the 3,000-foot ascent of El Capitan, in Yosemite National Park.

Is the way you train—memorizing and rehearsing your plan—typical?

Visualizing how you’re going to navigate a difficult section is pretty common. Where are my hands going to go? Where should I place my foot? Even recreational climbers in gyms make plans for themselves before they leave the ground. With free soloing, you’re both remembering or anticipating how to do certain climbs and trying to imagine the emotional component. What will it feel like to be up high in a crazy, contorted position without protection during a difficult stretch? When I’m not climbing, I spend most of my time reading books about training, psychology, and performance. If I get one good idea from one book, that’s a success.

As an aside, nonsubscribers to Harvard Business Review can read three articles, I believe, per month free of charge. So if Honnold’s interview piques your interest, head over to HBR to enjoy the article.

Also, sometimes when I read a book, I realize that I am not in the target audience. Even so, I keep reading because I might learn something interesting or helpful. And to penalize an author’s work by not giving a five-star rating just because I am not part of his target audience seems unfair.

My book reviews on my blog will be very similar, if not identical, to my reviews on Goodreads.

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Oil Update—December 2021

Although I was bullish last month, I did not provide a forecast for the month of December. And I am glad that I remained silent. Even though oil prices are up now, I was surprised that West Texas Intermediate (WTI) oil prices hit the low $60s last month.

Looking forward to January, I am expecting that WTI oil prices will range between $72.50 and $82.50. There are still several unknowns and critical developments waiting to be resolved in the near future.

OPEC+ is scheduled to meet in early January. Given that prices are relatively strong, I expect OPEC+ to maintain its schedule of an increase of 400 thousand barrels per day in February. There are three major issues, however, that have the potential to affect the price of oil. First, Omicron is still surging across the world. From my reading, some expect the Omicron wave to crest in early January, and others expect, mid- to late-February. Second, Russia and the US and NATO allies are scheduled to meet in early January to hold talks. While I hold some personal opinions, I do not think the general public, including myself, has sufficient information to render an informed opinion. Both sides are engaged in propaganda efforts to sway their public to their side. I just hope that the outcome does not result in a further escalation. And third, the Iran negotiations are ongoing. Just like the Russia and US and NATO negotiations, I do not think the general public has sufficient information. Given that any of these three major issues has the potential to affect oil prices, I am going to be cautious and wait until there is more clarity.

During the past month, I found it interesting watching experts opine on the effects of Omicron. Generally speaking, I noticed that those who began with a negative outlook never deviated from their negativity. Similarly, those who began with a positive outlook never deviated. Although I should not be surprised, I am. I believe that these various experts wanted and believed that they were providing the most realistic and unbiased information available. Yet they always seemed to find and circulate evidence that supported their initial positions, which is, of course, a demonstration of confirmation bias. Because Omicron is so transmissible and information is evolving quickly, I tend to be more uncertain. I would not be surprised if something were released tomorrow that refutes my prior position.

What I just wrote about Omicron applies equally to negotiations, generally. Major negotiations are always difficult and are fraught with high degrees of uncertainty. The participants of those negotiations struggle to corral all the issues and data and present an acceptable solution to their respective leaderships. If even they are uncertain how the future will unfold, how can someone far removed be certain of an outcome?

Of course, once a resolution has been reached in any negotiation, pundits will claim that it was all foreseeable. They will point to the breadcrumbs that led to this obvious outcome. The reality is that the breadcrumbs can be rearranged to suit any outcome that develops. Looking back, pundits and historians will always find a path through the chaos that seems logical and deterministic—as if someone who applied themselves could have accurately predicted the outcome. I believe that narrative is false.

I am reminded of a passage in Michael Lewis’s book (Amazon affiliate link) The Undoing Project: A Friendship That Changed Our Minds where he wrote the following:

It wasn’t just sports announcers and political pundits who radically revised their narratives, or shifted focus, so that their stories seemed to fit whatever had just happened in a game or an election. Historians imposed false order upon random events, too, probably without even realizing what they were doing. Amos had a phrase for this. “Creeping determinism,” he called it—and jotted in his notes one of its many costs: “He who sees the past as surprise-free is bound to have a future full of surprises.”

A false view of what has happened in the past makes it harder to see what might occur in the future. The historians in his audience of course prided themselves on their “ability” to construct, out of fragments of some past reality, explanatory narratives of events which made them seem, in retrospect, almost predictable. The only question that remained, once the historian had explained how and why some event had occurred, was why the people in his narrative had not seen what the historian could now see. “All the historians attended Amos’s talk,” recalled Biederman, “and they left ashen-faced.”1

For those unfamiliar with the book, the friendship is between Amos Tversky and Daniel Kahneman, who won a Nobel Prize “for having integrated insights from psychological research into economic science, especially concerning human judgment and decision-making under uncertainty.” If you have not read the book, I highly recommend it.

The key point is that the future is too uncertain to predict with certainty.

As mentioned, there is no consensus on what to expect regarding Omicron. On December 28, 2021, the New York Times featured a hopeful article “Omicron Variant Might Help Defend Against Delta, Lab Study Suggests” (subscription required).

If further experiments confirm these findings, they could suggest a less dire future for the pandemic. In the short term, Omicron is expected to create a surge of cases that will put a massive strain on economies and health care systems around the world. But in the longer term, the new research suggests that an Omicron-dominated world might experience fewer hospitalizations and deaths than one in which Delta continues to rage.

“Omicron is likely to push Delta out,” said Alex Sigal, a virologist at the Africa Health Research Institute in Durban, South Africa, who led the new study. “Maybe pushing Delta out is actually a good thing, and we’re looking at something we can live with more easily and that will disrupt us less than the previous variants.”

At present, my biggest concern is how Omicron will play out over the next several weeks. Even so, I expect that the price of oil has already discounted much of the bad news from Omicron. So now we need to wait to see if the future unfolds as some of the more optimistic pundits hope.

Again, I expect WTI to range between $72.50 and $82.50 for January 2022.

I wish you a Happy New Year, good health, and safe travels if you are traveling.

1Michael Lewis, The Undoing Project: A Friendship That Changed Our Minds, Kindle Edition, (W. W. Norton & Company), p. 208

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Oil Update—November 2021

My forecast for the November WTI price range was completely wrong because of at least three factors. First, the Biden administration was determined to reduce oil prices, either by having OPEC+ produce more oil or by coordinating with countries to withdraw oil from their respective strategic petroleum reserves. Having failed to convince OPEC+ to cooperate, oil will be released from strategic petroleum reserves of numerous countries, including the United States. Second, Austria went into lockdown because of its COVID situation. Some feared Austria might be the first domino in Europe. And third, last Friday, oil prices tanked on the WHO’s announcement of a new COVID variant named Omicron.

Later this week, OPEC+ will decide its production quotas for January. Many, including Morgan Stanley analysts, are expecting OPEC+ to pause its automatic 400 thousand barrel per day increase. Below is an excerpt from the Wall Street Journal article “Oil Prices Stabilize After Omicron-Driven Friday Selloff” (subscription required) on November 29, 2021.

Crude’s recent volatility marks the latest big swing in energy markets sparked by worries that Covid-19 travel restrictions will weaken the global economy and sap demand for fuel. In the past 20 months, oil has frequently fallen sharply when new variants and travel restrictions emerge, only to later rebound when demand picks up and large producers instill confidence in their supply curtailments.

Some analysts expect a similar pattern to play out after scientists detected the new, fast-spreading Omicron variant in South Africa. While new travel restrictions could dent the recent recovery in fuel demand, some traders now expect the Organization of the Petroleum Exporting Countries and allies to delay projected supply increases.

“With uncertainty over Omicron, we expect that OPEC will shelve its target to increase output in January and keep its quota flat,” Morgan Stanley analysts said in a note.

Because of the uncertainty concerning Omicron, traders’ reaction to Omicron developments, and OPEC+’s upcoming decisions, I am not going to provide a forecast range for the next month. While I remain bullish, I would not be surprised if oil prices just eke up slightly during December or recover the entire Friday loss. Of course, oil prices could fall, and I would be completely wrong. So I am going to watch and wait.

I wish everyone good health, a happy holiday season, and safe travels, if traveling.

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Oil Update—October 2021

Even though I increased my range by $5 per barrel last month, I underestimated the strength of oil prices. So this month, I am increasing my range by $7.50 per barrel to range between $77.50 and $87.50 per barrel for West Texas Intermediate oil.

Oil prices have, obviously, continued to strengthen. Backwardation is also strong, suggesting that prices are likely to remain firm. That said, when many are expecting strong prices to continue, that often sets up an opportunity for disappointment.

Political pressure is mounting for OPEC+ to provide more oil to the markets, and OPEC+ is meeting in a few days. Today, October 31, 2021, the Financial Times in an article titled “US Energy secretary blames Opec ‘Cartel’ for high petrol prices” (subscription required) quoted Biden administration officials:

The Biden administration’s senior energy official on Sunday blamed the Opec oil “cartel” for soaring petrol prices in the US, putting more pressure on the group to increase crude output ahead of a meeting later this week.

“Gas prices of course are based on a global oil market. That oil market is controlled by a cartel. That cartel is Opec,” said Jennifer Granholm, the US energy secretary. “So that cartel has more say about what is going on.”

Analysts including Goldman Sachs expect Brent, the global oil benchmark, to rise above $90 by the end of the year, boosted by an unexpected rise in Asian demand, as power generators stung by soaring natural gas prices switch to burning oil for electricity.

Most pundits expect that OPEC+ will not bow to political pressure and will instead proceed with its planned 400 thousand barrel per day increase. OPEC+ likely wants to see how 2022 unfolds. With its planned increases, does the market become more balanced, or perhaps, even enter into surplus.

Although not affecting oil prices in the near term, Iran has agreed to nuclear negotiations. Even if those negotiations are successful, I would not expect production from Iran to hit the market before the third quarter of 2022.

Although I do not have any longer-term predictions, I expect that November and December will continue to support strong prices.

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Oil Update—September 2021

My forecast range for the price of West Texas Intermediate oil in October is $70 to $80 per barrel, which is a five dollar per barrel increase over last month’s range.

Oil prices rebounded strongly in September, aided by a stabilizing or declining COVID-19 cases and the effects from Hurricane Ida. In fact, WTI prices were above $75 per barrel for brief period toward the latter part of September.

With the strength in oil prices, Goldman Sachs, according to a Reuters article, is calling for Brent prices to hit $90 per barrel by the end of the year. WTI prices are usually three to four dollars per barrel less than Brent prices. Although I am not expecting Brent to hit $90 per barrel in October, Brent prices could surpass $80 per barrel.

Adding fuel to the fire, the US will ease air travel in November, and that might push prices up in advance of November. As we around the world slowly acclimatize to the new normal of living with a background level of COVID, I expect economies around the world to continue to strengthen and demand more oil.

OPEC+ is having its monthly meeting in a few days. While I expect it will continue with its current planned increase of 400 thousand barrels per day, one can never be too sure. There are rumors that the US is pressuring OPEC+ to open the taps beyond the planned increase.

Switching topics, in Alberta and Saskatchewan, we are experiencing a surge in COVID cases, primarily affecting those who have not yet been fully vaccinated. Our ICUs are overflowing with COVID patients, which then forces others to defer their health needs. Therefore, I urge people to get vaccinated not only for themselves but also for others.

I hope everyone stays safe and well.

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Oil Update—August 2021

I am lowering my forecast from last month by $2.50 per barrel; West Texas Intermediate oil should range between $65 and $75 per barrel for September.

Oil prices went much lower than I expected in August, especially during the middle of the month when WTI was around $63 per barrel. Since then, WTI has rebounded considerably, but many are still cautious given that COVID-19 still is strong.

Having been overly bullish in August, I am more inclined to wait to see how September plays out before getting too bullish again. On September 1, OPEC+ will be meeting. Some believe that because of the latest variant of COVID, Mexico’s production issues, and Hurricane Ida, that OPEC+ will hold off on their 400 thousand barrel per day increase, while others believe that demand remains sufficiently strong and that the US administration wants more production, so the 400 thousand barrel per day increase will proceed as planned. I do not favor one argument or the other.

I remain optimistic that fourth quarter oil prices will be higher than they are today. By then, I hope that COVID cases will have peaked in many countries.

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Oil Update—July 2021

I am repeating my forecast from last month: I expect West Texas intermediate oil to range between $67.50 and $77.50 per barrel for August.

There was one brief spell where oil prices dipped below my expected range in July. The failure of OPEC+ to agree, the concomitant plunge in US 10-year bond yield and rise in the US dollar, and the rise in Delta variant cases all conspired against oil prices in early July.

OPEC+ appears to have settled their differences. Macro factors continue to be a concern. And I am hoping that the Delta variant will soon be brought under control.

The following article offers some optimism on the horizon: “Something strange is happening in Britain. Covid cases are plummeting instead of soaring.”

Neil Ferguson, an epidemiologist at Imperial College London whose models have shaped government policy in Britain and the United States, said it now appears possible that the pandemic could be in the rearview mirror.

“We’re not completely out of the woods,” he said. “But the equation has fundamentally changed. The effect of vaccines has been huge in reducing the risk of hospitalizations and death. And I’m positive that by late September or October…we will be looking back at most of the pandemic.”

I expect that we are going to be learning that many, perhaps even the majority, of the new COVID cases will come from fully vaccinated people. The Financial Times article on July 23 “Why are fully vaccinated people testing positive for Covid?” (subscription required) provides an excellent explanation with some graphics.

Anthony Masters, a member of the UK’s Royal Statistical Society, said fully vaccinated people were likely to make up a “bigger proportion” of cases as vaccine coverage was extended, particularly in younger groups who face a higher exposure risk because of greater social mixing.

“If you get extremely high coverage across the different ages, it’ss plausible that cases could become [in] majority among fully vaccinated people,” he said. About 55 per cent of the UK population had received both doses by July 21.

In Israel, where nearly 60 per cent of the population are fully vaccinated and coverage is spread more evenly across age cohorts, 52 per cent of about 6,000 people who tested positive in the week to July 21 were fully vaccinated.

If we had a population where everyone was fully vaccinated, then all new cases would be from vaccinated people. That does not mean that the vaccines do not work. Instead, it is just a reflection of the vaccination status of the population. To judge the efficacy of the vaccines, we would need to compare with a population that was completely unvaccinated.

I also expect that in most circumstances where people are mixing, people may need to wear a mask again until the COVID numbers come down. In some respects, this is like using your seatbelts and having airbags in your car: you should rely upon both to reduce injuries and death.

A Wall Street Journal article on July 31 “Rise in Car Crash Deaths Prompts New Seat-Belt Push” (subscription required) stated the following:

More drivers have engaged in risky behaviors, like speeding and driving under the influence, during the Covid-19 pandemic. Compounding the problem, safety officials say, these drivers often leave their seat belts unbuckled, raising the potential for deadly consequences.

More than half of all crash fatalities last year involved unbelted drivers or occupants, according to the National Highway Traffic Safety Administration’ss preliminary data on cases where seat-belt use is known. That is the highest level since 2012.

An estimated 38,680 people died in car crashes last year, 7% more than in 2019, even though total miles driven dropped 13% as many Americans stayed home, federal data show. The number of unbuckled vehicle occupants killed in crashes jumped an estimated 15% from 2019, NHTSA figures show.

As the percentage of our populations who are vaccinated increase and as we take more precautions, such as wearing masks, I am hopeful that our COVID numbers will decrease and we will gain more normalcy in our lives. Furthermore, I do not expect governments to enact harsh restrictive measures.

Last month, I mentioned that I was surprised by the low valuation of oil equities. I am even more surprised now that they have sold off 15 percent or more in the last month. Many oil equities are generating tremendous free cash flow with oil prices above $70 per barrel.

I remain positive on oil and oil equities and on our progress against COVID.

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Oil Update—June 2021

I expect West Texas intermediate oil to range between $67.50 and $77.50 per barrel for July. My June forecast range was five dollars per barrel lower. As we have seen, prices have gone higher than I anticipated.

The world economy continues to grow, and there is growing optimism for the rest of the year. On the other hand, the Delta variant warrants careful monitoring because it has the potential to slow the progress. Because Iran is building its inventories on the expectation that a deal will eventually be reached, investors and traders need to monitor the nuclear negotiations. And with price of oil above $70 per barrel, there may be some investors with large gains who may choose to sell their positions.

John Kemp, a Senior Market Analyst for Reuters, wrote in an article titled “COLUMN-Falling U.S. crude stocks draw hedge fund attention: Kemp – Reuters News” the following:

Investors have not been this bullish since before the coronavirus outbreak spread worldwide in early 2020 and prior to that when the U.S./China trade war intensified in late 2018.

Last week saw small sales of NYMEX and ICE WTI (-6 million barrels), Brent (-3 million) and European gas oil (-8 million) but purchases of U.S. gasoline (+8 million) and U.S. diesel (+6 million).

In WTI, bullish long positions outnumbered bearish shorts by a ratio of more than 11:1, compared with a ratio of 4:1 in Brent (https://tmsnrt.rs/2SDhzLO).

I encourage you to view Kemp’s information referenced by the prior link.

As I write this article, WTI is trading at $73.46, and I believe there is more risk to the upside of my range than to the downside. That said, as prices rise, there will be more pressure on OPEC+ to increase exports.

On Thursday, July 1, there will be several meetings between OPEC+ countries and their technical committees. Investors and traders will gain more clarity in a few days.

With oil prices well above $60 per barrel, I am surprised by the low prices of oil equities. Even with ESG concerns, I would have expected higher prices by now.

In general, I remain bullish on oil and oil equities as the world continues to make progress against COVID-19.

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