stigBy Stig Brodersen


21 March 2016


I’ve always been fascinated by oil. Countries, huge businesses, and even regular people like you and me are extremely dependent on the price of oil. Wars have been fought over the commodity that we use for everything from transportation to all products used in our daily lives.

I’ve always been fascinated by stocks. What I love about stocks is the simple process of calculating an intrinsic value. While that doesn’t mean that you are correct in your estimation – because the quality of your underlying assumptions such as growth and discount determine the quality of your estimation – the  good thing about stock is that (good) companies always generate a given cash flow that you can discount.

However, stocks are not what this blog post is about. I’ve mentioned this to highlight the difference between a commodity like oil and a cash generating asset like a stock. A barrel of oil doesn’t spin off cash you can discount, so how can you find the intrinsic value? When we think about it, oil must have some form of intrinsic value since everyone can agree that it has utility.

This has puzzled me for quite some time. My fascination about oil and stocks is likely also why I’ve started to research oil stocks in the first place. Still, it’s to be noted that it’s hard to estimate the value of oil stocks if you have no idea of the fundamental value of stocks since that is often the primary driver of the expected cash flow.

As you know, I’ve previously said on The Investors Podcast that I’m invested in oil and I felt that the value was way higher than the current price (trading around $40), and as a part of my research I investigated how to play the oil rebound if you were betting on the price of oil rather than individual companies. How did I come up with the conclusion that the current price is significantly lower than the fundamental value? Well, based on the demand and supply in the market, my expectations of the future and the cost structure in the industry, it was very clear to me that a bet on oil at the current price level was an obvious play when I weighted risk and reward. But no, I don’t know how I can put in these criteria with reliable calculations that could show you that the intrinsic value should be say $50, $70, or $90 for that matter.

But, is this possible?

The intrinsic value of oil according to Hotelling’s rule

I’ve praised my network multiple times (that is all of your guys in the community!) and together with Preston, Calin, Hari, and Toby from my mastermind group, you have all been very valuable in enhancing my knowledge about stocks and oil. I feel very fortunate to be surrounded by so many people much smarter than me who I can learn from. This time, I have to give credit to my colleague Professor, Morten Vibe Pedersen, who gave me the inspiration to write this blog post.

Morten’s specialty is forecasting models and I have previously seen his work on the fundamental value of S&P 500 and currencies, which I have been very impressed by (he’s usually right!). So you can imagine my excitement when he told me that he had been working on a model to calculate the intrinsic value of oil.

Okay, enough talk. Here it is:


Intrinsic value of oil

So what are we looking at, you might ask? Good question! If Morten’s model is correct, the intrinsic value of oil is $75.6 at a time where the market price hovers around $40. Okay, let me stop myself right here and provide Morten and all other academics with the disclaimer they rightfully deserve. Once you start including decimal points in the intrinsic value of anything, you are bound to distract yourself. The value of any asset can only be an approximation, so as all sound investors know, we need to have a margin of safety – especially for something as volatile as the price of oil.

Well, that takes me to the next point. We’re around the point where we can argue that oil is trading at one deviation below the intrinsic value. If you haven’t taken a course in Statistics, there is no reason to be confused by the fancy lingo. It’s just the academically way of measuring when the oil or any other asset is within a “normal range”. As a rule of thumb, you might want to consider selling a volatile asset like a stock or a barrel of oil if it’s trading one standard deviation above the intrinsic value ($145), and buy if it’s one standard deviation below ($39).  Obviously assuming that you estimated correct! For now, just think of standard deviation as something that provides you with a margin of safety and tells you about the volatility of the asset.

Another interesting point is to see how long the price of oil can vary from the intrinsic value. It’s not uncommon to have a period of 3-5 years where the fundamentals are out of whack and it can easily go on for longer. A good example is the oil shock in 1973, where the price of oil quadrupled and the next one in 1979, when it  more than doubled the price of oil from an already high level.  In other words, even if you are right in your estimate of the fundamental value of any asset, it can take a long time before your reap the benefits. Investing in oil in that sense is no different than it is for the stock investor.


The intuition behind Hotelling’s rule

As previously stated, no model is better than the assumptions you base it on, so let’s examine that. Morten Vibe Pedersen’s model is based on the mathematical statistician Harold Hotelling’s work originally published in 1931. Hotelling’s rule (not to be confused with Hotelling’s law) is built around the idea that all non-renewable resources have a value, and that value per unit (like a barrel of oil) is increasing over time. Think about it like this: Say there are 3 trillion barrels of oil, which includes both those barrels that are depleted and those that are not. After 1 trillion barrels have been used, the remaining 2 trillion barrels have a higher value and this is partly because the supply is now lower, but also because there has been an opportunity cost by investing in oil. This is similar to the opportunity cost you face when you buy a stock, and can’t buy another stock or a bond. The return of other assets is what you could have made by investing in another asset. Hotelling looks at this the same way and uses treasury rates as his opportunity cost – in this model the 10-year rates are used. The implication is that Hotelling’s intrinsic value grew a lot faster in the early eighties when the interest rate was double digit when compared to the present times where it’s around 2%.

Hotelling also believed that the market for oil in general is efficient  in the long run. But in the short run, it could be all over the place. This is not uncommon to what most people in the value investing community including myself believe. Looking back at the last 150 years, the stock market has, in the long run, been very good at reflecting the value of discounted cash flow of what the companies made in profit. But in the short run, for instance, prior to the great financial crisis in 2008 the stock market overreacted, just as it did in March 2009, when everyone was running for the hills and stocks were cheap.

The intuition behind the efficiency is not that far out. The oil price in July 2008 was $145 (the reason why you don’t see the spike in the graph is because 31 December values are used). In itself, a high oil price implies a variety of things worth discussing. The general demand for oil drops because a lot of the activities (think of a production plant) that were profitable at an oil price of $100 are no longer profitable at $145. Also, alternative energy sources like wind, solar and hydro, are now heavily invested in, and what increases the supply even more are the oil companies that produce at maximum capacity because they want to sell at an expensive price. Bottom line: The oil price drops. The reverse effect can be said for an oil price significantly below the intrinsic value.

The more geeky explanation of the model (which you can perfectly skip) is that it illustrates the relationship between the actual price of oil, and the fundamental price over time. In other words, 1970, which is where the data series starts should not be perceived like an actual starting point like you would when measuring the return S&P500 from 1970 until now. Rather, it’s examining the overall efficient relationship throughout the whole time period between the actual crude oil price and a data series compounded at the 10 year federal rate using a simple exponential ln-function.

Therefore, the underlying premise of the model is that there are no systematic errors when investors determine the price of oil or any other asset in the long run. This is also known as the “Arbitrage Pricing Theory”.  What this theory tells us is that if an asset like oil is underpriced (as I would argue oil currently is) the investor could short sell a portfolio of competing assets like stocks, bonds, real estate, other commodities, and go long in oil with the proceeds. When the price of oil is converging towards its equilibrium (think oil price going from $40 towards $75) the investor would do the opposite. He would sell oil and use the proceeds to buy back the portfolio of the other assets classes that he originally shorted. The net result would be a profit for the investor.

So you might be thinking: “There is a ton of systematic errors in the financial markets, so how can I believe in the Arbitrage Pricing model?” Well, let me provide you with an example of sound stock investing that all value investors apply. You find a cheap stock trading at $50 that you value at $100 and you decide to buy it. As the stock approaches $100, you decide to sell it, pocket the profit, and buy another undervalued asset with the intention to accomplish the same. As a value investor, you contribute to the Arbitrage Pricing Theory by conducting rational valuation of an asset and let time do the rest of the work.  So what can we conclude so far? Hotelling’s rule is valid in “theory” because it’s based on Arbitrage Pricing Theory being correct. Enough with the theory…but, where is the evidence?


How has Hotelling’s rule worked in the past?

So, now the obvious question: How has Hotelling’s rule performed in the past for oil? Well, the academics find that the empirical evidence is “weak”. What that basically means is that there is something to be said about it for different time periods, and it depends on your underlying assumptions. But… we surely can’t conclude that Hotelling’s rule is correct. I was quite disappointed when I realized that. Hey, which investor wouldn’t be, if he found a solid method to calculate the intrinsic value of oil?

So, shouldn’t I stop my blog post right there? And why even write the blog post in the first place when academics have tested the rule and rejected it?


Support of Hotelling’s Rule

Well, for one thing I usually don’t stop my research because the academics reach a given conclusion. They are the same folks who believe that Warren Buffett’s performance is pure luck and compares it to being the best coin flipper in the world.

Just as arguments can be made against Hotelling’s view about the price of oil, counter arguments can be made as well.

For instance, the concept of depleting the entire reserves of oil didn’t have the same focus a century ago as it has today. Another argument is that while there is a wide difference in the opinion about the magnitude of the global oil reserves, the market has arguable better data today than in the late 1800s when the industry grew rapidly and new reserves were quickly discovered. In lockstep with the improved information, it can be argued that the market’s long term’s efficiency improved as well, which means that only more recent data can be used (say 50-80 years) to test the validity of the rule.

So do I believe that the intrinsic value of oil is $75 and that Hotelling’s rule is better than most academics will give him credit for? I haven’t decided yet, but despite the weak historical evidence I like the overall intuition behind the more complex approach of estimating the intrinsic value of an asset that doesn’t spin off cash.

Said in another way:

Do I believe that financial markets in the long run are efficient? Yes I do!

Do I believe that financial markets in the short run are efficient? No way!

Do I believe that the current intrinsic value of oil is $75? I don’t know! But I’m confident that it is closer to $75 than $40 for the same reasons Hotelling lists.


So much for my thoughts on Morten Vibe Pedersen’s work Hotelling’s rule. I’m curious to learn what you think. Join our lively oil discussion with 150+ comments and 23K+ views.




*Dependent on the feedback from The Investor Podcast’s community, Professor Morten Vibe Pedersen and I will consider refining the model