Friday, March 16, 2018

Stream On: An IPO Valuation of Spotify!

In the last few weeks, we have seen two high profile unicorns file for initial public offerings. The first out of the gate was Dropbox, a storage solution for a world where gigabyte files are the rule rather than the exception, with a filing on February 23. Following close after, on February 28, Spotify, positioning itself as the music streaming analog to Netflix, filed its prospectus. With it's larger potential market capitalization and unusual IPO structure, Spotify has attracted more attention than Dropbox, and I would like to focus this post on it.

Spotify: The Back Story
Spotify was founded in 2008 in Sweden, by Daniel Ek and Martin Lorentzon, as a music streaming service. The timing was opportune, since the company caught and contributed to a shift in the music business, as users have moved away from paying for physical (records, CDs) to digital, as evidenced in the graph below:
Source: IFPI
Note that not only has the move towards streaming, in proportional terms, been dramatic, but disruption has come with pain for the music business, with a drop in aggregate revenues from $24 billion in 1999 to about $16 billion in 2016.  In a bright spot, revenues have started rising again in 2016 and 2017, and it is possible that the business will rediscover itself, with a new digital model. Spotify was not the first one in the business, being preceded by both Pandora and Soundcloud, but its success is testimonial to the proposition that the spoils seldom go to the first movers in any business disruption.

The Spotify business model is a simple one. Listeners can subscribe to a free version, with limited customization features (playlists, stations etc.) and online ads. Alternatively, they can subscribe to a premium version of the service, paying a monthly fee, in return for a plethora of customization options, and no ads. The company's standard service cost $9.99/month in the United States in 2018, with a family membership, where up to six family members living at the same address, can share a family service for $14.99/month, while preserving individualized playlists and stations. Prices vary globally, ranging from a high of $16.94 in the UK (for standard service) to much lower prices in Eastern Europe and Latin America. (You can check out the variations in this fascinating link that reports the prices across the world for Spotify, in dollar terms.) Spotify pays for its music content, based upon how often a song is streamed, but the rates vary depending on whether it is on the free or premium service and where in the world, creating some complexity in how it is computed.  To get a sense of where Spotify stands right now and how it got there, I looked the prospectus, with the intent of catching broad trend lines. I came up with the following:

  1. Explosive Growth: Spotify is coming off a growth burst, especially since 2015, in both number of users and revenues, as can be seen in the graph below. Revenues have increased from 1.94 billion Euros to 4.09 billion Euros, reflecting both a growth in subscribers from 91 million to 159 million, and a change in the composition, with premium members climbing from about 31% of total subscribers in 2015 to 45% of subscribers in 2017.
    Source: Spotify Prospectus
  2. Subscription Revenue dominates Ad Revenue: Spotify's focus on improving its premium subscriptions is explained easiest by looking at the breakdown of revenues each year, where subscription revenues have accounted for 90% of revenues each year from 2015 to 2017. The one discordant note is that average revenue per premium subscriber has dropped over the same period 7.06 Euros/month to 5.24 Euros/month, a change that the company ascribes to family memberships, but a problematic trend nevertheless:
    Source: Spotify Prospectus
  3. Content Costs are coming down: While Spotify insists that it is not scaling back payouts to music labels and artists, the company has been able to lower its content costs as a percent of revenues each year from 88.7% of revenues in 2015 to 79.2% of revenues in 2017. In fact, Spotify has conveyed to investors that its intent is to earn gross margins of 30%-35%, implying that it sees content costs dropping to 65%-70% of revenues. There is an inherent tension here between what Spotify has to convince its investors it can do and what it tells the music industry  it is doing and the tension will only intensify, after the company goes public.
    Source: Spotify Prospectus
  4. Other costs are trending up: There are three other buckets of cost at Spotify -R&D, Selling & Marketing and G&A- and these costs are not only growing but eating up larger proportion of revenues. If there are economies of scale, as you would expect in most businesses,  they are not manifesting themselves in the numbers yet. The collective load of these expenses are creating operating losses, and while margins have become less negative, it is primarily through the content cost controls.

    Source: Spotify Prospectus

At this stage of its story, Spotify is a growth company with lots of potential (no irony intended) but lots of rough spots to work out.

The Spotify IPO
I have posted ahead of IPOs for many companies in the last decade, ranging from Facebook to Twitter to Alibaba to Snap, but Spotify's IPO is different for two reasons:

  1. No Banks: In a typical IPO, the issuing company seeks out an investment bank, which not only sets an offering price (backed up by a guarantee) but also creates a syndicate with other banks  to market the IPO, in roadshows and private client pitches. The Spotify IPO will dispense with the bankers and go directly to the market, letting demand and supply set the price on the opening day.
  2. Cashing Out: In most IPOs, the cash that comes in on the offering, from the shares that are bought by the public, is kept in the company, either to retire existing financing that is not advantageous to the firm, or to cover future investment needs. Spotify is aiming to raise about $1 billion from its offering, but none of it will go to company. Instead, existing equity investors in the company will be receiving the cash in return for their holdings.
As a potential investor, I am less concerned about the "no banker" part of the IPO than I am by the "cash out:" part of the transaction: 

  • No bankers, no problem: I think that the banking role in IPOs is overstated, especially for a company as high profile as Spotify. Bankers don't value IPOs; they price them, usually with fairly crude pricing metrics, though they often reverse engineer DCFs to back up their pricing. Their guarantee on the offering price is significantly diluted in value by the fact that they set offering prices 10% to 15% below what they think the market will bear, and their marketing efforts are more useful in gauging demand than in selling the securities. From an investor perspective, there is little that I learn from road shows that I could not have learned from reading the prospectus, and there is almost as much disinformation as information meted out as part of the marketing.
  • Control or Growth: I find it odd that a company like Spotify, growing at high rates and losing money while doing so, would turn away a billion in cash that could be used to cover its growth needs for the near future. The cashing out of existing owners sends two negative signals.  The first is that they (equity investors who cash out) do not feel that staying on as investors in the company, as a publicly traded entity, is worth it. Since they have access to data that I don't, I would like to know what they see in the company's future. The second is that the structure of the share offering, with voting and non-voting shares, indicates a consolidation of control with the founders, and the offering may provide an opportunity to get rid of dissenting voices.

My Spotify Valuation
In keeping with my view that you need a story to provide a framework for you valuation inputs, and especially so for young companies, I constructed a story for Spotify with the following elements:

  1. Continued (but Slower) Revenue Growth: Spotify's success in scaling up over the last three years also sets the stage for a slowing down of growth in the future, with competition for Apple Music (backed by Apple's deep pockets) contributing to the trend. A combination of increases in subscriber numbers and a leveling off and even a mild increase in subscription per member will translate into a revenue growth of 25% a year for the next five years, scaling down to much lower growth in the years after. Since I am projecting revenues for Spotify in 10 years that are larger than the reported global music business revenues today, implicit in this story is the assumption that the music business overall has turned the corner and that aggregate revenues will not only continue to post increases like they did in 2016 and 2017, but that streaming will be the savior of the music business, allowing it expand its reach into emerging markets and pick up more paying customers. 
  2. With Reduced Content Costs: Spotify's entire value proposition rests on improved operating margins and a large portion of the improvement has to come from continuing to reduce content costs as a percent of revenues. Since Spotify pays for its content based upon song streams, those savings have to come from either paying less per stream (which is going to and should create push back from labels and artists) or finding ways to create economies of scale on this cost component. In it's defense, Spotify can point to its track record from 2015 to 2017 in reducing content costs. I assume that they can reduce content costs to 70% of revenues, while finding a way to keep artists and labels happy. That is not going to be an easy balance to maintain, especially with the top artists, as evidenced by Taylor Swift's and Jay-Z's decisions to pull their music from Spotify. (I have been told that they have reversed their decisions, but this fight is ongoing.)
  3. And Economies of Scale on Other Costs: Of the three other costs, the marketing expenses are the ones most likely to scale down as growth declines, but for Spotify to deliver solid operating margins, it also has to bring R&D costs and G&A costs under control. I may be over optimistic on this front, but here is what my projected values yield for my target operating margin (ten years from now):
  4. With Limited Capital Investments: Spotify's business model is built for scaling, with little need for capital reinvestment, except for R&D. Consequently, I assume that small capital investments can generate large revenues, using a sales to capital ratio of 4.00 (putting it at the 90th percentile of global companies) to estimate reinvestment.
  5. Manageable Operating Risk but Significant Failure Risk: Spotify's subscription based model and low turnover rate among subscribers does lend some stability to revenues, though adding more subscribers and going for growth is a riskier proposition. Overall, allowing for their business mix (90% entertainment, 10% advertising) and their global mix of revenues yields a  cost of capital of 9.24%, at the 80th percentile of global companies; the firm is planning to convert much of its debt into equity at the time of the IPO, giving it a equity dominated capital structure. However, the company is still young, losing money and faces deep pocketed competition, suggesting that failure is a very real possibility. I assume a 20% chance of failure, with failure translating into selling the company to the highest bidder at half of its going concern value.
  6. Loose Ends: To estimate equity value in common shares, I add the cash balance of the company of 1.5 billion Euros, ignore the proceeds from the IPO because of the cash-out structure and net out the value of 20.82 million options/warrants outstanding, with an average strike price of 42.56 Euros per share. Dividing the equity value by 177.17 million shares (including restricted shares) yields a value per share of 88.26 Euros per share or $108.97. The shares that you will be buying will be non-voting, implying a discount on this number, though how much you discount it will depend on how much you like and trust the company's founders.
The entire picture, with the story embedded in it, is shown below. You can also download the spreadsheet here. (The base year numbers in the prospectus were all in Euros, but all of the valuation inputs (growth, cost of capital) are in US dollars, making it a US dollar valuation. In hindsight, I should have restated the base year numbers in US dollars. While it would not have changed the valuation, it would have reduced currency confusion. Alternatively, I could have valued the company entirely in Euros, with lower growth rates and costs of capital, and arrived at Euro valuation that yield roughly similar results):
Download spreadsheet
It goes without saying, but I will say it anyway, that I made lots of assumptions to get to my value and that you may (and should) disagree with me or some or even all of these assumptions. You are welcome to download the spreadsheet that contains my valuation of Spotify and make it your own.

Bottom Line
There are three elements missing in this post. First, I have argued in my prior IPO posts that what happens after initial public offerings is more of a pricing game than a value game. To those of you who want to play that game, I don't think that this post is going to be very helpful. In my next post, I will look at how best to price Spotify, why you will hear pessimists about the company talk a lot about Pandora and optimists about Netflix. Second, there is the argument that top down valuations, like the one in this post, are ill equipped to value user or subscriber based companies. I will also use the user-based model that I introduced last year to value an Uber rider and an Amazon Prime member to value a Spotify subscriber. Finally, there is the lurking question of what Spotify is learning about its subscriber music tastes and how that data can be used to not only modify its offerings but perhaps create content that is more closely tailored to these tastes. That too has to wait for the next post.


Data Links
  1. Spotify Prospectus
  2. Spotify Valuation (Mine)

Monday, March 5, 2018

Damodaran Online: There is an App for that!

My posts over the last two months have been heavy, dealing first with my data update from January 2018, and with the market and its volatility in the last few weeks. I felt like taking a break and talking about something lighter and more personal, and giving you an update on my teaching, writing and data plans for this year, with news about an app for the iPhone or iPad that you might (or might not) find useful. I won't fault you if you are not in the least bit interested in what I am doing, and if so, please do skip this post, since it will bore you!

Teaching Update
As some of you may know, I have taught at the Stern School of Business at NYU since 1986, teaching two classes, a Corporate Finance class every spring and a Valuation class every fall and spring. If you have been reading this blog for a while, you also know that I invite the rest of the world to join me in these classes, through a multitude of platforms (iTunes U, Online, YouTube). If you are wondering why you have not received an invite to the classes this academic year, the answer is simple.

I am on sabbatical this academic year, living in California, and will not be teaching at Stern at least through September 2018.  I am enjoying keeping what I call beach bum hours (8.30 am-12.30 pm), but I have to confess that I miss teaching, and my weeks feel unstructured without my Monday/Wednesday classes, but I love teaching too much to take a complete break from it. I continue to teach my compressed valuation classes, trying to fit in everything in my regular classes into one or two days, with stints coming up in Amsterdam (March 7), London (March 8-10), Mumbai (April 19,20), Manila (May 15-16), Bangkok (May 17-18), Warsaw and Prague (June 2018) just in the next few months.

I am also planning on redoing the investments philosophies class that I have only online, but which is showing its age, in the next three months and adding to the in-practice videos that I supplement my valuation and corporate finance classes. 

Research Writing Update
After my most recent post on interest rates and stock prices, I received one response that made me laugh and here is what it said: “Bro, Please stop. get your head out of academia and into reality’. I assume, since I was not this person’s brother, that the “Bro” was an attempt to establish street cred (though I am not sure that it works on this audience), but it was the “academia” part that I found humorous. If I am an academic, I am one in awfully bad standing, since I have not submitted a paper for publication in close to two decades and spend little time at academic conferences.  That said, I love to write and I am continuing to do so on my sabbatical, on several fronts.
  • First, there are my blog posts, which I know are way too long and not very frequent, but I try (though I sometimes fail) to not spout off about things I do not understand or know much about. 
  • Second, I spent the last few months of last year finishing the third edition of one my books, The Dark Side of Valuation, the first edition of which was born at the peak of the dot com boom, about valuing difficult-to-value companies from start-ups to banks. The book is in its final printing stages and should be available in bookstores shortly (Amazon link). 
  • Third, I am turning my attention to what I hope will be my next project, which I hope will become a book, on the difference between pricing an asset and valuing it, a theme that I have mined for multiple posts over the last few years. Fourth, In a couple of weeks, I hope to post the updated installment of my Equity Risk Premium paper, which I first wrote and posted in 2008 (right after the crisis) and have revisited every March since. (Link to 2017 version). Later this summer, I will update my Country Risk Premium paper, focusing more closely just on country risk. (Link to 2017 version
  • Finally, during the course of the next few months, I will also be taking the work that I have done on valuing users and converting into a paper. 
I will keep you updated as each project is complete.

Data & Tools Update
I maintain a number of data sets on corporate finance and valuation that I update on an annual basis at the start of the year. I wrote a series of posts on what I learned looking at the data this year, in January, and you can read all ten posts, if you are so inclined. 
While I will not update much of this data during the course of the year, I will continue to post my estimates for the equity risk premium for the S&P 500 at the start of every month, continuing a series that started in September 2008. 

The tools that I offer are three fold.

  • First, I have excel spreadsheets for corporate finance and valuatoion, and they are not polished, lacking formatting finesse and macro add-ons, but I view them as raw material that you can mold to your liking. 
  •  Second, my YouTube videos are classified by playlists into my class videos, tool videos and blog post videos. 
  • Finally, I do have an app for the iPhone and iPad called uValue, that I co-developed with Anant Sundaram, professor at Dartmouth, that does intrinsic valuation. Give it a shot!
You welcome to use these tools, but please recognize that this is all they are, and it is your insight and common sense that will make them shine.

Interface Update
As the material that I have grows, I have struggled with how best to organize it and present it. My website has much of the material but you need to be on a computer, with an internet connection, to access much of it, and finding what you want can be a challenge. I am glad that there are some people who find the material useful and am humbled by their gratitude and their offers to help. To illustrate, a few months ago, I received an email from Taha Maddam, who had used the site, and he offered to create an app that would contain the material. I thanked him, but I pointed out that since the site was not commercial, I could not spend much to make the conversion, but he graciously offered to do it for nothing. Knowing how much work was involved, I did not expect him to follow through, especially since he works full time in Shanghai and has a young family.

Taha surprised me just over a week ago, when he said the app was ready and that I could take it for a spin.  I did and I was dazzled, since it contained all the information in my website, on my blog and on YouTube, in one location. If you have an Apple device (iPhone or iPad), you can download the app either from the app store (type in "Damodaran" in the search box, and it should pop up) or by going to the launching page that Taha has created for the app. If you like our app (while the material is mine, this app is Taha’s doing), please pass on the word and compliment Taha for a job well done. If you are an Android user, I am truly sorry that the app does not work on your devices yet, but I will have to wait on the kindness of strangers, for that to happen. In the meantime, if you can think of what we can add on to the app to make it more useful, please let us know. 

Friday, March 2, 2018

Interest Rates and Stock Prices: It's Complicated!

Jerome Powell, the new Fed Chair, was on Capitol Hill on February 27, and his testimony was, for the most part, predictable and uncontroversial. He told Congress that he believed that the economy had strengthened over the course of the last year and that the Fed would continue on its path of "raising rates". Analysts have spent the next few days reading the tea leaves of his testimony, to decide whether this would translate into three or four rate hikes and what this would mean for stocks. In fact, the blame for the drop in stocks over the last four trading days has been placed primarily on the Fed bogeyman, with protectionism providing an assist on the last two days. While there may be an element of truth to this, I am skeptical about any Fed-based arguments for market increases and decreases, because I disagree fundamentally with many about how much power central banks have to set interest rates, and how those interest rates affect value.

1. The Fed's power to set interest rates is limited
I have repeatedly pushed back against the notion that the Fed or any central bank somehow sets market interest rates, since it really does not have the power to do so. The only rate that the Fed sets  directly is the Fed funds rate, and while it is true that the Fed's actions on that rate send signals to markets, those signals are fuzzy and do not always have predictable consequences. In fact, it is worth noting that the Fed has been hiking the Fed Funds rate since December 2016, when Janet Yellen's Fed initiated this process, raising the Fed Funds rate by 0.25%. In the months since, the effects of the Fed Fund rate changes on long term rates is debatable, and while short term rate have gone up, it is not clear whether the Fed Funds rate is driving short term rates or whether market rates are driving the Fed.

It is true that post-2008, the Fed has been much more aggressive in buying bonds in financial markets in its quantitative easing efforts to keep rates low. While that was  started as a response to the financial crisis of 2008, it continued for much of the last decade and clearly has had an impact on interest rates. To those who would argue that it was the Fed, through its Fed Funds rate and quantitative easing policies that kept long term rates low from 2008-2017, I would beg to differ, since there are two far stronger fundamental factors at play - low or no inflation and anemic real economic growth. In the graph below, I have the treasury bond rate compared to the sum of inflation and real growth each year, with the difference being attributed to the Fed effect:
Download spreadsheet with raw data
You have seen me use this graph before, but my point is a simple one. The Fed is less rate-setter, when it comes to market interest rates, than rate-influencer, with the influence depending upon its credibility. While rates were low in the 2009-2017 time period, and the Fed did play a role (the Fed effect lowered rates by 0.77%), the primary reasons for low rates were fundamental. It is for that reason that I described the Fed Chair as the Wizard of Oz, drawing his or her power from the perception that he or she has power, rather than actual power. That said, the Fed effect at the start of 2018, as I noted in a post at the beginning of the year, is larger than it has been at any time in the last decade, perhaps setting the stage for the tumult in stock and bond markets in the last few weeks. 

To examine more closely the relationship between moves in the Fed Funds rate and treasury rates, I collected monthly data on the Fed Funds rate, the 3-month US treasury bill rate and the US 10-year treasury bond rate every month from January 1962 to February 2018. The raw data is at the link below, but I regressed the changes in both short term and long term treasuries against changes in the Fed funds rate in the same month:
Looking at these regressions, here are some interesting conclusions that emerge:
  1. Short term T.Bill rates and the Fed Funds rate move together strongly: The result backs up the intuition that the Fed Funds rate and the short term treasury rate are connected strongly, with an R-squared of 56.5%; a 1% increase in the Fed Funds rate is accompanied by a 0.62% increase in the T.Bill rate, in the same month. Note, though, that this regression, by itself, tells you nothing about the direction of the effect, i.e., whether higher Fed funds rates lead to higher short term treasury rates or whether higher rates in the short term treasury bill market lead the Fed to push up the Fed Funds rate. 
  2. T.Bond rates move with the Fed Funds rate, but more weakly: The link between the Fed Funds rate and the 10-year treasury bond rate is mush weaker, with an R-squared of 6.7%; a 1% increase in the Fed Funds rate is accompanied by a 0.19% increase in the 10-year treasury bond rate. 
  3. T. Bill rates lead, Fed Funds rates lag: Regressing changes in Fed funds rates against changes in T.Bill rates in the following period, and then reversing direction and regressing changes in T.Bill rates against changes in the Fed Funds rate in the following period, provide clues to the direction of the relationship. At least over this time period, and using monthly changes, it is changes in T.Bill rates that lead changes in Fed Funds rates more strongly, with an R squared of 23.7%, as opposed to an R-squared of 9% for the alternate hypothesis. With treasury bond rates, there is no lagged effect of Fed funds rate changes (R squared of zero), while changes in T.Bond rates do predict changes in the Fed Funds rate in the subsequent period. The Fed is more a follower of markets, than a leader. 
The bottom line is that if you are trying to get a measure of how much treasury bond rates will change over the next year or two, you will be better served focusing more on changes in economic fundamentals and less on Jerome Powell and the Fed.

2. The relationship between interest rates and stock market value is complicated
When interest rates go up, stock prices should go down, right? Though you may believe or have been told that the answer is obvious, that higher interest rates are bad for stock prices, the answer is not straight forward. To understand why people are drawn to the notion that higher rates are bad for value, all you need to do is go back to the drivers of stock market value:

As you can see in this picture, holding all else constant, and raising long term interest rates, will increase the discount rate (cost of equity and capital), and reduce value. That assessment, though, is built on the presumption that the forces that push up interest rates have no effect on the other inputs into value - the equity risk premium, earnings growth and cash flows, a dangerous delusion, since these variables are all connected together to a macro economy.
Note that almost any macro economic change, whether it be a surge in inflation, an increase in real growth or a global crisis (political or economic) affects earnings growth, T.Bond rates and the equity risk premiums, making the impact on value indeterminate, until you have worked through the net effect. To illustrate the interconnections between earnings growth rates, equity risk premiums and macroeconomic fundamentals, I looked at data on all of the variables going back to 1961:
The co-movement in the variables and their sensitivity to macro economic fundamentals is captured in the correlation table. Higher inflation, over this period, is accompanied by higher earnings growth but also increases equity risk premiums and suppresses real growth, making its net effect often more negative than positive. Higher real economic growth, on the other hand, by pushing up earnings growth rate and lowering equity risk premiums, has a much more positive effect on value.

3. Value has to be built around a consistent narrative
In my post from February 10, right after the last market meltdown, I offered an intrinsic valuation model for the S&P 500, with a suggestion that you fill in your inputs and come up with your own estimate of value. Some of you did take me up on my offer, came up with inputs, and entered them into a shared Google spreadsheet and, in your collective wisdom, the market was overvalued by about 3.34% in mid-February. While making assumptions about risk premiums, earnings growth and the treasury bond rate, I should have emphasized the importance of narrative, i.e., the macro and market story that lay behind your numbers, since without it, you can make assumptions that are internally inconsistent. To illustrate, here are two inconsistent story lines that I have seen in the last few weeks, from opposite sides of the spectrum (bearish and bullish).
  • In the bearish version, which I call the Interest Rate Apocalypse, all of the inputs (earnings growth for the next five years and beyond, equity risk premiums) into value are held constant, while raising the treasury bond rate to 4% or 4.5%. Not surprisingly, the effect on value is calamitous, with the value dropping about 20%. While that may alarm you, it is unclear how the analysts who tell this story explain why the forces that push interest rates upwards have no effect on earnings growth, in the next 5 years or beyond, oron  equity risk premiums.
  • In the bullish version, which I will term the Real Growth Fantasy, all of the inputs into value are left untouched, while higher growth in the US economy causes earnings growth rates to pop up. The effect again is unsurprising, with value increasing proportionately. 
While neither of these narratives is fully worked through, there are three separate narratives about the market that are all internally consistent, that can lead to very different judgments on value.
  • More of the same: In this narrative, you can argue that, as has been so often the case in the last decade, the breakout in the US economy will be short lived and that we will revert back the low growth, low inflation environment that developed economies have been mired in since 2008. In this story, the treasury bond rate will stay low (2.5%), earnings growth will revert back to the low levels of the last decade (3.03%) after the one-time boost from lower taxes fades, and equity risk premiums will stay at post-2008 levels (5.5%). The index value that you obtain is about 2250, about 16.4% below March 2nd levels.
    Download spreadsheet
  • The Return of Inflation: In this story line, inflation returns, though how the story plays out will depend upon how much inflation you foresee. That higher inflation rate will translate into higher earnings growth, though the effect will vary across companies, depending upon their pricing power, but it will also cause T. Bond rates to rise. If the inflation rate in the story is a high one (3% or higher), the equity risk premium may also rise, if history is any guide. With an inflation rate of 3% and an equity risk premium of 6%, the index value that you obtain is about 2133, about 20.7% below March 2nd levels.
    Download spreadsheet
  • The Growth Engine Revs Up: In this telling, it is real growth in the US economy that surges, creating tailwinds for growth in the rest of the world. That higher real growth rate, while pushing up earnings growth for US companies (to 8% for the near term), will also increase treasury bond rates (to 3.5%), as in the inflation story, but unlike it, equity risk premiums will drift back to pre-2008 levels (closer to 4.5%). The index value that you obtain is about 3031, about 12.7% above March 2nd levels.
    Download spreadsheet
  • A Melded Version: I believe in a melded version of these stories, where inflation returns (but stays around 2%) and real growth in the economy increases, but only moderately. That will translate into higher treasury bond rates (my guess would be 3.5%), with a proportionate increase in earnings growth (at least in steady state) and an equity risk premium of 5%, splitting the difference between pre-crisis and post-crisis periods. The index value that I obtain, with these assumptions, is about 2610, about 3.1% below March 2nd levels.
Download spreadsheet
You can see, even from this limited list of scenarios, that to assess how stock prices will move, as interest rates change, you have to also make a judgment on why interest rates are moving. An inflation-driven increase in interest rates is net negative for stocks, but a real-growth driven increase in interest rates is a net positive. In fact, the scenario where interest rates go down sees a much bigger drop in value than two of three scenarios, where interest rates rise. 

The Bottom Line
When macro economic fundamentals change, markets take time to adjust, translating into market volatility. During these adjustment periods, you will hear a great deal of market punditry and much of it will be half baked, with the advisor or analyst focusing on one piece of the valuation puzzle and holding all else constant. Thus, you will read predictions about how much the market will drop if treasury bond rates rise to 4.5% or how much it will rise if earnings growth is 10%. I hope that this post has given you tools that you can use to fill in the rest of the story, since it is possible that stocks could actually go up, even if rates go up to 4.5%, if that rate rise is precipitated by a strong economy, and that stocks could be hurt with 10% earnings growth, if that growth comes mostly from high inflation. I also hope that, after you have listened to the narratives offered by others, for what markets will or will not do, that you start developing your own narrative for the market, as the basis for your investment decisions. You've seen my narrative, but I will leave the feedback loop open, as fresh data on inflation and growth comes in, and I plan to revisit my narrative, tweaking, adjusting or even abandoning it, if the data leads me to. 

YouTube Video

Data Links
  1. T.Bond Rates, Inflation and Real GDP Growth - 1954-2017
  2. Fed Funds Rate and Treasury Rates - 1962-2017
  3. T.Bond Rates, Earnings Growth Rates and ERP - 1961- 2017
Spreadsheet Links
  1. Intrinsic Valuation Spreadsheet for S&P 500
  2. More of the Same: Spreadsheet
  3. The Return of Inflation: Spreadsheet
  4. The Growth Engine Revs Up: Spreadsheet
  5. The Melded Version: Spreadsheet
Blog Post Links

Saturday, February 10, 2018

Testing Times: Market Turmoil and Investment Serenity

The last week has been a roller coaster ride, though more down than up, and investors have done what they always do during market crises. The fear factor rises, some investors sell and head for the safer pastures, some are paralyzed not knowing what to do, and some double down as contrarians, buying into the sell off. In the last week, I found myself drawn to each of three camps, often at different points in the same day, as the market went through wild mood swings. These are my most vulnerable moments as an investor, since good sense is replaced by "animal spirits", and I feel the urge to abandon everything I know about investing, and go with my gut, never a good idea. I know that I have to step back from the action, regain perspective and return to what works for me in markets, and it is for that reason that I find myself going through the same sequence, each time I face a market crisis.

Step 1: Assess the damage and regain perspective
The first casualty in a crisis is perspective, as drawn into the news of the day, we tend to lose any sense of proportion. The last week has been an awful week for stocks, with many major indices down by 10% since last Thursday. If your initial investment in stocks was on February 1, 2018, I feel for you, because the pain has no salve, but most of us have had money in stocks for a lot longer than a week. In the table below, I look at the change in the S&P 500 last week and then compare it to the changes since the start of the year (which was less than 6 weeks ago) to a year ago and to ten years ago.

S&P 500 on date
S&P 500 on 2/8/18
% Change
I know that this is small consolation, but if you have been invested in stocks since the start of the year, your portfolio is down, but by less than 3.5%. If you have been invested a year, you are still ahead by 13.25%, even after last week, and if you've been in stocks, since February 2008, you've not only lived through an even bigger market crisis (with the S&P 500 down 38% between September 2008 and March 2009), but you have seen your portfolio climb 90.48% over the entire period, and that does not even include dividends. That is why when confronted by perpetual bears, with their "I told you so" warnings, I try to remember that most of them have been bearish since time immemorial.

Returning the focus to the last week, let's first look across sectors to see which ones were punished the most and which ones endured. Using the S&P classification for sectors, here is how the sectors performed between February 2, 2018 and February 9, 2018;
Not surprisingly, every sector had a down week, though energy stocks did worse than the rest of the market, with an oil price drop adding to the pain.  Continuing to look at equities, let's now look geographically at returns in different markets over the last week.
While the S&P 500 had a particularly bad week, the rest of the world felt the pain, with only one index (Colombo, Sri Lanka) on the WSJ international index list showing positive returns for the week. In fact, Asia presents a dichotomy, with the larger markets (China, Japan) among the worst hit and the smaller markets in South Asia (Thailand, Indonesia, Malaysia and Philippines) showing up on the least affected list. 

While equities have felt the bulk of the pain, it is interest rates that have been labeled as the source of this market meltdown, and the graph below captures the change in treasury rates and corporate bonds in different ratings classes (AAA, BBB and Junk) over the last week and the last year:
The treasury bond rate rose slightly over the week, at odds with what you usually see in big stock market sell offs, when the flight to safety usually pushes rates down. The increases in default spreads, reflected in the jumps in interest rates increasing with lower ratings, is consistent with a story of a increased risk aversion. Here again, taking a look across a longer time period does provide additional information, with treasury rates at significantly higher levels than a year ago, with a flattening of the yield curve. In summary, this has been an awful week for stocks, across sectors and geographies, and only a mildly bad week for bonds. Looking over the last year, it is bonds that have suffered a bad year, while stocks have done well. That said, the rates that we see on treasuries today are more in keeping with a healthy, growing economy than the rates we saw a year ago.

Step 2: Read the tea leaves
It is natural that when faced with large market moves, we look for logical and rational explanations. It is in keeping then that the last week has been full of analysis of the causes and consequences of this market correction. As I see it, there are three possible explanations for any market meltdown over a short period, like this one:
Market Meltdowns: Reasons, Symptoms and Consequences
Market Consequences
Panic Attack
Sharp movements in stock prices for no discernible reasons, with surge in fear indices.
Market drops sharply, but quickly recovers back most or all of its losses as panic subsides
Event or news that causes expected cash flows, growth or perceived risk in equities to change significantly.
Market drops sharply and stays down, with price moves tied to the fundamental(s) in focus.
Repricing of Risk
Event or news that leads to repricing of risk (in the form of equity risk premiums or default spreads).
As price of risk is reassessed upwards, market drops until the price of risk finds its new equilibrium.
The question in any meltdown is which explanation dominates, since stock market crisis has elements of all three. As I look at what's happened over the last week, I would argue that it was triggered by a fundamental (interest rates rising) leading to a repricing of risk (equity risk premiums going up) and to momentum & fear driven selling. 
  1. The Fundamentals Trigger: This avalanche of selling was started last Friday (February 1, 2018) by a US unemployment report that contained mostly good news, with 200,000 new jobs created, a continuation of a long string of positive jobs reports. Included in the report, though, was a finding that wages increased 2.9% for US workers, at odds with the mostly flat wage growth over the last decade. That higher wage growth has both positive and negative connotations for stock fundamentals, providing a basis for strong earnings growth at US companies that is built on more than tax cuts, while also sowing the seeds for higher inflation and interest rates, which will make that future growth less valuable.  
  2. The Repricing of Equity Risk: That expectation of higher interest rates and inflation seems to have caused equity investors to reprice risk by charging higher equity risk premiums, which can be chronicled in a forward-looking estimate of an implied ERP. I last updated that number on January 31, 2018,  and I have estimated that premium, by day, over the five trading days between February 1 and February 8, 2018. There is little change in the growth rates and base cash flows, as you go from day to day, partly because neither is updated as frequently as interest rates and stock prices, but holding those numbers, the estimated equity risk premium has increased over the last week from 4.78% at the start of trading on February 1, 2018 to 5.22% at the close of trading on February 8, 2018. 
  3. Implied ERP, by Day: January 31, 2018 (Close) to February 8, 2018 (Close)
    Date (Close)
    S&P 500
    T.Bond Rate
    Implied ERP
    Link to spreadsheet
  4. The Panic Response: Most market players don't buy or sell stocks on fundamentals or actively think about the price of equity risk. Instead, some of them trade, trying to take advantage of shifts in market mood and momentum, and for those traders, the momentum shift in markets is the only reason that they need, to go from being stock buyers to sellers. Others have to sell because their financial positions are imperiled, either because they borrowed money to buy stocks or because they fear irreparable damage to their retirement or savings portfolios. The rise in the volatility indices are a clear indicator of this panic response, with the VIX almost tripling in the course of the week. Just in case you feel the urge to blame millennials, with robo-advisors, for the panic selling, they seem to be staying on the side lines for the most part, and it is the usual culprits,  "professional" money managers, that are most panicked of all.
At this point, you are probably confused about where to go next. If you are trying to make that judgment, you have to find answers to three questions:
  1. Where are interest rates headed? There has been a disconnect between the equity and the bond market, since the 2016 US presidential election, with the equity markets consistently pricing in more optimistic forecasts for the US economy, than the bond markets. Stocks prices rose on the expectation that tax cuts and more robust economic growth, but bond markets were more subdued with rates continuing to stay at the 2.25%-2.5% range that we have seen for much of the last decade. As I noted in my post at the start of this year on equity markets, the gap between the US 10-year T.Bond rate and an intrinsic measure of that rate, computed by adding inflation to real GDP growth, has widened to it's highest level in the last decade. The advent of the new year seems to have caused the bond market to notice this gap, and rates have risen since. If you are optimistic about the US economy and wary about inflation, there is more room for rates to rise, with or without the Fed's active intervention.
  2. Is the ERP high enough? Is the repricing of equity risk over? The answer depends upon whether you believe the numbers that underlie my estimates, and if you do, whether you think 5.22% is a sufficient premium for investing in equities. The only way to address that question is to examine it in the context of history, which is what I have done in the picture below:
    Download historical ERP data
    With all the caveats about the numbers that underlie this graph in place, note that the premium is now solidly in the middle of the distribution. There is always the possibility that the earnings growth estimates that back it up are wrong, but if they are, the interest rate rise that scares markets will also be reversed.
  3. When will the panic end? I don't know the answer to the question but I do know that it rests less on economics and more on psychology. There will be a moment, perhaps early next week or in two weeks or in two months, where the fever will pass and the momentum will shift. If you are a trader, you can get rich playing this game, if you play it well, or poor in a hurry, if you play it badly. I choose not to play it all.
Is there a way that we can bring this all together into a judgment call in the market. I think so and I will use the same framework that I used for my implied equity risk premium to make my assessment. You will need three numbers, an expected growth rate in earnings for the S&P 500, you estimate of where the 10-year treasury bond rate will end up and what you think is a fair equity risk premium for the S&P 500. For instance, if you accept the analyst forecasted growth in earnings of 7.26% for the next five years as a reasonable estimate, that the the T.Bond rate will settle in at about 3.0% and that 5.0% is a fair value for the equity risk premium, your estimate of value for the S&P 500 is below:
Download spreadsheet
With these estimates, you should be okay with how the market is valuing equities at the close of trading February 8, 2018; it is slightly under valued at 3.90%. To provide a contrast, if you feel that analysts are over estimating the impact of the tax cuts and that the historical earnings growth rate over the last decade (about 3.03%) is a more appropriate forecast for future growth, holding the risk free rate and ERP at 3% and 5% respectively, the value you will get for the index is 2233, about 16% below the index level of February 8, 2018. If you want put in your own estimates of earnings growth, T.Bond rates and equity risk premiums, please download this spreadsheet. In fact, if you are inclined to share your estimates with a group, I have created a shared google spreadsheet for the S&P 500. Let's see what we can get as a crowd valuation.

Step 3: Review your investment philosophy
I firmly believe that to be a successful investor, you need a core investment philosophy, a set of beliefs of not just how markets work but who you are as a person, and you need to stay true to that philosophy. It is the one common ingredient that you see across successful investors, whether they succeed as pure traders, growth investors or value investors. The best way that I can think of presenting the different choices you have on investment philosophies is by using my value/price contrast:
To the question of which of these is the best philosophy, my answer is that there while there is one philosophy that is best for you, there is no one philosophy that is best for all investors. The key to finding that "best" philosophy is to find what makes you tick, as an individual and an investor, not what makes Warren Buffett successful.

I see myself as an investor, not a trader, and that given my tool kit and personality, what works for me is to be a investor grounded in value, though my use of a more expansive definition of value than old-time value investors, allows me to buy both growth stocks and value stocks. I am not a market timer for two reasons.

  • First, the overall market has too many variables feeding into it that I do not control and cannot forecast, making my valuations inherently too noisy to be useful. 
  • Second, I see little that I bring to the overall market in terms of tools or information that will give me an edge over others.  
The truest test of whether you have a solid investment philosophy is a week like the last one, where you will be tempted to or panicked into abandoning everything that you believe about markets. I  would lying if I said that I have not been tempted in the last week to time markets, either because of fear (driving me to sell) or hubris (where I want to play market contrarian), but so far, I have been able to hold out.

Step 4: Act consistently
During every market crisis, you will be tempted to look and ask that ever present question of "What if?", where you think about all of the money you could have saved, if only you had sold last Thursday. Not only is this pointless, unless you have mastered time travel, but it can be damaging to your future returns, as your regrets about past actions taken and not taken play out in new actions that you take.  My suggestion is that you return to your core investment philosophy and start to think about the actions that you can take on Monday, when the market opens, that would be consistent with that philosophy. I am taking my own suggestion to heart and have started revisiting the list of companies that I would love to invest in (like Amazon, Netflix and Tesla), but have been priced out of my reach, in the hope that the correction will put some of them into play. More painfully, I have been revaluing every single company in my existing portfolio, with the intent of shedding those that are now over valued, even if they have done well for me. If nothing else, this will keep me busy and perhaps stop me from being caught up in the market frenzy!

YouTube Video


  1. S&P 500 Intrinsic Value Spreadsheet
  2. Google Shared Spreadsheet of Intrinsic Valuations

Monday, February 5, 2018

January 2018 Data Update 10: The Price is Right!

In my first nine posts on my data update for 2018, I focused on the costs that companies face in raising equity and debt, and their investment, financing and dividend decisions. In assessing those decisions, though, I looked at their actions through the lens of value creation, arguing that investing in projects that earn less than their cost of capital is not a good use of shareholder capital. While this may seem like a reasonable conclusion, it is built on the implicit assumption that financial markets reward value creation and punish value destruction. As any market observer will tell you, markets have minds of their own, sometimes rewarding companies for bad behavior and punishing companies that take the right actions. In this post, I look at market pricing around the world, and point to potential inconsistencies with the fundamentals.

Value vs Price
In multiple posts on this blog, I have argued that we need to stop using the words, value and price, interchangeably, that they not only can be very different for the same asset, at any point in time, but that they are driven by different forces, require different mindsets to understand, and give rise to different investment philosophies. The picture below summarizes the key distinctions:

Understanding the difference between value and price, at least for me, is freeing, because it not only makes me aware of the assumptions that I, as an investor who believes in value and convergence, am making, but also makes me respect and recognize those who might have a different perspective. The bottom line, though, is that the pricing process can sometimes reward firms that take actions that no tonly have no effect on value, but may actually destroy value, and punish firms that are following financial first principles. Even though I believe that value ultimately prevails, it behooves to me to try to understand how the market is pricing stocks, since it will help me be a better investor.

The Pricing Process
I will begin with what sounds like a over-the-top assertion. Much of what we see foisted on us as valuation, including those that you see backing up IPOs, acquisitions or big investment decisions, are really pricing models, masquerading as valuations. In many cases, bankers and analysts use the front of estimating cash flows for a discounted cashflow valuation, while slipping in a multiple to estimate the biggest cash flow (the terminal value) in what I call Trojan Horse DCFs. I am not surprised that pricing is the name of the game in banks and equity research, but I am puzzled at why so much time is wasted on the DCF misdirection play. There are four steps to pricing an asset or company well, and done well, there is no reason to be ashamed of a pricing.

1. Similar, Traded Assets
To price an asset, you have to find "similar" assets that are traded in the market. Note the quote marks around similar, because with publicly traded stocks, you will be required to make judgment calls on what you view as similar. The conventional practice in pricing seems to be country and sector focused, where an Indian food processing company is compared to other food processing companies in India, on the implicit assumption that these are the most comparable companies. That practice, though, can not only lead to very small samples in some countries, but also can yield companies that have very different fundamentals from the company that you are valuing.
1.1: With equities, there are no perfect matches: If you are valuing a collectible (Tiffany lamp or baseball card), you might be able to find identical assets that have been bought and sold recently. With stocks, there are no identical stocks, since even with companies that are close matches, differences will persist.
1.2: Small, more similar, sample or large, more diverse, sample: Given that there are no stocks identical to the one that you are trying to value in the market, you will be faced with two choices. One is to define "similar" narrowly, looking for companies that are listed on the same market as yours, of similar size and serving the same market. The other is to define "similar" more broadly, bringing in companies in other markets and perhaps with different business models. The former will give you more focus and perhaps fewer differences to worry about and the latter a much larger sample, with more tools to control for differences.  

2. Pricing Metric
To compare pricing across companies, you have to pick a pricing metric and broadly speaking, you have three choices:
Post on differences in value
The market capitalization is the value of equity in a business, the enterprise value is the market value of the operating assets of the firm and the firm value is the market value of the entire firm, including any cash and non-operating assets. While firm value is lightly used, because non-operating assets and cash can skew it, both enterprise value and equity value are both widely used. In computing these metrics, there are three issues that do complicate measurement. One is that market capitalization (market value of equity) is constantly updated, but debt and cash numbers come from the most recent balance sheets, creating a timing mismatch. The second is that the market value of equity is easily observable for publicly traded companies, but debt is often not traded (if bank debt) and book debt is used as a stand in for market debt. Finally, non-operating assets often take the form of holdings in other companies, many of which are private, and the values that you have for them are book values. 
2.1: When leverage is different across companies, go with enterprise value: When comparing pricing across companies, it is better to focus on enterprise value, when debt ratios vary widely across the companies, because equity value at highly levered companies is much smaller and more volatile and cannot be easily compared to equity value at lightly levered companies.
2.2: With financial service companies, stick with equity: As I have argued in my other posts, debt to a bank, investment bank or insurance company is more raw material than source of capital and defining debt becomes almost impossible to do at financial service firms. Rather than wrestle with his estimation problem, my suggestion is that you stick with equity multiples.

3. Scaling Variable
When pricing assets that come in standardized units, you can compare prices directly, but that is never the case with equities, for a simple reason. The number of shares that a company chooses to have will determine the price per share, and arguing that Facebook is more expensive than Twitter because it trades at a higher price per share makes no sense. It is to combat this that we scale prices to  a common variable, whether it be earnings, cash flows, book value, revenues or a driver of revenues (users, riders, subscribers etc.).

3.1: Be internally consistent: If your pricing metric is an equity value, your scaling variable has to be an equity value (net income, book value of equity). If your pricing metric is enterprise value, your scaling variable has to be an operating variable (revenues, EBITDA or book value of invested capital). 
3.2: Life cycle matters: The multiple that you use to judge pricing will change, as a company moves through the life cycle.
Early in the life cycle, the focus will be on potential market size or revenue drivers, since the company's own revenues are small or non-existent and it is losing money. As it grows and matures, you will see a shift to equity earnings first, since growth companies are mostly equity funded, and then to operating earnings and EBITDA, as mature companies use debt, ending with a focus on book value as a proxy for liquidation value, in decline.

4. Control for differences
As we noted, when discussing similar companies, no matter how carefully you pick comparable firms, there will be differences that persist between the company that you are trying to value and the comparable firms. The test of good pricing is whether you detect the variables that cause differences in pricing and how well you control for the differences. In much of equity research, the preferred mode for dealing with these differences is to spin them to justify whatever pre-conceptions you have about a stock.
4.1: Check the fundamentals: In intrinsic value, we argued that the value of a  company is a function of its cash flows, growth and risk. If you believe that the fundamentals ultimately prevail in markets, you should tie the multiples you use to these fundamentals, and using algebra and a basic discounted cash flow model will lead you to fundamentals drivers of any multiple.

4.2: Let the market tell you what matters: If you are a pure trader, who has little faith that the fundamentals will prevail, you can can take a different path. You can look at other data, related to the companies that you are pricing, and look for correlation. Put simply, you are trying to use the data to back out what variables best explain differences in market pricing, and using those variables to price your company.
To illustrate the differences between the two approaches, take a look at my pricing of Severstal, where I used fundamentals to conclude that it was under priced, and my pricing of Twitter, at the time of its IPO, where I backed out the number of users as the key variable driving the market pricing of social media companies and priced Twitter accordingly.

Pricing around the Globe
Assuming that you have had the patience to get to this part of the post, let's look at the pricing numbers at the start of 2018, around the world, starting with earnings multiples (PE and EV/EBITDA), moving on to book value multiples (Price to Book, EV to Invested Capital) and ending with revenue multiples (EV/Sales).

1. Earnings Multiples
Earnings multiples have the deepest roots in pricing, with the PE ratio still remaining the most used multiple in the world. In the last two to three decades, there has been a decided shift towards enterprise value multiples, with EV/EBITDA leading the way. While I am skeptical of EBITDA as a measure of accessible cash flow, since it is before taxes and capital expenditures, I understand its pull, especially in aging companies with significant depreciation charges. If you assume that depreciation will need to go back into capital expenditures, there is an intermediate measure of pricing, EV to EBIT.

In the chart below, I look at the distribution of PE ratios globally, and report on the PE ratio distributions, broken down region, at the start of 2018.

I know that it is dangerous to base investment judgments on simple comparisons of pricing multiples, but at the start of 2018, the most expensive market in the world on a PE ratio basis, is China, followed by India, and the cheapest market is Eastern Europe and Russia. If you would like to see the values for earnings multiples, by country, please click at this link.

If you are more interested in operating earnings multiples, the chart below has the distribution of EV/EBIT and EV/EBITDA multiples:
China again tops the scale, with the highest EV/EBITDA multiples, and Eastern Europe and Russia have the lowest EV/EBITDA multiples. Earnings multiples also vary across sectors, with some of the variation attributable to fundamentals (differences in growth, risk and cash flows) and some of it to misplacing. The sectors that trade at the highest and lowest PE ratios are identified below:
Download industry spreadsheet
You can download the full list of earnings multiples for all of the sectors, by clicking on this link

2. Book Value Multiples
The delusion of fair value accounting is that balance sheets will one day provide better estimates of how much a business in worth than markets, and while I believe that day will never come, even accountants are entitled to their dreams. That said, there are investors who still put their faith in book value and compare market prices to book value, either in equity terms or operating asset terms:

  • Price to Book Equity = Market Value of Equity / Book Value of Equity
  • EV to Invested Capital = (Market Value of Equity + Market value of Debt - Cash)/ (Book value of equity + Book value of Debt - Cash)
In the table below, I report on price to book and enterprise value to invested capital ratios, by sub-region of the world:

The most expensive sub-region of the world is  India, on both a price to book and EV/Invested capital basis, and the lowest priced stocks are again in Eastern Europe and Russia. If you would like to see book value multiples, by country, click at this link.  With book value multiples, the differences you observe across sectors not only reflect differences in fundamentals and pricing errors, but also accounting inconsistencies on how capital expenditures in non-manufacturing companies are dealt with, as opposed to manufacturing firms. I tried to correct for these inconsistencies, by capitalizing R&D at all firms, but that correction goes only part way and the most expensive and cheapest sectors, with my corrected book values, are listed below:
Download industry PBV spreadsheet
You can download the book value multiple data, by sector, by clicking here.

3. Revenue Multiples
To the question of why investors and analysts look at multiples of revenues, my one word answer is "desperation". When every other number in your income statement is negative, you have to keep climbing the statement until you hit a positive value. That said, there is value in focusing on a variable that accountants have the least influence over, and the heat map below captures differences in the enterprise value to sales ratios across the globe.

Unlike earnings and book value multiples, which have a pronounced peak in the middle of the distribution, revenue multiples are more evenly distributed, with quite a few firms trading at more than ten times revenues. As with earnings and book value multiples, I report revenue multiples, by country at this link and  by sector at this link. Note that there no revenue multiples reported for financial service firms, where neither enterprise value nor revenues can be meaningfully measured or estimated.

I am an investor, who believes in value, but it would be foolhardy on my part to ignore the pricing game, since I am dependent upon it ultimately to cash out on my value gains. In this post, I have looked at the pricing differences around the globe, at least based upon market prices at the start of 2018. Of all of my data posts, this is the one that is the most dynamic and likely to change over short periods, since markets can react to change far more quickly than companies can. 

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