Monday, May 2, 2016

DCF Myth 3: You cannot do a valuation, when there is too much uncertainty!

Uncertainty, both imminent and resolved, has been on my mind these last two weeks. I posted my valuation of Valeant on April 20, making the argument that, at least based on my expectations on what could be revealed in the delayed financial filings, the stock was worth about $44, approximately $12 more than the prevailing stock price. Many of you were kind enough to comment on my valuation, and one of the more common refrains was there were too many unknowns on the stock to be taking a stand. In fact, one of the comments on the post was that "regardless of the valuation, a sufficient margin of safety does not exist (on the stock)". On April 21, we got news that Volkswagen had come to an agreement with US authorities on the compensation that they would offer buyers of their cars and a day later, the company announced that it would take an $18.2 billion charge to cover the costs of its emissions misrepresentations. It was a chance for me to revisit my valuation of Volkswagen, in the immediate aftermath of the scandal in October 2015, and take stock of how the the investment I made in the stock then looks, as the uncertainty gets slowly resolved. All through these last two weeks, there were signs that Yahoo's journey, that was starting to resemble the Bataan Death March lately, was nearing its end, as the company reviewed bids for its operating assets. Since it is a stock that I valued almost two years ago (and bought after the valuation) and labeled as a Walking Dead company, I am interested, both financially and intellectually, to see how this end game plays out. As I wrestle with the resolution of uncertainties from the past and struggle with uncertainties in the future on every one of my investments, I thought it would be a good time to look at good and bad ways of responding to I uncertainty in investing and valuation.

The Uncertainty Principle
Uncertainty has always been part of human existence, though it has transitioned from the physical uncertainty that characterized the caveman era to the economic uncertainty that is more typical of today, at least in developed markets. Each generation, though, seems to think that it lives in the age of the greatest uncertainty. That may be partially a reflection of a broader sense of "specialness" that afflicts each generation, where it is convinced that its music and movies were the very best and that it had to get through the biggest challenges to succeed. The other is a variation of hindsight bias, where we can look at the past and convince ourselves that what actually happened should have been obvious before it occurred. I am surprised at how many traders, investors and portfolio managers, who lived through the 2008 crisis, have convinced themselves that November 2008 was not that bad and that there was never a chance of a catastrophic ending.  That said, uncertainty not only ebbs and flows over time but also changes form, making enduring fixes and lessons tough to find. As investors bemoan the rise of uncertainty in today's markets, there are three reasons why they may feel more under siege now than in prior decades:
  1. Low Interest Rates: In my post on negative interest rates, I pointed to the fact that as interest rates in many of the leading currencies have dropped to historic lows, risk premiums have increased in both stock and bond markets. The expected return on the S&P 500 in early 2008, before the crisis, was 8% and it remains at about that level today, even though the treasury bond rate has dropped from 4% to less than 2%, but the equity risk premium has risen to compensate. Even though the expected return may be the same, the fact that more of it can be attributed to a risk premium will increase the market reaction to news, in both directions, adding to price volatility.
  2. Globalization: Globalization has not only changed how companies and investors make choices but has also had two consequences for risk. The first is that there seem to be no localized problems any more, with anyone's problem becoming everyone's problem. Thus, political instability in Brazil and too much local government borrowing to build infrastructure in China play out on a global stage, affecting stock prices in the rest of the world. The second is that the center of global economic power is shifting from the US and Europe to Asia, and as it does, Americans and Europeans are starting to bear more of world's economic risk than they used to.
  3. Media/Online Megaphones: As an early adopted of technology, I am far from being a Luddite but I do think that the speed with which information is transmitted around the world has allowed market risks to go viral. It is not just the talking heads on CNBC, Bloomberg and other financial news channels that are the transmitters of these news but also social media, as Twitter and Facebook become the place where investors go to get breaking investing news.
I am sure that you can add other items to this list, such as the disruption being wrought by technology on established businesses, but I am not sure that these are either uncommon or unusual. Every decade has its own disruptive factors, wreaking havoc on existing business models and company values.

The Natural Responses to Uncertainty
Much of financial theory and a great deal of financial practice was developed in the United States in the second half of the last century and therein lies a problem. The United States was the giant of the global economy for much of this period, with an economy on an upward path. The stability that characterized the US economy during this period was unusual, if you look at long term history of economies and markets, and much as we would like to believe that this is because central bankers and policy makers learned their lessons from the great depression, there is the very real possibility that it was just an uncommonly predictable period. That would also mean that the bedrock of financial practice, built on extrapolating from past data and assuming mean reversion in all things financial, may be shaky, and that we have to reevaluate them for the economies that we operate in today. It is unfair to blame the way we deal with uncertainty entirely on the fact that our practices were honed in the United States. After all, it is well chronicled in both psychological annals and behavior studies that we, as human beings, deal with uncertainty in unhealthy ways, with the following being the most common responses:
  1. Paralysis and Inaction: The most common reaction to uncertainty, in my experience, is inaction. "There is too much uncertainty right now to act" becomes the refrain, with the promise that action will come when more of the facts are know. The consequences are predictable. I have friends who have almost entirely been invested in money market funds for decades now, waiting for that moment of clarity and certainty that never seems to come. I have also talked to investors who seem to view investing when uncertain as a violation of value investing edicts and have found themselves getting pushed into smaller and smaller corners of the market, seeking elusive comfort.
  2. Denial and Delusion: At the other end of the spectrum, the reaction that other investors have to uncertainty is go into denial, adopting one of two practices. The number crunchers fall back on false precision, where they add more detail to their forecasts and more decimals to their numbers, as a defense against uncertainty. The story tellers fall back on story telling, acting as if they have the power to write the endings to every uncertain narrative, when in fact they have little control over either the players or the outcome.
  3. Mental Accounting and Rules of Thumb: The brain may be a wondrous organ but it has its own set of tics that undercut investing, when uncertain. As Richard Thaler has so convincingly shown in his work on mental accounting, investors and analysts like to use rules of thumb, often with no basis in fact or reality, when making judgments. Thus, a venture capitalist who is quick to dismiss the use of intrinsic value in a young start-up as too fraught with estimation error, seems to have no qualms about forecasting earnings five years out for the same company and applying a price earnings ratio to those earnings to get an exit value.
  4. Outsourcing and Passing the Buck: When stumped for answers, we almost invariably turn to others that we view as more knowledgeable or better equipped than we are to come up with solutions. Cynically, you could argue that this allows us to avoid taking responsibility for investment mistakes, which we can now attribute to consultants, text book writers or that person you heard on CNBC. 
  5. Prayer and Divine Intervention: The oldest response to uncertainty is prayer and it has had remarkable staying power. There are large segments of the world where big investment and business decisions are preceded by prayers and divine intervention on your behalf. 
If the first step in change is acceptance, I have come to accept that I am prone to do some or all of the above, when faced with uncertainty, but I have also discovered that these reactions can do damage to my portfolio. 
Dealing with Uncertainty
To reduce, if not eliminate, my unhealthy responses to uncertainty, I have developed my own coping mechanisms that will hopefully push me on to healthier tracks. I am not suggesting that these will work for you, but they have for me, and please feel free to modify, abandon or adjust them to your own needs.
1. Have a narrative: As many of you who read this blog know, I have long believed that a company valuation without a story to bind it together is just numbers on a spreadsheet and a story that uses no numbers at all is a fairy tale. There is another advantage in having a narrative underlie your valuation and tying numbers to that narrative. When faced with uncertainty about specifics, the question that I ask is whether these specifics affect my narrative for the company and if yes, in what way. In my valuation of Volkswagen, right after the diesel emissions scandal, I did not find a catastrophic drop in value for the company because my underlying narrative for Volkswagen, that of a mature business with little to offer in terms of expansion or growth opportunities, was dented but largely unchanged as a result of the scandal. With Valeant, in my November 2015 valuation, I argued that the attention brought to the company by its drug pricing policies and connections to Philidor would result in it having to abandon its strategy of growth driven by acquisitions and growth and to shift to being a less exciting, lower growth pharmaceutical company. That shift in narrative drove the inputs into my valuation and my lower assessment of value. 
2. Categorize uncertainty: Uncertainty can come from many sources and it is useful, when valuing a company in the face of multiple uncertainties, to classify them. Here are my groupings:

Since it is easy to miss some uncertainties and double count others, I find it useful to keep them isolated in different parts of my valuation:

Specifically, in my Volkswagen and Valeant valuations, it was micro risk that concerned me, with some of that risk being continuous (the effect of the diesel emissions scandal on Volkswagen car sales) and some being discrete (the fines levied by the EPA on Volkswagen and the risk of default in Valeant). That is why both companies, at least in my conventional valuations, have low costs of capital, notwithstanding the risky environment, but their values are then adjusted for the expected costs of the discrete events occurring.
3. Keep it simple:  This may seem ironic but the more uncertainty there is, the simpler my valuation models become, with fewer inputs and less levers to move. One reason is that it allows me to focus on the variables that really drive value for the company and the other is that it reduces my need to estimate dozens of variables in the face of uncertainty. Thus, in my valuations of start-up companies, my focus is almost entirely on three variables: revenue growth, operating margins and the reinvestment needed to sustain that growth. 
4. Make your best estimates: As I start making my estimates in the face of uncertainty, I hear the voice in the back of my mind pipe up, saying "You are going to be so wrong!" and I silence it by  reminding myself that I don't have to be right, just less wrong than everyone else, and that when uncertainty is rampant, most investors give up.
5. Face up to uncertainty: Rather than cringe in the face of uncertainty and act like it is not there, I have found that it is freeing to admit that you are uncertain and then to take the next step and be explicit about that uncertainty. In my valuations of tech titans in February 2016, I used probability distributions for the inputs that I felt most shaky about and then reported the values as distributions. Since some of you have been curious about the mechanics of this process, I will take a lengthier journey through the process of running simulations in a companion piece to this post.
6. Be willing to be wrong: If you don't like to be wrong, it is best not  to value companies in the face of uncertainty. However, if you think that Warren Buffet did not face uncertainty in his legendary investment in American Express after the salad oil scandal in 1964 or that John Paulson knew for sure that his bet against the housing bubble would pay off in 2008, you are guilty of revisionist history. There is a corollary to this point and it relates to diversification. As I have argued in my post on diversification, the more uncertain you feel about individual investments, the more you have to spread your bets. It is not an admission of weakness but a recognition of reality.

If you are a value investor, you will notice that I have not mentioned one of value investors' favorite defenses against uncertainty, which is the margin of safety. Seth Klarman is one of my favorite investment thinkers but I am afraid that the margin of safety, at least as practiced by some in the investing community, has become an empty vessel, an excuse for inaction rather than a guide to action in risky times. I will come back to this measure as well in another post in this series.

If you are an active investor, you are constantly looking for an edge, something that you can bring to the table that most other investors cannot or will not, that you can exploit to earn higher returns. As the investing world gets flatter, with information freely accessible and available to almost all investors, and analytical tools that anyone can access, often at low cost, being comfortable with uncertainty may very well be the edge that separates success from failure in investing. There may be some who are born with that comfort level, but I am not one of them. Instead, my learning has come the hard way, by diving into companies when things are most uncertain and by valuing businesses in the midst of market crises, "by going where it is darkest". That journey is not always profitable (see my experiences with Vale as a precautionary note), sometimes makes me uncomfortable (as I have to make forecasts based upon little or bad information), but it is never boring. I am wrong a hefty percent of the time, but so what? It's only money! I am just glad that I am not a brain surgeon!

YouTube Video

Uncertainty Posts
  1. DCF Myth 3: You cannot do a valuation, when there is too much uncertainty
  2. The Margin of Safety: Excuse for Inaction or Tool for Action?
  3. Facing up to Uncertainty: Probabilities and Simulations
DCF Myth Posts
  1. If you have a D(discount rate) and a CF (cash flow), you have a DCF.  
  2. A DCF is an exercise in modeling & number crunching. 
  3. You cannot do a DCF when there is too much uncertainty.
  4. It's all about D in the DCF (Myths & 4.5)
  5. The Terminal Value: Elephant in the Room! (Myths & 5.5)
  6. A DCF requires too many assumptions and can be manipulated to yield any value you want.
  7. A DCF cannot value brand name or other intangibles. 
  8. A DCF yields a conservative estimate of value. 
  9. If your DCF value changes significantly over time, there is something wrong with your valuation.
  10. A DCF is an academic exercise.


  1. Dear Mr. Damodaran, with all due respect would request you to please be more succinct. Your posts are more likely to be read thoroughly & appreciated with reduced verbosity. Appreciate it, thanks.

  2. You miss 100% of the shots you don't take! Would love to see an up to date Apple valuation and your comments on the latest quarterly results. Any chance we will see one?

  3. Anonymous,
    Much as I would like to say that I will try to write shorter posts, I write only partly to be read. The other part is catharsis, a way of working through things that I am still uncertain about and writing helps me do that. So, I am afraid that the post will always be as long as I need it to be to get to that point of (relative) clarity. The fact that very few readers may want to hang in there with me till the end is reality but it is what it is..

  4. Hi Professor,

    I wonder if the talk about uncertainty pertains to Knightian uncertainty, which is something that by definition cannot be measured. It's a bit of a philosophical point, but most of the valuation mitigants you list seem to be aimed at capturing an estimate of the risk involved, which presumably would still miss the uncertainty that investors may be worried about here.

    That said, viewed in that light if it's impossible to measure or predict, then it's impossible to capture in a valuation, and hence it's not something that investors should be worried about because they cannot predict, hedge, or otherwise protect themselves from such uncertainty.

    Curious to hear your thoughts on this, and on whether this concept pertains to the type of uncertainty your blog addressed.

    Andy MacNamara

  5. Hi Professor Damodaran, I recently discovered your blog. IMHO, please don't worry about the length of your posts:

    Blaise Pascal — 'I have only made this letter longer because I have not had the time to make it shorter.(Letter 16, 1657)'

    I appreciate all your little side notes here and there! Your reflections on risk and human bias / limitations are very timely and relevant to me. Thank you for taking the time to post your thoughts.

    Apropos of the topic.. FWIW, I keep noticing that Wall Street (WS) analysts frequently fall drastically behind the tsunami waves of sudden market revaluation.

    To take Valeant as an example, it took WS absurdly long to collectively mark down their estimates. I presume that most analyst estimates chiefly reflect DCF methodology? Were they paralyzed by the scary new narrative? Further, look at Bill Ackman's decision to massively average down in the $80s and $90s. To what extent would you imagine that classic DCF analysis informed Ackman to make such a colossal misstep?

    My own view is that survival bias plays a huge part here. For every heroic Amex or GGP turnaround story out there, I would think there may be 3 - 5 analogous ones where the corporation did not pull through, and ended up going through bankruptcy, or was liquidated, or bought out at substantial discount to peak valuation. I recall that the Borders Books founder pumped in something like $150MM, just months before they closed their doors.

    So I completely agree with your thesis: analysis of the financial statements can only go far in capturing the ultimate, unknowable investment prospects of any firm. It would be great, wouldn't it, to have some heuristics for how much weight to put on the valuations!

    Thank you in advance for any response.

  6. Brad,
    Thank you, especially since Pascal is one of my heroes, a mathematical genius who also seemed to understand behavioral finance. I do think that it is easy to get trapped in your own narrative and then get sucked into protecting it at all costs. Bill Ackman is a very smart guy and that may be part of the problem, since when you are very smart, you are used to being right and that breeds hubris. I have resolved to write a "I was wrong" post at least once every three month about some aspect of what I have taken a stand on before, just to get used to saying those three words over and over again. In the meantime, though, I just watch and marvel from the sidelines.

  7. I fully agree with your comment that writing helps to work through and sort your own ideas. I keep experiencing myself that if forced to put something on paper which has a red line, the reasoning and logic becomes clearer and better (not saying more correct, but at least clear).

    So for the few of us who like reading and do not get distracted after five lines of text, please continue doing so. If I feel something is not that interesting - speed reading helps.

    I am also excited to hear that you will do a post on Monte Carlo simulation and valuation, a topic I have been wondering about a bit (more precise the part where you get your distribution assumptions from), so looking forward to this.

  8. Thank you Professor Damodaran for time and efforts in laying out your thoughts so clearly.

    I enjoy reading you posts, and I agree with your views about the long post and looks like Albert Einstein quote “"A scientific theory should be as simple as possible, but no simpler." If it takes longer to explain, so be it.

    I would like to add my two cents to one of the points you have mentioned related to dealing with uncertainty.

    When we are dealing with micro- uncertainty, we know the problem is affecting a particular or few companies and if analyzed properly, we can understand the situation better and take the things in perspective.

    However, the picture changes completely, when we are dealing with Macro-uncertainty. For example in 2008 or late 2001, when the market was crashing (it does quite regular now a day, but I have mentioned this just to highlight my point) the prices were plummeting, but very people were able to benefit from it. There could be genuine reasons for not buying stocks, but there were many individuals who didn't take up any bargains due to psychological reasons. As noted behavioral scientists (Daniel Kahneman or Richard Thaler. I think) has pointed out in their experiments that we pick up a bargain if there is one offer. But there are multiple offers; our brain gets confused we resort to our default behavior “inaction”.

    Thank you in advance for any response.


  9. Prof. Damodaran,

    Thanks for your response, do note that regardless of word count I for one admire your work. It's a privilege to be able to learn from you & understand your thought process.

    In fact, am currently working on a fintech startup which is partly influenced by learnings from your lectures, DCF models, course material & posts such as these - all without formal training.

    My suggestion came from the amount of time I had to spend connecting the dots in your post (didn't stop me from going through it in-depth though).

    To allow for shorter attention spans, perhaps you would consider having an executive summary (when possible) for casual visitors to get the gist of your original post. This would hopefully compel them to read further & discover the value in your content & benefit from it.

    It is of course your prerogative to write as you choose. You have a follower in me regardless.

    Anonymous :)

  10. Hugo Francisco Caycedo GodoyMay 4, 2016 at 11:54 AM

    Hi, prof. I really appreciate that now your valuations include probability distributions. I see this feature really useful in two ways:

    first, the narrative is well complemented with different scenarios in a fast changing environment.

    Second, probabilistic support to our (valuable)judgment when valuing a company protects our reputation from attacks made by people who still conceive the valuation of a business as an exact science.

  11. Dear Prof
    An excellent post .I have a question on the alternative risk measure you mentioned. what are these risk measures and how they can substitute the beta .

  12. Prof. I`ve learned a lot reading your blog and appreciate your contribution to society by making public your thoughts and processes.

    However to my surprise I was shocked by your statement: " I am wrong a hefty percent of the time, but so what? It's only money! " I wonder, aren't your courses and teachings about making money ? Isn´t money the goal in finance ? Isn't money the way we keep score ? What would you say to a student If in one of your exams answers: "the DCF is X dollars or the cost of capital is x% and even if I am wrong I should get an "A" because whatever the correct answer is, so what? it´s only money." ? I don't think it is an effective way to motivate students to learn about finance telling them at the beginning or at the end of the course: "if you apply what you learn and you are wrong, so what ? It's only money."

  13. David,
    Making money may be the only thing that matters in investing, but it cannot become the focus of my life. The mistakes I make in investing affect my portfolio and perhaps my life style but the actions that I take that affect other people in negative ways have much greater consequences. The world will not end or even notice if I lose money on Valeant or Apple and by acknowledging this fact, I get the freedom to make mistakes. And this is exactly the lesson I hope I convey in my classes as well. Don't take yourself and your financial tools too seriously and keep perspective. I see no contradictions, even if you do.

  14. Please dont ever make your posts shorter. In all fairness, make them longer.
    If someone thinks the post is long and they have a better idea of using their time they can always stop reading and do the more useful thing but if someone thinks the post is short and they would like to know more about your thoughts they cannot receive the em waves generated by your thinking process if you don't communicate it in a way our senses can decode it.
    If not for anything else, just for fairness sake, your posts should be very long.
    Stay well professor, proud of you as a human being.

  15. Prof Damodaran,

    First of all - apologies for posting the query here, but I am not sure of the right page to post it.

    I am trying to find the valuation of a bio diesel (BD) manufacturing company in India which has just been established a year back. BD manufacturing is at a nascent stage in India, with no listed company engaged in the same. The company is procuring used cooking oil as raw material from restaurants/fast food outlets and producing BD via tolling arrangement with another company. The company plans to sell BD to state road transport utilities in the country, at a selling price based on the prevailing diesel price. The company doe not really have an asset base and the projections have to be largely based on optimistic growth plans into multiple regions in India (nearly 25 times its current revenue in 2 years), based on the assumption of equity capital infusion to support working capital requirement. Further, the company intends to use either - used cooking oil, palm oil or styrene to produce the BD, depending on prevailing price of either of these. What is the best approach to value the company, in your opinion?

    Also, could you help answer the following queries:
    1. To estimate the earnings and raw material purchases, am I correct in estimating it by determining the probability distribution for diesel price (bi monthly over 10 years), coconut oil and styrene and then considering the mean for terminal year? The numbers would be inflation adjusted, I presume.
    2. Is there a way by which I could tackle the growth numbers projected by the company - the business entails very little capex and will primarily be driven by margins realized from purchase of raw material and processing cost added to it by way of tolling arrangement to derive the final output.

    Thank you for attention


  16. Great post.

    An image that helps me with this is the popular optical illusion with the twonoramge squares that are the same color but because of the background being a different color, your brain can not understand they are the same.

    That's obvious. What's less obvious is even when you KNOW they are the same color, your brain STILL won't allow you to see them correctly.

    I think investing has similar characteristics. Even when you know a market is crashing and high fear means you should invest, your brain will not let you see it.

    So.... I think this is why investors need a process that lets them act despite being fooled by the optical illusions.

    What makes this doubly hard is it's a game of probabilities... so being right but unlucky can be materially different than being lucky when the final numbers are added up. Since we can't objectively measure luck... I guess that's the best we can do :)


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