Numbers and Narrative: Modeling, Story Telling and Investing

When I put together the outline for my very first valuation class in 1986, I was warned by a senior faculty member not to go down that path. I was told that there was really not enough theory in valuation to warrant a class and that I would end up teaching a glorified accounting class. I chose to ignore that advice and I have not regretted it since, for two reasons. The first is that I love teaching a subject where there is little theory, the questions are entirely about practice, you draw on a unique blend of skills and tools to accomplish your tasks and the market acts as your task master.  The second is that I have learned almost everything I know about valuation and more importantly, how much I don't know, in the process of teaching this class. This post is about one of the recurring themes in my class which is the interplay between narratives and numbers that makes for a good valuation.

The Numbers Game

When most people think about valuation, they generally visualize dense financial statements and elaborate excel spreadsheets, and those coming into my valuation class are no exception. They expect me to immerse them in accounting rules and the building of models and are either deeply disappointed, if their background is in accounting or banking, or relieved, if it is not, to find out that the only thing I know about accounting rules is that there lots of them and that I am not an Excel Jedi Master. Don't get me wrong! I do draw on accounting statements for my information and use Excel incessantly, but here is how I see their place in valuation:

1. Accounting statements provide me with the raw material for my valuation, nothing more and nothing less. Like all raw material, I have to decide what I will use and what I will discard, and I discard far more than I use. As the end user of the raw material, I get to determine what makes sense for me and what does not and not GAAP, IFRS or the accounting profession. As for fair value accounting, I am sympathetic with the motives (which is to make accounting more relevant) but unimpressed with the results. To me, fair value accounting estimates are like microwave frozen dinners, quick and convenient, but you will never mistake them for the real thing.
2. Excel (or Numbers) is a versatile and powerful multi-purpose tool, but like all tools, it can be misused or over used. My knowledge of Excel is limited to those parts of it that help me complete my valuation and I frankly have no interest in expending time and resources mastering the parts that I can get done with simpler tools or none at all.

So, why do so many appraisers and analysts emphasize their mastery (at least in their minds) of the numbers side of valuation? The answer, I think, lies in the trifecta of illusions that go with numbers-based models.

1. The illusion of precision: For better or worse, we seem to feel better about uncertain outcomes, if we can attach numbers (expected values, risk adjusted discount rates) to them. That, by itself,  is healthy but what is unhealthy is the belief that quantifying risk somehow makes it dissipate. 
2. The illusion of objectivity: I believe that all valuations are biased, with the only questions being how much bias and in what direction. That is because we bring in our preconceptions and beliefs about companies into our valuations and we sometimes add to the bias because we have other agendas at play. Here again, analysts point to numbers as their defense against the bias charge, with the implicit argument that numbers don't lie, when the most effective way to shade the truth is with a selective use of numbers.
3. The illusion of control: I believe that "numbers people" often use numbers to intimidate "non-numbers people" into mute acceptance. The intimidation factor is dialed up by adding more detail  (500 line items, anyone?) and buzz words (free cash flow, a few greek alphabets and a host of acronyms) to your valuations.

In my view, there are at least three significant dangers, when numbers are used without any narrative (or story line) in constructing valuations. First, valuations become plug-and-point exercises, tools to advance sales pitches or confirm pre-conceived values. Second, if a valuation is built around line items and individual inputs, there is a strong possibility that you may be creating a business that can exist only in spreadsheet nirvana, where revenues double every year, margins expand without challenge and growth comes without significant reinvestment. Finally, discussions and debates about inputs become shallow exercises in quibbling about the "right" values to use, with no logical tie breaker.

The Narrative as Valuation

If one extreme of the numbers/narrative spectrum is inhabited by those who are slaves to the numbers, at the other extreme are those who not only don't trust numbers but don't use them. Instead, they rely entirely on narrative to justify investments and valuations. Their motivations for doing so are simple.

1. Story telling is a powerful attention getter/keeper: Research in both psychology and business point to an undeniable fact. Human beings respond better to stories than to abstractions or numbers, and remember them for longer. After all, the Harvard Business School has taken story telling almost to an art form with its cases, tightly wound narratives that are supposed to convey larger lessons.
2. Unrestrained creativity: "Creative" people through the ages have always fought back against any restraints on their creativity, especially those imposed by those that they view as less imaginative than they are. 
3. The Creative Superiority Complex: Just as numbers people intimidate with mounds of numbers, good narrators can browbeat "bean counters" with superior story telling, especially if they can back their stories up with personal experience. 

Narrative-driven investing is not uncommon, especially with younger firms and start-ups, and I have been taken to task for even trying to value these companies using number-driven models. Paraphrasing some of the comments on my valuations of Twitter and Uber, the argument seems to be that while cash flow based valuations may work on Wall Street and with mature companies, they are not useful in analyzing the type of companies that venture capitalists look at. While it is true that rigid cash flow based models will not work with companies where promise and potential are what is driving value, staying with just narrative exposes you to two significant risks. The first is that, without constraints, creativity can carry you to the outer realms of reason and into fantasy. While that may be an admirable quality in a painter or a writer, it is a dangerous one for an investor. The second is that, when running a business as a manager or monitoring it as an investor, you need measures of whether you are on the right path, no matter where your business is in its life cycle. When narrative alone drives valuation and investing, there are no yard sticks to use to see whether you are on track, and if not, what you need to do to get back on the right path. 

Numbers plus Narrative

If numbers without narrative is just modeling and narrative without numbers is story telling, the solution, as I see it, is both obvious and difficult to put into practice. In a good valuation, the numbers are bound together by a coherent narrative and story telling is kept grounded with numbers. Implementing this solution does require work and I would suggest a five-step process, though I am not rigid about the sequencing.

Step 1: Develop a narrative for the business that you are valuing or considering investing in: Every business has a story line and the place to start a valuation is with that narrative. While managers and founders get to present their narrative first, and some of them are more persuasive and credible than others, you and I have to develop our own narratives, sometimes in sync with and sometimes at odds with the management story line. As an example, in my valuation of Uber, my narrative was this: Uber is an innovative car service company, with the untested potential to expand into other logistics businesses. It will expand the car service business (by attracting new users), while gaining a significant (though not dominant) market share and preserving its profitability.  The counter narrative that some of you presented is the following (and I am paraphrasing): Uber is a logistics company that will find a way to expand its profitable car service business model into the moving, car rental and electric car businesses.

Step 2: Test the narrative against history, experience and common sense: This is the stage at which you put your narrative through a reality test and examine whether it withstands multiple tests. The first is the test of history, where you look at the past to see if there have been companies that have lived the narrative that you are claiming for your company and what they share in common.  The second is the test of experience, where you draw on investments based upon similar narratives that you have made in the past and remember or recognize road bumps and barriers that you ran into in practice. The third is the test of common sense, where you draw on first principles in economics and mathematics, to evaluate your narrative's weakest links. With Uber, here is how I justified my narrative. Uber will be able to gain (10%) is that the car service (taxi and limo) business is a splintered, regulated and inefficient business that is ripe for disruption. The reason I did not assume a dominant market share for Uber (40% or 50%) is because I don't see as large a networking effect in the car service business, where the service is both physical and localized, as there are in online technology businesses (search, merchandising or advertising). At the same time, I am assuming that Uber will be able to preserve its profitability in the face of competition and overcome regulatory hurdles.

Step 3: Convert key parts of the narrative into drivers of value: Ultimately, even the most gripping narratives have to show up in the numbers. While this may seem like an insurmountable obstacle to those without a valuation background, it can be simplified by looking at the big picture. Here is my attempt to connect different narratives with key value drivers:

Narratives and Value Drivers

Step 4: Connect the drivers of value to a valuation: I use discounted cash flow models (DCF) to connect the drivers of value to value, because I am comfortable with the mechanics of these models. It is a tool that not everyone is comfortable with and you may find a different and perhaps better way to connect value drivers to value. In fact, the classic VC valuation takes a short cut by using three drivers of value: an expected earnings (or revenue) in a future period, an exit multiple (based on what others seem to be willing to pay today for similar companies) that converts that number into a future value and a target return to discount that value back to the present (and adjust for risk). To those of you who have never done valuation before, trust me when I say that valuation at its core is simple and that anyone should be able o do it. If you don't believe me, you are welcome to try my online valuation class on iTunes U. It comes with a money back guarantee.

Step 5: Keep the feedback loop open: My kids and spouse are quick to remind me that the three words that I find most difficult to say are "I was wrong" and I am sure that I am not alone in my reluctance. The biggest enemy that we (whether numbers or narrative driven) face is hubris, where we get locked into our initial points of views and view changing our minds as a sign of weakness. While it does not come easily to me, I do try to stay open to the possibility that as events unfold, my narrative will change or even shift, sometimes dramatically. With Uber, if the next few months bring evidence of tangible success of the business model in other logistics markets, I will change my story, expand the potential market and with it, the value. If, in contrast, the company gets bogged down in regulatory and legal fights in its existing car service markets or a competing service improves its offering dramatically, I will have to dial down my optimism, reduce both market share and profit margins and change value. In either case, I will view these changes as part of investing rather than as a failure in my initial valuation.

In my experience, it is easiest to play to your strengths (which, for me, are on the numbers side), but you will gain the most when you work on your weaknesses (which, for me, are on the narrative side). Consequently, I learn more from listening to those who think differently from me and disagree with me, even if they do not always do so constructively, than I do from those who agree with me. On my Uber valuation, the comments that I found most useful in fine tuning my valuation were those that I heard from those in the venture capital and technology space. After telling me that I had no idea what I was talking about and that "DCF won't work for these companies", they then proceeded to give me ideas that I incorporated into my DCF valuation. Here, for instance, are my attempts to quantify four of the most common narratives I heard about Uber, and the consequences for value.

Narrative	Total Market	Market Share	Uber Cut	Cost of capital	Failure Probability	Value for Uber
Car service company, facing significant competitive and regulatory hurdles, forced to make trade off of lower profitability for market share.	$100 billion	10%	10%	12%	10%	$3.2 billion
Car service company with potential to expand into other logistics markets, significant market share, sustained profitability (Mine)	$100 billion	10%	20%	12% ->8%	10%	$5.9 billion + $2-3 billion for disruption option
Car service company with dominant market share (from networking effects) and sustained profitability (New York Times)	$100 billion	50%	20%	12% ->8%	0%	$29.1 billion
Logistics company with expansion of car service business model into other logistics businesses, while preserving profitability.	$600 billion	5%	20%	12% ->8%	0%	$17.5 billion

There are two points I hope to make with this exercise. First, even the most imaginative and far-reaching narratives can and should be converted into numbers. So, let's retire the argument that some companies cannot be valued. Second, big differences in valuation almost always result from differing narratives about companies, not disagreements about the "small stuff".

Finally, since this is a discussion of how best to marry narrative to numbers, I cannot pass the opportunity to plug Shark Tank, one of my favorite shows, where narrative (from those pitching their businesses) meets numbers (from the venture capitalists/investors who challenge the business models while bidding on them), generating both drama and humor. 

Implications

If you view value as narrative overlaid with numbers, there are implications for both the founders/managers of businesses and the investors in these firms. To attract capital, managers need to develop coherent narratives about the firms that they run, convey these narratives to investors/markets effectively, and act consistently. To manage that capital well, they need to  identify value drivers, set yard sticks that measure how the narrative is unfolding and change in response to unforeseen events, both positive and negative.

For investors, the lessons are just as profound. They need to find companies that have compelling narratives, convert these narratives into value and make sure that they are not paying too much.  They need to spread their bets across several good narratives and be open to changes in narratives and numbers. It is true that having a great narrative and the numbers to back them up is not a guarantee of investment success. The best laid plans of mice and men can go to waste, but to not plan at all will guarantee that waste.

Attachments:
Uber: A Challenged Car Service company 
Uber: A Successful Car Service company 
Uber: A Car Service company with networking effects
Uber: A Logistics company

Bubble, Bubble, Toil and Trouble: The Costs and Benefits of Market Timing

If you believe that the stock market is in a bubble, you have lots of company. You have long-time market watchers, the New York Times and even a Nobel Prize winner in your camp. But what exactly is a bubble? How can you tell if you are in one?  And if you do believe you are in a bubble, what is your best course of action? Not only are these questions difficult to answer, but the answers can vary across markets, investors and time. 

The Bubble Machine

Every market has a bubble machine, though it is less active in some periods than others, and that machine creates an ecosystem of metrics and experts, as well as warnings about bubbles about to burst, corrections to come and actions to take to protect yourself against the consequences. In periods like the current one, when the bubble machine is in over drive and you are confronted by "bubblers" with varying credibilities, motives and methods, you may find it useful to first categorize them into the following groups.

1. Doomsday Bubblers have been warning us that the stock market is in a bubble for as long as you have known them, and either want you to keep your entire portfolio in cash or in gold (or bitcoins). They remind me of this character from Winnie the Pooh and their theme seems to be that stocks are always over valued.
2. Knee Jerk Bubblers go into hibernation in bear markets but become active as stocks start to rise and become increasingly agitated, the more they go up. They are the Bobblehead dolls of the bubble universe, convinced that if stocks have gone up a lot or for a long period, they are poised for a correction.
3. Armchair Psychiatrist Bubblers use subtle or not-so-subtle psychological clues from their surroundings to make judgments about bubbles forming and bursting. Freudian in their thinking, they are convinced that any mention of stocks by shoeshine boys, cab drivers or mothers-in-law is a sure sign of a bubble.
4. Conspiratorial Bubblers believe that bubbles are created by small group of evil people who plan to profit from them, with the Illuminati, hedge funds, Goldman Sachs and the Federal Reserve as prime suspects. Paranoid and ever-watchful, they are convinced that stocks are manipulated by larger and more powerful forces and that we are all helpless in the face of this darkness.
5. Righteous Bubblers draw on a puritanical streak to argue that if investors are having too much fun (because stocks are going up), they have to be punished with a market crash. As the Flagellants in the bubble world, they whip themselves into a frenzy, especially during market booms.
6. Rational Bubblers uses market metrics that are both intuitive and widely used, note their divergence from historical norms and argue for a correction back to the average. Viewing themselves as smarter than the rest of us and also as the voices of reason, they view their metrics as infallible and mean reversion in markets as immutable.

There are three things to keep in mind about bubblers. The first is that bubblers will receive disproportionate attention in the media, for the same reasons that a reality show about a dysfunctional family will have higher ratings than one about a more normal family. The second is that even the most misguided bubblers will be right at some point in time, just as a broken clock is right twice every day. The third is that being right is often the worst thing that can happen to bubblers, because it seems to feed into the conviction that they are always right and leads to increasingly bizarre predictions. It is no coincidence that every market correction in history has created its gurus (who called that correction right) and those gurus have almost always found a way to discredit themselves ahead of the next one.

Defining a Bubble

What is a bubble? The lazy definition is that any time you see a large market correction, it is the result of a bubble bursting, but that is neither a useful definition, nor is it true. To me, a bubble reflects a market disconnect from fundamentals, where prices go up steeply, with no help from the fundamentals. The best way of illustrating this is to go back to an intrinsic value model, where the value of stocks can be written as a function of three fundamentals: the base year cash flows that investors are receiving, the expected growth in these cash flows and the risk in the cash flows:

If cash flows increase, growth rates surge, risk free rates drop or macroeconomic risk subsides, stocks should go up, and sometimes steeply, and there is no bubble.  At the other extreme, if stock prices go up as cash flows decrease, growth rates become more negative and risk free rates and equity risk increase, you have a bubble. It is far more likely, though, that you will be faced with a more ambiguous combination, where shifts in one or more fundamentals (higher growth, higher cash flows, a lower risk free rate or lower macroeconomic risk) may explain the increase in stock prices and you will have to make judgments on whether the increase is larger than warranted. 

Detecting a Bubble
The benefits of being able to detect a bubble, when you are in in its midst rather than after it bursts, is that you may be able to protect yourself from its consequences. But are there any mechanisms that detect bubbles? And if they exist, how well do they work?

a. PE and variants

The most widely used metric for detecting bubbles is the price earnings (PE) ratio, with variants thereof that claim to improve its predictive power. Thus, while the conventional PE ratio is estimated by dividing the current price (or index level) by earnings in the last year or twelve months, you could consider at least three modifications. The first is to clean up earnings removing what you view as extraordinary or non-operating items to come up with a better measure of operating earnings. In 2002, in the aftermath of accounting scandals, S&P started computing core earnings for US companies which can differ from reported earnings significantly. The second is to average earnings over a longer period (say five to ten years) to remove the year-to-year volatility in earnings. The third is to adjust the earnings from prior periods for inflation to get a inflation-consistent or real PE ratio. In fact, Robert Shiller has a time series of PE ratios for US stocks stretching back to 1871, that uses normalized, inflation-adjusted earnings.

In the graph below, I report on the time trends between 1969 and 2013 in four variants of the PE ratios, a PE using trailing 12 month earnings (PE), a PE based upon the average earnings over the previous ten years (Normalized PE), a PE based upon my estimates of inflation-adjusted average earnings over the prior ten years (My CAPE) and the Shiller PE. 

Normalized PE used average earnings over last 10 years & My CAPE uses my inflation adjusted normalized earnings. Shiller PE is as reported in his datasets

While the Shiller PE has become the primary weapon wielded by those who believe that we are in a bubble, perhaps because of the pedigree of its creator,  the reality is that all four measures of PE move together much of the time, with a correlation of close to 90%. (If you are wondering why my time series starts in 1969, I use the S&P 500 and earnings on the index and I was unable to get reliable numbers for the latter prior to 1960. Since I need ten years of earnings to get my normalized values, my first estimates are therefore in 1969.)

To examine whether any of these PE measures do a good job of predicting future stock returns and thus market crashes, I computed the correlation of each PE measure with annual returns on the S&P 500 over one-year, two-year and three-year periods following the computation.

T statistics in italics below each correlation; numbers greater than 2.42 indicate significance at 2% level

First, the negative correlation values indicate that higher PE ratios today are predictive of lower stock returns in the future. Second, that correlation is weak with one-year forward returns (notice that none of the t statistics are significant), become stronger with two-year returns and strongest with three-year returns. Third, there is little in this table to indicate that normalizing or inflation adjusting the PE ratio does much in terms of improving its use in prediction, since the conventional PE ratio has the highest correlation with returns over time periods

Defenders of the PE or one its variants will undoubtedly argue that you don't make money on correlations and that the use of PE is in detecting when stocks are over or under price. For instance, one rule of thumb suggests that a Shiller PE above 15 would indicate an over valued market, but that rule would have kept you out of US equities since 1988. To create a rule that is more reflecting of the 1969-2013 time period, I computed the 25th percentile, the median and the 75th percentile of each of the PE ratio measures for this period.

PE measures: 1969-2013

I then broke my sample down into four quartile classes with each PE ratio, from lowest to highest, and computed the annual stock market returns in the years following:

One-year and Two-year stock returns

The predictive power improves for PE ratios with this test, since returns in the years following high PE ratios are consistently lower than returns following low PE ratios. Normalizing the earnings does help, but more in detecting when stocks are cheap than when they are expensive. Finally, the inflation adjustment does nothing to improve predictive returns.

Note, though, that this test is biased by the fact that the quartiles were created using data from the period on which the test is run. Thus, the conclusion that you can draw from this table is that if you had known, in 1969, what the distribution of PE ratios for the S&P 500 would look like for the next 45 years (which would suggest amazing foresight on your part), you could have made money by buying when PE ratios were in the bottom quartile of the distribution and selling in the top quartile.

b. EP Ratios and Interest Rates

One of the biggest perils of using the level of PE ratios as an indicator of stock market pricing, as we have in the last section, is that it ignores the level of interest rates. If  interest rates are lower, PE ratios should be higher and ignoring that relationship will lead us to conclude far too frequently (and erroneously) that stocks are over priced in low-interest rate environments. The link between PE ratios and interest rates is best illustrated by looking at how the EP ratio (the inverse of the PE ratio) moves with the T.Bond rate over time. In the figure below, I graph the movements of all four variants of EP ratios as the T.Bond rates changes between 1969 and 2013:

It is clear that EP ratios are high when interest rates are high and low when interest rates are low. In fact, not controlling for the level of interest rates when comparing PE ratios for a market over time is an exercise in futility.

This insight is not new and is the basis for the Fed Model, which looks at the spread between the EP ratio and the T.Bond rate. The premise of the model is that stocks are cheap when the EP ratio exceeds T.Bond rates and expensive when it is lower. To evaluate the predictive power of this spread, I classified the years between 1969 and 2013 into four quartiles, based upon the level of the spread, and computed the returns in the years after (one and two-year horizons):

The results are murkier, but for the most part, stock returns are higher when the EP ratio exceeds the T.Bond rate.

c. Intrinsic Value
Both PE ratios and EP ratio spreads (like the Fed Model) can be faulted for looking at only part of the value picture. A fuller analysis would require us to look at all of the drivers of value, and that can be done in an intrinsic value model. In the picture below, I attempt to do so on June 14, 2014:

Intrinsic valuation of S&P 500: June 2014

It is true that this intrinsic value is a function of my assumptions, including the growth rate and the implied equity risk premium. You are welcome to download the spreadsheet and try your own variations.

If your concern is that I have used too low an equity risk premium, you can solve, as I do at the start of each month, for an implied equity risk premium (by looking for that equity risk premium that will give you the current index level) and then comparing that value to historical values for that input:

The current implied ERP of 4.99% is well above the historic average and median and it clearly is much higher than the 2.05% that prevailed at the end of 1999.

Are we in a bubble?
In the table below,  I summarize where the market stands today on each of the metrics that I discussed in the last section:

If you focus on PE ratios, it is true the current levels in the market put it in the danger zone, given past history. However, bringing the level of interest rates into the measure (in the EP spreads) reverses the diagnosis, since stocks look under valued on these measures. Finally, expanding the assessment to look at growth and risk as well in the intrinsic value and ERP measures reinforces suggests that stocks are fairly valued. 

While there are some who are adamant in their belief that the market is in a bubble, I remain unconvinced, especially given the level of rates today. To those who argue that earnings could drop, growth could turn negative, interest rates could go up or that there could be another global crisis lurking around the corner, has there ever been a point in time in stock market history where these concerns have not existed? And even if they do exist, the reason we demand an equity risk premium in the first place is for the uncertainty that we feel about macroeconomic variables driving value.

Bubble Belief to Bubble Action: The Trade Off

While I believe that the risk that we are in a bubble is over stated by PE ratio comparisons, you may come to a very different conclusion. Even if you do, though, should you act on that belief? The answer is not clear cut, since there are two ways you can respond to a bubble. The first, which I will term the passive defense, is to reduce the amount of your portfolio allocated to equity to a lower number than you would normally hold (given your age, liquidity needs and risk aversion). The second which I term the active defense is to try to profit off the market correction by selling short (or buying puts). The trade off is then between the cost and the benefit of acting:

• The cost of acting: If you decide to act on a bubble, there is a cost. With the passive defense,  the money that you take out of equities has to be invested somewhere safe (earning a risk free rate, or something close to it) and if the correction does not happen, you will lose the return premium you would have earned by investing stocks. With an active defense, the cost of being wrong about the correction is even greater since your losses will increase in direct proportion with how well stocks continue to do. (Note that using derivatives to protect yourself against market corrections or for speculation will deliver variants of these defenses.)
• The benefit of acting: If you are right about the bubble and a correction occurs, there is a payoff to acting. With the passive defense, you protect your investment (or at least that portion that you shift out of equities) from the drop. With the active defense, you profit from the drop, with the magnitude of your profits increasing with the size of the correction.

The trade off then becomes a function of three variables: how certain you feel about the existence of a  bubble, how big a correction you see occurring as a result of the bubble bursting and how soon you see the correction coming.

To illustrate the trade off, consider a simple (perhaps simplistic) scenario, where you are fully invested in equities and believe that there is 20% probability of a  market correction (which you expect to be 40%) occurring in 2 years. In addition, let's assume that the expected return on stocks in a normal year (no bubble) is 7.51% annually and that the expected annual return if a bubble exists will be 9% annually, until the bubble bursts. In the table below, I have listed the payoffs to doing nothing (staying 100% in equities) as well as a passive defense (where you sell all your equity and go invest in a  risk free asset earning .5%) and an active defense (where you sell short on equities and invest the proceeds in a risk free asset):

Future value of portfolio in 2 years (when correction occurs)

If you remain invested in equities (do nothing), even allowing for the market correction of 40% at the end of year 2, your expected value is $1.0672 at the end of the period.  With a passive defense, you earn the risk free rate of 0.5% a year, for two years, and the end value for your portfolio is just slightly in excess of $1.01. With an active defense, where you sell short and invest int he risk free rate, your portfolio will increase to $1.3072, if a correction occurs, but the expected value of your portfolio is only $0.9528, which is $0.1144 less than your do-nothing strategy.

If you feel absolute conviction about the existence of a bubble and see a large correction coming immediately or very soon, it clearly pays to act on bubbles and to do so with an active defense. However, that trade off tilts towards inaction as uncertainty about the existence of the bubble increases, its expected magnitude decreases and the longer you will have to wait for the correction to occur. I know that I am pushing my luck here but I tried to assess the trade off in a spreadsheet, where based upon your inputs on these variables, I estimate the net benefit of acting on a bubble for the passive act of moving all of your equity investment into a risk free alternative:

Payoff to Passive Defense against Bubble (Correction of 40% in 2 years)

The net payoff to acting on a bubble generates positive returns only if your conviction that a bubble exists is high (with a 20% probability, it almost never pays to act) and even with strong convictions, only if the market correction is expected to be large and occur quickly.

On a personal note, I have never found a metric or metrics that  allow me to have the combination of conviction that a bubble exists, that the correction will be large enough and/or that the correction will happen within a reasonable time frame, to be a market timer. Hence, I don't try! You may have a better metric than I do and if it yields more conclusive results than mine, you should be a market timer.

Bubblenomics: My perspective
It is extremely dangerous to disagree with a Nobel prize winner, and even more so, to disagree with two in the same post, but I am going to risk it in this closing section:

1. There will always be bubbles: Disagreeing with Gene Fama, I believe that bubbles are part and parcel of financial markets, because investors are human.  More data and computerized trading will not make bubbles a thing of the past because data is just as often an instrument for our behavioral foibles as it is an antidote to them and computer algorithms are created by human programmers.
2. But bubbles  are not as common as we think they are: Parting ways with Robert Shiller, I would propose that bubbles occur infrequently and that they are not always irrational. Most market corrections are rational adjustments to real world shifts and not bubbles bursting and even the most egregious bubbles have rational cores.
3. Bubbles are more clearly visible in the rear view mirror: While bubbles always look obvious in hindsight, it is far less obvious when you are in the midst of a bubble. 
4. Bubbles are not all bad: Bubbles do create damage but they do create change, often for the better. I do know that the much maligned dot-com bubble changed the way we live and do business. In fact,  I agree with David Landes, an economic historian, when he asserts that  "in this world, the optimists have it, not because they are always right, but because they are positive. Even when wrong, they are positive, and that is the way of achievement, correction, improvement, and success. Educated, eyes-open optimism pays; pessimism can only offer the empty consolation of being right." In market terms, I would rather have a market that is dominated by irrationally exuberant investors than one where prices are set by actuaries. Thus, while I would not invest in Tesla, Twitter or Uber at their existing prices, I am grateful that companies like these exist.
5. Doing nothing is often the best response to a bubble: The most rational response to a bubble is to often not change the way you invest. If you believe, as I do, that it is difficult to diagnose when you are in a bubble and if you are in one, to figure when and how it will dissipate, the most sensible response to the fear of a bubble is to not change your asset allocation or investment philosophy. Conversely, if you feel certain about both the existence of a bubble and how it will burst, you may want to see if your certitude is warranted given your metric.

Attachments:
Raw Data used to estimate PE and EP ratios
PE, EP and other ratios by year: 1969-2013
Intrinsic value for S&P 500: June 14, 2014
Trade off on acting on bubbles

A Disruptive Cab Ride to Riches: The Uber Payoff

On June 3, news reports carried the story that multiple investors (including big name institutional investors like Wellington & Fidelity) had invested $1.2 billion into Uber, a technology company that matches consumers to car services in many cities around the globe. Based on the investment (and the percentage of ownership that these investors were getting in exchange), the imputed value for Uber (pre-money, i.e., prior to the influx of $1.2 billion) was $17 billion, a mind-boggling sum for a business that generates a few hundred million in revenues and has little to show in terms of operating income. That said, Uber has lots of company in this high-value space, with Airbnb and Dropbox being two other companies that in recent months have been valued at more than $10 billion by investors. With all these companies, the key selling point is disruption, the latest buzzword in strategy, with company owners arguing that they are upending existing ways of doing business (hailing a taxi, with Uber, and finding lodging, with Airbnb) and given the sizes of the businesses that they were disrupting, that the sky is the limit on value. 

If you are old enough to remember market fevers from past booms, you are probably inclined to dismiss both the claims and the valuations as fantasy. I do believe, however, that there is a kernel of truth to the disruption argument though I think investors are being far too casual in accepting it at face value. As I attempt to attach a value to Uber, I have to confess that I just downloaded the app and have not used it yet. I spend most of my of life either in the suburbs, where I can go for days without seeing a taxi, or in New York City, where I find that the subways are a vastly more time-efficient, cheaper and often safer mode of transportation than taxis. 

Uber: The business model

Uber is not in the taxi business, at least in the conventional sense, since it owns no cabs and has no cab drivers as employees. Instead, it plays the role of matchmaker, matching a driver/car with a customer looking for a ride and taking a slice of the fare for providing the service. Its value comes from the screening that it does of the drivers/cars (to ensure both safety and comfort), its pricing/payment system (where customers choose the level of service, ranging from a car to a SUV, are quoted a fare and pay Uber) and its convenience (where you can track the car that is coming to pick you up on your phone screen). The figure below captures the steps in the Uber business model, with comments on what it is that Uber offers at each stage and whether that offering is unique:

Uber has been able to grow at exponential rates since its founding in 2009 by Garrett Camp and Travis Kalanick, with the latter (who is new CEO) claiming that it is doubling its size every six months. While we have no access to the company's financials, there have been periodic leaks of information about the company that allow us to get a sense of its growth. Here, for instance, was a picture that was widely dispersed in December 2013 of a five-week period in late 2013:

While the company claimed to be outraged by the leak, it played nicely into the narrative of growth that it was selling to its investors. In fact, the December leaks suggested that the company generated gross receipts (the fares paid by customers for cab rides) of $1.1 billion, which would translate into revenues of $220 million (based on the 20% slice that Uber claims for itself). That was a few months ago and at the rates at which the company is growing, I would not be surprised if the updated values for both numbers are higher; I will be using $1.5 billion for the gross receipts and $300 million as revenues for Uber as base year numbers.

There was no information that I could find on the company's expenses and income, but according to public sources, the company has 900 employees in its different locations and that it pays them reasonably well. Uber has been active in both marketing its service and offering deals to attract firms time customers and has an active technology department (doing the equivalent of R&D). In summary, these expenses are likely to have been much larger than the revenues (of $300 million) posted during the period. Since the company can legitimately argue that some of these expenses (such as the R&D and customer acquisition costs) are more in the nature of capital expenditures than operating expenses, I will assume (generously) that the company generated an operating income of $10 million in the most recent 12 months. (The effect on value of changing this number is relatively small).

An intrinsic valuation of Über

There are many who will argue that this too young a company and that there is too much uncertainty for an intrinsic valuation. I have argued in prior posts and in this paper that this argument is a cop-out, since not dealing with uncertainty does not make it go away. Having said that, I would hasten to add that what follows is my estimate of value for Uber, not the true value.

A. Potential Market: Size and Growth

For my base case valuation, I am going to assume that the primary market that Uber is targeting is the taxi and limo service market, globally. I know that there is talk (some from Uber's management and some from analysts) that Uber could extend its reach into other businesses (car rentals, moving and even driverless cars), but I don't see any evidence that it has succeeded in making any breakthroughs  (yet) and will come back to this question later in my post.

The global market for taxis and car services may be a big one but it very splintered, with lots of small, local operators dominating each city. In many cities,  this is also a cash business where there are no easy ways to track the total revenues generated by all operators. However, there is data that we can build on. For instance, there seems to be consensus that the most lucrative cab market in the world is in Japan, where revenues are estimated to be about $20-$25 billion annually just in Tokyo, followed by the UK (with revenues of $14 billion, with the bulk from London) and the US (with $11 billion overall and about $3 billion in New York). Making a judgment that taxi revenues currently in the rest of the world will add another $50 billion to this total, I arrive at a total market for taxi and limo services of $100 billion.

It is true that many cities, especially in Asia and Latin America, are under served currently and that the taxi business globally will continue to grow at  well above the 2-3% rate that we have observed in the US, Japan and UK, and that services like Uber will contribute to the faster growth. I will estimate an expected growth rate of 6% a year for the next decade, increasing the overall market to $183 billion in 2024.

B. Status quo, competition, market share and Über's slice (revenues)

The taxi and limo market currently is dominated by small, local players and is regulated in most cities. The cities restrict entry into the market and in return, they regulate the prices that cabs can charge their customers (more effectively in some cities than others). While Uber has only a minuscule slice of the overall revenues currently, the market share that it can aspire to get will depend upon the following factors:

1. The efficiency of the status quo or producers/consumers:  Under the existing system, cab drivers get a relatively small share of the taxi revenue pie (5-10%) and customers in many cities (which are under served) either find themselves without taxis, have to wait a long time or have to pay outlandishly high prices (as attested by the carfare from Narita airport in Tokyo into the city). Thus, both cab drivers and customers may be open to a different way of doing business.
2. Competition: Uber uses technology to deliver car services to customers, but it is not the only company that is doing so. Other competitors like Lyft aad Hailo also provide similar services and they have their own deep pocketed investors. As I said up front, I am not familiar enough with these different services to have any preferences, but this article compares the experiences of Wall Street Journal reporters with different services and does not find a dominant one.
3. Regulation: The cities where Uber and its competitors are trying to generate their revenues are regulated at the moment, and the the existing players (taxi owners, taxi drivers in traditional companies, city regulators) will make it difficult for these new players to compete. These difficulties will affect the speed with which these services are able to penetrate these markets and increase the costs of operating in the business.

Even an optimist on Uber will have to accept that the combination of regulatory restrictions protecting the status quo and the stream of me-too competitors will make it difficult for the company to dominate this market. Even in an optimistic scenario, the former will add costs to Uber's business model and the latter will put pressure on Uber (as it already seems to be doing in some markets) to reduce it's slice of the gross receipts from 20% to 10-15% or even lower. My estimate that Uber will get a 10% market share of the overall market is at the optimistic end of the spectrum, especially if you view it in conjunction with my assumption that Uber will continue to be able to keep its slice of these gross receipts at 20%.

3. From revenues to profits

To get from revenues to operating profits, we have to consider what Uber's operating expenses will be, once it hits steady state, i.e., does not have to incur large expenses attracting new customers. The structure of the business is such that the operating expenses are largely on creating the infrastructure to provide taxi services in different cities and that once established, the cost of these services should decline relative to revenues. This should lead to healthy operating margins, similar to those earned by other established technology companies. I will assume that Uber's operating margin, in steady state, will be 40%,  towards the top decile of technology companies. 

4. Investing for growth

Right now, Uber does not own the cars that the drivers use and the bulk of the investment is in technology infrastructure (R&D and related expenses). At first sight, this would suggest that the company should be able to grow at high rates, with relatively little reinvestment. However, our experiences with technology companies (including Google, Twitter and Facebook) suggest that Uber will be forced to reinvest, especially as it scales up, and that this reinvestment will take the form of acquiring new technologies and companies. (Consider how much Facebook has spent on acquisitions just in this year)

The metric that I will using for reinvestment is one that you may be familiar with, if you have seen my other young company valuations, and it is the sales to capital ratio. This number measures how much incremental revenue you expect to generate for each incremental dollar of investment; the higher this number, the less capital investment is needed to expand this business. The median value for technology companies on this is about 2.50, the median value for all US companies is about 2.00 and a really high number would be about 10.00. I will assume that the sales to capital ratio for Uber will be 5.00, towards the high end of the spectrum.

5. Risk

Is there a lot of risk in investing in a young, start-up like Uber? Of course, but much of the risk in the investment is survival risk (i.e., that the company will not make it as a going concern) and not operating risk. The discount rate, the primary mechanism for adjusting for risk in a discounted cash flow valuation, is designed to capture the latter and is ill-suited for reflecting the former, notwithstanding venture capitalists'  attempts to push it into a target rates of return. 

Looking at the operating risk side of the equation, the taxi business is a cyclical one, with revenues tied to economic growth. There are only a handful of publicly traded cab companies in the world, but the cost of capital of companies in the transportation business in US dollars is about 7.08% for US companies and 6.93% for global companies.  As a young, start-up with higher fixed costs, Uber is undoubtedly more risky than the average company in this sector and I will assume that its cost of capital is 12% (the top decile of US companies). As it matures and becomes a larger, more profitable company, I will assume that the cost of capital will decline towards 8%, the median for US companies. (I don't think that Uber will carry the debt that a typical transportation company carries and thus will not be able to push its capital towards the industry average of 7%.)

On the risk of failure, Uber has passed its most critical tests. It has a product/service that is generating revenues, has relatively little debt or fixed commitments and most importantly, it has access to capital. In fact, the $1.2 billion in cash that it will raise in its latest round of capital should provide it with enough of a cash cushion to survive leaner times, at least in the near term. As a result, I will assume that there is only a 10% chance of failure in Uber and that the company's liquidation value will be zero.

6. The value

With these pieces in place, I arrive at a base case valuation of $5.895 billion for Uber, as shown in the figure below:

Valuation of Uber, June 8, 2014

The value of $5,895 million is a value for the operating assets and any existing cash would have to be added back and debt netted out. Given that neither debt nor cash is likely to be a large number right now, it is directly comparable to the value that venture capital investors are attaching to the company now. As with my other valuations, you can download this one and make your own judgments on what the future holds for Uber. (This is a generic spreadsheet that you can use to value any start-up and you can try it on Airbnb and Dropbox, if you are so inclined.)

7. Break even points

The imputed value for Uber, based on what investors demanded for their $1.2 billion last week, is $17 billion, well above my estimate of value. It is entirely possible that the error is mine and that I have under estimated a key input into value. In particular, there are three key drivers of Uber's value:
(a) the potential market, which I estimated to be $100 billion

(b) the market share that Uber will command of that market (my estimate is 10%) and

(c) the slice of gross receipts that Uber will get to keep (which I have left at 20%)

Changing any or all of these assumptions will change value. In the table below, I hold the gross receipt slice constant, at 20%, and change the potential market size and Uber's market share to arrive at the following numbers:

Value of operating assets for Uber, keeping revenue slice at 20% and other inputs fixed

The shaded numbers indicate the combinations of total market/market share that you would need to deliver. In particular, the total market has to be either three times bigger than my estimate (around $300 billion) or the market share has to be more than twice my estimate (20% and higher) to justify the $17 billion value.

Holding the market share fixed at 10%, I looked at the effect on value of changing the potential market and the percent of gross receipts that Uber receives, and the effects are summarized below:

Uber operating asset value, holding market share and other inputs fixed.

The effects of a reduced market slice are more devastating to value, with even a $300 billion total market (with a 10% market share) being insufficient to break even, with a $17 billion value, if Uber keeps less than 20% of gross receipts.

The bottom line: Viewed as a car service company, even with optimistic assumptions about market growth, market share and profitability, Uber's value is about $6 billion. The combination of assumptions that you would need to get to $17 billion is improbable, at least in my view. It is possible that I am missing the value of new markets that Uber may be able to enter but I will reexamine that possibility later in this post.

Pricing Uber

As I have argued in many of my blog posts over the last two years, the value of an asset can be very different from its price. The former is determined by the interplay of fundamentals (cash flows, growth and risk) whereas the latter is a function of demand and supply. To price an asset, you follow two simple steps. In the first, you look for a metric that the market is scaling the price to; that metric can be an operating number like revenues or earnings or an intermediate number like number of users or customers. In the second, you identify "comparable" companies, i.e., companies that are like the one that you are valuing and compare the scaled price (the multiple) across these companies. Most investors and analysts are more comfortable pricing assets, rather than valuing them, and this is especially the case with young companies like Uber. So, is that what investors are doing to arrive at the $17 billion price for Uber? To make that judgment, let's look at the choices when it comes to pricing metrics and comparable firms.

Pricing Metric

You cannot compare values or market capitalizations across companies, because companies can vary in terms of size and scale. Dividing the estimated value by a scaling variable creates a multiple that can be compared across companies. With mature companies, you scale market value (equity or enterprise) to measures of earnings, dividing market capitalization by net income to get to a PE ratio or enterprise value by operating income or EBITDA to get an enterprise value multiple. With young companies, where earnings are often negative or minuscule, earnings multiples either cannot be computed or are not meaningful. In fact, the only current operating number that is consistently positive at those companies is earnings, explaining why revenue multiples are so widely used at this stage in the life cycle. The fact that revenue multiples can be computed does not necessarily mean that they are useful in valuation. Dividing Uber's value ($17 billion) by the revenues ($300 million) yields a revenue multiple of 56.67, an outlandishly high number but one that tells you little about the pricing of the company, partly because investors are pricing these young companies on potential, not current performance.

One solution to the problem with current numbers not reflecting potential is to use expected future revenues or earnings in computing multiples. Thus, you could divide the enterprise value today by the expected revenues in five or ten years and compare these forward multiples across companies. Applying this approach to Uber, I divided the enterprise value of $17 billion by my expected revenues in ten years ($3.59 billion) to yield 4.75, still a high number and one that should be compared to the same multiple (enterprise value to future sales) computed for other companies. The problem with this approach is two-fold. The first is that you need to forecast revenues for each company in your sample, not just the company that you are valuing. The second is that these multiples are only as good as your revenue forecasts, making this a joint test of the multiple and your forecasting ability.

In my post on Whatsapp and Facebook's valuation of it, I noted that the metric that best explains the difference in values across companies is not revenues or earnings, but the number of users. While that may strike some as being irrational, it is not unreasonable to assume that companies with more users are better positioned in terms of potential. If Uber, Lyft and Hailo (all of which operate in the taxicab market) were all publicly traded, what equivalent metric would investors focus on? It could be the number the subscribers to the service, the number of rides taken by these subscribers or even the number of cabs covered  by the service.  For the moment, though, we are still in the dark about all of these statistics for these companies.

Comparables

In pricing, the choice of companies that you compare your company to is critical. In fact, one simple way to tilt the pricing in the direction that you want it to go is to change the firms that you use in your comparison. In the case of Uber, we will first try to value it, relative to other publicly traded young technology firms and then try again, relative to private technology companies that have received venture capital infusions in the last year.

If we define Uber's comparable companies as young, technology companies that are being priced on potential, the most obvious subset of companies that we can compare it to are social media companies. In the table below, I update the numbers for social media companies, with key multiples  computed in the last four columns:

Enterprise and market values from June 2014, Trailing 12 month numbers

Since the only number that we have some measure of (and a rough one at that) is Uber's revenues ($300 million), applying the median multiple of 9.22 yields a value of $2.766 billion for Uber. Even applying the highest value (Twitter's EV/Sales of 21.82) yields a value of $6,546 million, well below the  $17 billion estimate. Uber reports the number of cities that it operates in, but it provides no detail on the exact number of subscribers to the service and the number of rides that it provides. Even extrapolating from the leaked report (shown towards the top of this post), that shows up 90,000 new users signing up each week, I get 4.68 million sign ups for a year and perhaps 15 million subscribers overall. Applying the median value of $70/user to this number leaves you with $1.05 billion and even applying the high (Netflix's $568/user) yields a value of just over $8.5 billion.

It is possible that the investors in Uber are comparing its pricing to the imputed pricing of the other non-public "big" companies in this space. In the table below, I have highlighted the largest private technology companies with VC investments in the last 12 months, the imputed valuations and the revenues in 2013 (or at least the best estimates that I could find):

VC investments, imputed valuations and revenues in 2013

Even in the rarefied air of VC valuations, Uber's $17 billion dollar value stands out as an outlier. Applying the median multiple of revenue (32.14) across just these companies to Uber's revenues would still leave you with a valuation just under $10 billion. 

The bottom line: Even if I use the most favorable pricing metric (revenue) and comparable firms (other favored VC targets), it is difficult to justify a price greater than $10 billion. 

Uber, the disruptor

This brings us back full circle to the disruption argument. When Clayton Christensen coined the term "disruptive innovation" a few decades ago, I am sure that he never foresaw its popularity with investors, analysts and companies. Christensen draws a contrast between sustaining innovations, which advance the status quo (and established players) and disruptive innovations, which new entrants introduce to disrupt the status quo. With the latter, Christensen's story mirrors David and Goliath, with the new entrants winning out over larger, entrenched entities, partly because they have little to lose from upending the status quo.

While I admire the big picture perspective that strategists like Michael Porter and Christensen have brought to business, I am, by nature, a skeptic and feel the urge to tie the big picture to the bottom line. As I see it, disruptive innovation affects value at two levels. In the first, it allows a new entrant to enter a targeted market, disrupt the status quo and then capture the excess profits in that market. That can be captured in a discounted cash flow valuation, which is what I attempted to do in my intrinsic valuation of Uber. The second level at which disruptive innovation affects value is more subtle. Assuming that the disruptor is able to succeed in its targeted market, success in that market may allow the disruptor to enter new and potentially larger markets in the future. The fact that these markets are undefined at the moment and the odds of success are low mean that the intrinsic value added from this possibility is small. However, the fact that the disruptor does not have to commit to investing in these new markets until the outcome from the initial market is known, as well as the potentially large profits from this expansion, give it the characteristics of an option. I do not want to entangle myself in the mechanics of option pricing in this post, but the value of this disruption option is an add-on to the intrinsic value and will increase with the size of the potential markets, the uncertainty/risk in these markets and the competitive advantages that the disruptor brings to these markets.

Applying these very general concepts to Uber, the attraction to investors is clear. Uber's contention is that it is targeting the car service market for the moment but its intention is to use success in this market to expand into other markets. While we can be skeptical and uncertain about its chances of success in these fuzzily defined markets, that uncertainty, which would reduce intrinsic value, increases the value of the disruption option. To give Travis Kalanick, the co-founder and CEO of Uber, credit, his subtle pitch that Uber is in the logistics business plays into the option narrative, as does the fog that the company has created around specifics. 

It is easy to see the allure of the option argument, where uncertainty becomes your ally and big markets beckon, but as investors, we need to understand that most deep out-of-the-money options never get exercised and that the company owners/managers cannot be given free rein over narratives. I am not privy to the questions that investors in Uber asked before they made their investment, but I would hope that they pushed Mr. Kalanick to be specific about his expansion plans, the details of  growth and what it is costing to deliver that growth, and most importantly, what will give Uber the exclusivity to be able to advance into new markets faster and more profitably than its competitors (both current and new).

Bottom line: Can the disruption option explain the difference between the assessed value ($17 billion) and the estimated value ($6 billion, with intrinsic valuation)? It is possible but not probable. For the option to be worth $11 billion, the potential markets that Uber can enter, assuming it is successful in the car service business, will have to be at least four times larger than the base market (the $100 billion taxicab market). I know that there is talk of Uber becoming a player in a futuristic world of driverless electric cars, but even if that scenario unfolds, I don't see why Google and Tesla would let Uber have anything more than crumbs off the table.

The end game

The numbers seem to indicate that Uber is being overpriced by investors who have valued it at $17 billion. Since these investors are presumably sophisticated players, how would I explain their pricing? I will not try, since I did not pay the price, but it is worth remembering that even smart investors can collectively make big mistakes, especially if they lose perspective. The tech world is a cloistered one, where the leading players (venture capitalists, managers, serial entrepreneurs) immerse themselves in minutiae and know and talk to each other (and often only to each other). Not surprisingly, they develop tunnel vision where technology (or at least their version of it) is the answer to every problem, the status quo is both inefficient and easily disrupted and 50 times revenues is cheap! If history is any guide, tech geeks are just as capable of greed and irrational exuberance as bankers are.

Attachments
Intrinsic Valuation of Uber
Uber Pricing: Multiples and Comparables