Equities as discounted outcomes

First, some theoretical mumble jumble to make sure we are all on the same page.

Two main theorems are currently at the core of financial asset valuation:

1. The Dividend Discount model (or the two associated theorems, Modigliani-Miller and Discounted Cash Flow model)
2. The Capital Asset Pricing model (itself part of the Modern Portfolio theory)

In one way or another, market participants are using a combination of the two theoretical frameworks when allocating capital to assets.

The Dividend Discount model (DDM) states the following:

which can be simply re-stated as 

where the discount rate is equal to the cost of capital minus the growth rate of dividends.

Unfortunately, this equation only works for companies paying out earnings as dividends. To generalize it, we need to use a combination of Modigliani-Miller (MM) and the Discounted Cash Flow model (DCF). The main conclusion of MM is that the value of a firm is unaffected by how that firm is financed (between debt and equity). The main conclusion of the DCF states that:

This is where the Capital Asset Pricing model (CAPM) comes in. As is commonly known, the main conclusion from the CAPM states that:

where the important variable is

which represents the extra return market participants require to take on risk above the risk-free rate. In equity markets, we refer to this term as the Equity Risk Premium (ERP). This can be thought of as the discount rate to be used for cash flow valuation.

For reference sake, the S&P500 ERP looks something like the following historically (using the forward P/E as the inverse of the expected return and 10y inflation protected yield as the risk free rate):

Tying in all of the above, we can see that when evaluating a stock, a market participant relies heavily on three variables: the estimation of dividends, the estimation of the terminal value and the discounting factor.

Re-writing the DDM, we can see that:

where the PV factor is driven by 

The main issues with the model are that 1) it assumes perfectly knowable dividends and 2) doesn't take into account the volatility of the terminal value.

To give an example, assume a stock that pays out 1$ in dividend in year 1, has a dividend growth of 2% and an equity risk premium of 5%. Using a DDM, the value of the stock should be:

As we can see in this example, roughly 82% of the value of the stock is derived from the terminal value (40.8 / 49.19).

Now let's look at what a change in the ERP will have as an effect on the stock value:

We could break it down between changes in the terminal value and the discounted dividends, but the general idea is that minute changes in the volatility (as represented by the ERP) of the discounted dividends and the terminal value have a dramatic impact on the value of the stock but the delta between changes in volatility and changes in the stock value will move lower with higher volatility levels. 

As a side note, the above is the reason why I don't like comparing bonds and equities in the first place, something that the CAPM forces you to do. Why would I compare two assets with fundamentally different volatility, especially in regards to the terminal value (remember that a bond terminal value under no default is known in advance).

But the market also has a tautological statement that we can use to value assets. Under the assumption of no arbitrage (a very important assumption which I think "mostly" holds), we know that the put-call parity holds at all times:

which can also be re-written as

again, re-arranging we get

What conclusions can we draw from the above? 

First of all, it becomes quite clear that the relationship between stock and bond yields is "unknowable": Call - Put is positively correlated with interest rates (rho), PV(strike) is clearly negatively correlated with interest rates and finally PV(dividends) has a lets say complicated relationship with interest rates (do dividend grow faster than the reduction in the present value?).

Second, and this is the main conclusion from the long diatribe, it becomes quite clear that the future value of an asset is positively correlated with changes in implied volatility. The distribution of outcomes identified by Call - Put increases with implied volatility (i.e. the distribution is more spread out). 

What I find interesting is that when volatility rises, we generally say that "the market is less certain about the future" when we should actually be saying, the market is discounting more varied outcomes. (and here comes the key sentence) Hence, the potential for the realized volatility to be higher than the implied volatility is dramatically reduced the higher the implied volatility, offering the potential for positive gamma P&L. This is the source of the forward returns and why I think of equities as discounted outcomes and not discounted cash flows.

Of course, this falls apart if you don't agree with the no arbitrage environment (which does sometimes happen).

The illusion of debate

I was at a book PR event yesterday (sold as a debate) between Michael Lewis and Owen Jones (a columnist for the Guardian among other things). The subject was Michael's new book The Fifth Risk (which I haven't read yet) on the "ignorance and corruption that is fuelling the destruction of [the US'] fabric". I have been to similar events in the past but typically not on such a polarizing subject (let's just say high frequency trading and genomic research don't draw the masses). 

I was really struck at how one sided both the "debate" (if we can call it that) and the audience was. The evening quickly moved from presenting various stories from the book to a generalized rant against Donald Trump with bursts of laughter from the audience. Now, while I have no sympathies for the current US administration and agree with the view that he is acting more like a dictator than president, I wonder if the lack of debate isn't actually detrimental to my side of the political spectrum. 

This draws me back to what I wrote on the "paradox of tolerance". There are two postures we can adopt when discussing Trump and his supporters:

• Position 1 argues that we are still part of the same country, share the same set of foundational rules and thereby we should be acting in good faith towards one another, refraining from mockery and focusing on the content of the ideas being presented by both sides.
• Position 2 argues that we are facing an intolerant side, that the common values and rules that we used to abide by have been thrown out the window, and thereby we should actively try to squash the opposition by any means necessary.

I think unfortunately most people haven't yet clearly chosen a position and oscillate between the two depending on the comfort they feel (i.e. whether or not they are in the presence of like minded people). I believe one needs to clearly lay out his position and been consistent with it or otherwise run the risk of being portrayed as another angry mob trying to elicit chaos. 

The problem with arguing that we are facing an intolerant side comes from the fact that while we no longer share type 2 ("The shared experience core value set") and type 3 ("The idealist core value set") foundational rules but we nonetheless still share type 1 ("The legal core value set") foundational rules with the opposite side. Ideally, we would be able to create new common experiences and idealised values with the opposite side of the electorate, but the probability of that happening with a divisive figure like Trump is extremely low outside of a war situation. I unfortunately think this is what we should expect going into the next presidential election as Trump will need to find common ground with a larger part of the electorate.

The paradox of tolerance (4/n)

The final question pertaining to the paradox of tolerance is: "how and when should the incoming society accept changes to the set of foundational rules?"

I don't really think it's a question that our societies have changed massively over the course of history and thereby have accepted new sets of foundational rules relatively often. For instance, prior to slavery being outlawed, the set of foundational rules in European nations included the rule "the white race is superior to other races". I tend to think that both progress in science, showing that hierarchy between races isn't verifiable biologically, as well as changes in the moral landscape, where freedom seemed to be the primary goal, led to the decision to make slavery illegal. Over time, the legal decision has become a foundational rule of our western societies, and there is close to no contest of it.

Using the example above, I tend to think that there are two mutually necessary ways for foundational rules to evolve: scientific progress and universal values.

• Scientific progress: in the event that science can be prove that one of our foundational rules is "false" in the scientific sense, that is unverifiable/unfalsifiable, then it follows necessarily that we should (I insist on should and not will, changes take time) dismiss this rule from our foundational set of rules and come up with a new one, based on a falsifiable hypothesis. 
• Universal values: I like the definition of Amartya Sen on this "universal values are values that all people have reason to believe in, not values that all people currently value". Non-violence is the obvious candidate to universal values (and probably the only clear one) as all individuals have reason to believe in it even if some don't currently. 

The paradox of tolerance (3/n)

The third question after 1) what constitutes intolerant behavior? and 2) how do you identify a set of foundational rules? is 3) how do you make sure they are clearly communicated to the whole of society?

Our societies have mostly relied on two mediums of communication.

• Education: education seems the most straightforward way of communicating the set of foundational rules of our society. By promoting these rules from an early age and making sure they are enforced in a non punitive manner has the largest probability of being "ingrained" into our brains. Problems arise when you either do not put the means behind the endeavor and / or if you resort to punitive action against the individuals attending the classes when they transgress a rule. The aim is to keep them in the "educational game". Also, it seems straightforward that having a majority of children whose families abide by another set of foundational rules in a class is probably a bad recipe for getting the new set of foundational rules across. Having a class solely composed of Animist following individuals is probably not the best way to get the set of foundational Manichean rules across. Better to have a mix of Manichean and Animist in the class. 

• Communal events: establishing a sense of belonging to a group through rituals is the second way of clearly communicating the rules to incoming individuals. In our modern societies, these rituals take various forms from attending a permanent residency ceremony to shared cultural events, such as concerts or sports events. The main goal of the receiving society is to make sure that the event is accessible to the incoming individuals. In the event that the incoming individual feels unease or simply doesn't have the means to attend to this communal gathering, the probability that he recreates communal events dedicated to his set of foundational rules drastically goes up.

The capacity of a society to communicate its set of foundational rules clearly to incoming individuals comes down to the capacity to educate and create a sense of belonging. Of course, individuals in the receiving society must have agreed upon a set of foundational rules and feel confident in their moral superiority to be sure to accept incoming individuals who have a different set of foundational rules. 

The paradox of tolerance (2/n)

As identified in the previous piece, the main issue of the paradox of tolerance is in identifying the core rules that our society won't tolerate any transgression of. But how do we recognize something which isn't always vocalized? For instance, I may believe that one of the core values of Dutch society is to let people decide for themselves what is harmful to their person on the observation that coffee shops and prostitution are tolerated. But how can I know for sure? And more importantly, how can I identify the less obvious core values, i.e. those that do not necessarily have physical representation or those that are only made explicit when transgressed.

I can see three different core value sets:

1. The legal core value set which includes everything that has been legislated upon. This is the most explicit and also the most rigid core value set. The list of core values are easily identifiable as well as the punishment for not following these core values.
2. The shared experience core value set which includes all the activities where we lose ourselves into the mass. These experiences include political groups, religions but also concerts and sports events. While some of the rules aren't explicit, the group will typically signify forcefully any transgression. Think about wearing the jersey of the visiting team while sitting in the home fan part of a stadium.
3. The idealist core value set which includes all the figures and events we "look up to" for lack of a better word. These include all experiences of sacrifice of the individual for the collective. For instance, when we talk about the courage this soldier had in defending a strategic position or when we talk about the tenacity of this investigative journalist in identifying the truth at the heart of this political scandal. 

Now in our modern societies, there is a hierarchy that exists between these three different sets. The legal core value set supersedes the shared experience core value set which in turn supersedes the idealist/sacrifice core value set.

The paradox of tolerance (1/n)

From Wikipedia (highlights my own): 

Philosopher Karl Popper defined the paradox in 1945 in The Open Society and Its Enemies Vol. 1 (in note 4 to Chapter 7).

"Less well known is the paradox of tolerance: Unlimited tolerance must lead to the disappearance of tolerance. If we extend unlimited tolerance even to those who are intolerant, if we are not prepared to defend a tolerant society against the onslaught of the intolerant, then the tolerant will be destroyed, and tolerance with them. — In this formulation, I do not imply, for instance, that we should always suppress the utterance of intolerant philosophies; as long as we can counter them by rational argument and keep them in check by public opinion, suppression would certainly be unwise. But we should claim the right to suppress them if necessary even by force; for it may easily turn out that they are not prepared to meet us on the level of rational argument, but begin by denouncing all argument; they may forbid their followers to listen to rational argument, because it is deceptive, and teach them to answer arguments by the use of their fists or pistols. We should therefore claim, in the name of tolerance, the right not to tolerate the intolerant."

This is a subject that has come up repeatedly in my discussions with friends and family over the past couple of years. Two distinct societal movements have brought me back to this question:

1. Immigration of societies with different cultural "values" into European societies
2. Feminism and other identity driven groups

In simple terms, the argument Popper makes is that if we aren't all operating by the same set of foundational rules, then a society cannot be fully tolerant without sowing the seeds of its own demise. The argument can be split into the question of what and how are foundational rules established on one side and what constitutes intolerant behavior. 

Starting with the second question (which is the easy one of course), any intolerant behavior can be deemed as behavior that threatens the viability of the set of foundational rules. Using the recent immigration crisis as an example, if we agree that one rule of the set of European/Western foundational rules is "women have the same rights as men", then tolerating migrants that abide by the foundational rule that "women should be the property of men" puts into question the viability of European/Western societies.

So if the set of foundational rules U1 which includes n rules has any rule that is opposite to the set of foudational rules U2 which includes m rules then U1 and U2 are mutually exclusive. Any individual that would want to  adhere to the set U1 cannot at the same time adhere to the set U2. He can though create a new set U3 which includes some rules from U1 and some rules from U2. But this will again be mutually exclusive with U1 and U2. 

Of course, this is obviously the easy part of the argument. The tough parts are 1) how do you identify rules that are part of a set U(i) of foundational rules? 2) how do you communicate those rules? 3) how can those rules be modified? 

The fraud triptych: Bad blood, Black Edge and Billion Dollar Whale (3/n)

The third and final common thread or theme one can pick up reading these books is the amount of energy spent avoiding getting caught. I find it incredible that they were all able to avoid getting caught for years and the only reasonable explanation is that they put an inordinate amount of energy into the endeavor. Should they be commended for that? Absolutely not. But not recognizing that they are "good" at hiding in plain sight would also be avoiding an inconvenient truth. They are obviously crafty individuals with an uncanny capacity for 1) controlling the message and 2) controlling the feelings of others towards them.

On the issue of "controlling the message", we can discern two types of methods used. The first is being a real PR machine and making sure to be one step ahead of any reporters question. This is what Theranos did. Instead of waiting for the press to come to her, Elizabeth Holmes went straight after the press and exploited the laziness / credulity of reporters covering her company. She did check all the boxes that made a good story from a journalists perspective: young, check, woman, check, mission to save the world, check. The second method is to operate in the shadows. This is what Mathew Martoma of SAC and Jho Low of the 1MBD fund did so effectively. They were able to control the message by operating in an entity that itself carried the message: a hedge fund out to make its investors rich and a sovereign wealth fund making sure the future of the country was secure.

On the issue of "controlling the feelings of others towards them" each of them manufactured trust with the individuals surrounding them. The method through which they created trust was different of course: appearing like the long lost daughter for Elizabeth, being a reliable money maker for Mathew or promising re-election to the prime minster for Jho. They were able able to create trust with people that would open doors for them to perpetrate their fraudulent scheme. In a way they were aided / sponsored by these individuals to go down the route of fraud, either in an interested or disinterested fashion. 

The obvious question one asks after reading each of these books is "What if they had put all their energy into doing something non-fraudulent?". I actually think that is the wrong question to ask. Rather the question that should be asked is "Why weren't they able of doing something non-fraudulent?". The three parts of this brief essay try to outline the reasons: 1) a broken moral compass from an early age, 2) operating in an environment that rewards ends and not means 3) an uncanny capacity for building trust and controlling that trust. And yes of course, they all have sociopathic tendencies in the sense that they are selfish, egocentric individuals using any means necessary to get their needs (power and money) fulfilled.