Financial Mathematics Text

Sunday, March 17, 2013

On the Subject Matter of Philosophy

Most disciplines have a very specific, known (and in some cases quite narrow) subject matter. The subject matter of the discipline specifies a domain over which research might take place. For biology, for example, the Greek origins of the term suggest the domain of study is life. Psychology is the study of the mind.

While it's not always the case we can define clear-cut boundaries, there are definite subject matters which we can point and say "that's a question that the psychologists should investigate".

This raises the question of what counts as the genuine subject matter of philosophy. In a broad sense, the term philosophy means "love of wisdom". It seems to encompass all that might be learned or discovered. For example, in its early stages, physics was often referred to as "natural philosophy".

While I am very much sympathetic to this idea, in practice, philosophers have tried to separate their discipline from other disciplines. So what is it that makes philosophy a unique discipline?

Sunday, March 10, 2013

The Dollar is an Excellent Store of Value

To start off, I don't believe the title of this blog, at least not in the usual sense of how the dollar is defined. I would like to suggest, however, that the dollar has been, historically speaking, a good store of value. Whether or not it will do be so in the future is anyone's guess.

If you've ever had the "privilege"  of reading an economics textbook, it will give you a functional definition of money - money is defined in terms its functions. For example, according to the wikipedia article on money, money serves the following four functions:
  1. Medium of Exchange
  2. Unit of Account
  3. Store of Value
  4. Standard of Deferred Payment
The article notes that many economics texts do not list "standard of deferred payment", instead, treating it as parts of the other functions.

As far as the dollar is concerned, it's frequently acknowledged to satisfy 1, 2 an 4 but not 3.  I can use dollars to make all sorts of purchases (medium of exchange), all of the goods and services and debts are denominated in dollars (unit of account) and all of my debts can be dispelled by the use of dollars as a result of legal tender laws (standard of deferred payment).

But regarding store of value, the dollar has not served so well. As I illustrated in Figure 2 from my blog on Currency and Price Stability (reproduced here), the dollar has lost a significant amount of purchasing power over the years.

Wednesday, February 20, 2013

Einhorn and AAPL's preferred shares

So there's a lot of fuss regarding David Einhorn's proposal that Apple (AAPL) issue preferred shares in order to "unlock value".  To be clear, I like Einhorn and even liked his book, Fooling Some of the People All of the Time (in spite of the fact that it was excruciatingly detailed oriented).

But I concur with Prof Damodaran that this doesn't really create value; it simply changes capital structure. Granted, as Damodaran points out this might unlock price (I suspect it would since the market sometimes overprices leveraged situations. The fact that many analyses of Einhorn's strategy assumes that PE ratios will stay the same in spite of the leverage is evidence of this fact. They make the mistake that one wouldn't make if one understood the ideas in this post.)

But it does enhance value in at least one sense. Cash distributed now is worth more than cash sitting in an account earning next to nothing in interest. 

But I'm more interested in this question: is 4% the correct price for the preferred shares?

Monday, February 18, 2013

Understanding Enterprise Value

There's a procedure used when evaluating stocks of subtracting cash or subtracting "net cash". I don't think it's well understood so I'll give a brief presentation here.

The procedure is actually based upon two observations:

Thursday, January 31, 2013

Grassmann's Real versus Formal distinction

So I'm currently reading A History of Vector Analysis written by Michael J. Crowe (or to say it another way, I'm not normal). I came across the book after reading this article: Hermann Grassmann and the Creation of Linear Algebra which I read because I have an interest in the development of linear algebra (aka I'm not normal).

Crowe quotes at some length from a book written by Grassmann entitled: Die lineale Ausdehnungslehre ein neuer Zweig der Mathematik: dargestellt und durchAnwendungen auf die übrigen Zweige der Mathematik, wie auch auf die Statik,Mechanik, die Lehre vom Magnetismus und die Krystallonomie erläutert (which in German means tl;dr). But he makes the following distinction:
The primary division in all the sciences is into the real and the formal. The former represent in thought the existent as existing independently of thought, and their truth consists in their correspondence with the existent. The formal sciences on the other hand have as their object what has been produced by thought alone, and their truth consists in the correspondence between the thought processes themselves.
From what I'm gathering from what little bits Crowe has quoted, Grassmann thinks that his system (which from what I gather was an early form of modern day linear algebra) as being merely "formal". It's existence has been posited through pure thought but it doesn't correspond to anything in the world (outside of the correspondence to human thought). Contrast that with geometry which corresponds with space and is therefore an example of a "real" science. He even went so far as to suggest that geometry properly ought not be included within mathematics:
It had for a long time been evident to me that geometry can in no way be viewed, like arithmetic or combination theory, as a branch of mathematics; instead geometry relates to something already given in nature, namely, space.
What he calls "pure mathematics", by contrast is:
... the science of the particular existent which has come to be through thought. The particular existent, viewed in this sense, we name a thought-form or simply a form. Thus pure mathematics is the theory of forms.
I'm not sure how far these distinctions would go today. Consider space for example. In a post-Einstein world, space has different structure when in the presence of objects of mass. Mass actually bends or warps space. And it's not entirely restricted to 3 dimensions as it was in Grassman's day.

On the more "abstract" side of things, the lines are even more blurred. We now deal with infinitely dimensional complex vector spaces to explain such phenomenon as matter waves.

At this point there should be a cue for a joke about Hilbert spaces but I'm too lazy to write one. So I'll just get a room in his hotel and crash for the night.




Sunday, January 13, 2013

What is a Financial Bubble? Part I

The idea that drives this metaphor is blowing a bubble. One can blow it larger and larger but eventually it pops. Some economists have denied the existence of bubbles while others have expressed skepticism that the concept is well-defined enough to be scientifically meaningful. Eugene Fama, a prominent supporter of the Efficient Markets Hypothesis, stated as much in an interview in The New Yorker.

I share these reservations over defining a bubble but I still suspect it's a useful concept. As a result, I'd like to explore the issue a bit. I'll be doing so in a series looking at various examples and aspects of financial bubbles in order to get a better grip on whether or not we can give it a meaningful definition.

Sunday, January 6, 2013

Gettier Intuition

One common criterion used to determine whether or not something is knowledge is the "justified true belief" criterion (JTB). It has many forms but the basic idea is this:

S knows that P means:
  1. S believes that P.
  2. S has justification for believing P.
  3. S is true.
In 1963 Edmund Gettier proposed counterexamples to the above relationship. The idea is pretty simple. Construct a scenario in which (1), (2) and (3) are satisfied, but it fails to be knowledge. We'll look at an example from his original paper: Is Justified True Belief Knowledge? In particular, we'll look at Case I.

Wednesday, January 2, 2013

Downside Risk Investing

I'd like to give some consideration to a class of investment strategies which I call Downside Risk Investing. These strategies earn returns by taking on downside risk while at the same time having limited upside potential. There are a number of strategies that fit this bill which I'll outline below giving several examples.

There's a metaphor that goes around talking about "picking up pennies in front of a steamroller". It's in reference to investment strategies in which the investor risks getting run over by a steamroller (taking the risk of getting wiped out) for the benefit of receiving a couple of pennies. This entire reference is to Downside Risk Investing.

Now in some sense, many investment strategies have the potential for huge losses with limited upside. The question we should be asking is this: how many pennies do I need to be able to pick up for a particular Downside Risk Investing to be a good strategy? I don't know if I have an answer to that question but I'd like to present a discussion. So without further ado, here are some examples of strategies that I think fit the bill (some of which may be good strategies to employ).