Financial Mathematics Text

Monday, December 31, 2012

New Year's Resolutions - 2013

It's a tradition around the New Year to set "New Year's Resolutions". The idea is to reflect on your life and the past year and set goals to achieve certain things or improve oneself. I suppose in principle it's not a bad idea but in practice most people actually fail.

For starters, many people make rather vague goals such as "I'm going to exercise" or "I'm going to be a nicer person". It's not entirely clear what would count as "accomplishing" such goals.

A better approach is to make specific, achievable goals such as "I want to lose 10 lbs by the end of the year" or "I'm going to donate $1000 to charities". These are measurable goals so that when you fail in a couple weeks (and you know you will!) there will be no denying it.

So enough of this nonsense introduction. Here are my resolutions for next year.

Thursday, December 27, 2012

Who are the 1%?

In Income Inequality in the US, I noted that the top 1% (and especially the top 0.1%) have been taking a greater share of productivity gains over the last 50 years (especially since the 1980's).

But that raises the question who are these 1%-ers and why have they been able to take a larger share of productivity gains?

We'll start by looking at some data found in this study which gives a breakdown of the top 1% and top 0.1% for years between 1979 and 2005. Here's a summary of the 2005 data:

Sunday, December 23, 2012

Deriving Graham's Intrinsic Value Formula

In Chapter 11 of Benjamin Graham's The Intelligent Investor, Graham introduces a formula for valuing growth stocks.

$$P = E (8.5 + 2G)$$

where P is the value or price, E are current (or normal) earnings and G is the growth rate. 

In a footnote, Graham remarks:
Note that we do not suggest that this formula gives the "true value" of a growth stock, but only that it approximates the results of the more elaborate calculations in vogue.
He mainly used the formula to show how absurd some implied growth expectations are. In other words:

Thursday, December 20, 2012

That's an Empirical Question: Part IV

This is the 4th part in a series called "That's an Empirical Question". For the other parts of this series see here:

Part I
Part II
Part III

I think this one deserves an appropriate subtitle.

Is Induction Always Empirical?

In Part II, I suggested that induction is an important "empirical tool". Assuming that's true, that still raises the question whether all uses of the "induction tool" necessarily amounts to an "empirical investigation".

To explore this, as per usual, I will use an example: The Goldbach Conjecture.

Wednesday, December 19, 2012

Dave Ramsey and Asset/Liability Matching

While I don't personally follow Dave Ramsey's advice, I do occasionally read his column in the Sunday paper. In spite of that, generally I think it's good advice and more people would do well to follow it. With private debt levels at very high levels right now, especially household debt, it makes sense to take a close look at how we use debt and whether or not its appropriate.

His most recent post gave me pause for concern though. A family has some money saved in a mutual fund for their son's college tuition. Dave recommends keeping the money there "until right before you write the checks." His rationale is that he returned 16% last year and he's hoping to get at least another 10% this year.

This is not sound advice. The reason comes down to asset/liability matching.

Tuesday, December 18, 2012

Is Housing an Investment?

The conventional wisdom says that it is. I'd like to suggest it's a little more complicated than that. Rather than suggesting that housing is an investment, I will argue that housing can be an investment and spell out under what conditions it is.

To some extent I will be relying on the Graham & Dodd definition of an investment. According to Graham & Dodd (from Security Analysis):
An investment operation is one which, upon thorough analysis, promises safety of principal and a satisfactory return. Operations not meeting these requirements are speculative.
 Regarding speculation, two types of speculation are classified (Graham & Dodd):
  1. Intelligent Speculation - The taking of a risk that appears justified after careful weighing of the pros and cons.
  2. Unintelligent Speculation - Risk taking without adequate study of the situation.
Most home buyers would classify as not giving "adequate study of the situation".

So when is a house an investment? 

Monday, December 17, 2012

That's an Empirical Question: Part III

This is a follow-up in a series exploring what the difference between "empirical" versus "mathematical" versus "philosophical" questions. For the other posts in the series see:

That's an Empirical Question: Part I
That's an Empirical Question: Part II

I'd like to consider a thought experiment though I think you can probably find some similar at manufacturing firms in the real world.

Sunday, December 16, 2012

Income Inequality in the US

Here's income inequality in one simple chart.

Friday, December 7, 2012

Are stocks a good value relative to alternatives?

To explore the question about stocks we'll need some criteria and we'll need to look at some various metrics. For simplicity, I will be assuming that "stocks" means the "market" and more specifically the S&P 500. All data and conclusions will be relative to that. The main alternative investment we'll look at are Baa rated corporate bonds.

Sunday, December 2, 2012

Do philosophers know particulars?

In Methodists Vs Particularists, I suggested that philosophers who are particularists may not, in fact, be so. It's possible that there are no particulars that are known per se but rather a broad set of "methods" that are employed. This may not be explicit criterion per se; as a result I shall refer to these simply as "heuristics".

We'll consider a common "simple" example in philosophy: color identification. I believe that most children learn color identification via ostensive definitions. Consider the following scenario: