tag:blogger.com,1999:blog-74580358237877598852026-01-30T07:23:13.949-05:00This is a broad exploration of philosophy, science, mathematics, economics, finance, politics, history and everything else in between. Unknownnoreply@blogger.comBlogger125125tag:blogger.com,1999:blog-7458035823787759885.post-3301998950978308862017-01-31T04:00:00.000-05:002017-01-31T10:31:12.481-05:00

In my post, CAPE - An Alternative Calculation and its followup CAPE Alternative - Update, I discussed an alternative method to average historical earnings which I suggested had some benefits while still remaining  in the spirit in which Benjamin Graham proposed (and Robert Shiller used) it. Today I'll be updating the calculation. A correction. But first there's a correction that needs to

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-18286994487801316022015-01-14T04:00:00.000-05:002015-01-14T04:18:52.727-05:00

Probability distributions have a number of properties which help us summarize and characterize them. We'll look at some of these properties, how they are calculated and what they are used for. Contents: I) Mean II) Median III) Variance IV) Skewness V) Kurtosis I) Mean The mean, or average or "expected value", we've previously defined as: \[\begin{align*} \mu = E(X) &= \sum_x xf(x)

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-25909210660233807202015-01-01T20:00:00.000-05:002015-01-01T20:00:00.113-05:00

Every year we perform a collection of rituals which include, but are not limited to: Staying up late. Drinking, lots of drinking.1 Watching a big colorful ball drop.  Writing "resolutions", a list of things we'll fail to do in the upcoming year (or week.) We dub these rituals "New Year's Celebrations" for the New Year's holiday. But what's most concerning to me is the utter waste of it

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-78343940302930043492014-12-17T04:00:00.000-05:002014-12-17T04:00:01.499-05:00

So I'd like to suggest there's an ambiguity in measuring the cost of capital. As far as I can tell, there isn't always a straight forward consensus on how this should be handled. There are a number of arguments in favor of particular positions. Today I'm going to very briefly present the issue. Real versus Nominal So the first issue is whether the "cost of capital" should we use a "real" rate

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-38227172838114913812014-11-21T04:00:00.000-05:002014-11-21T04:00:10.426-05:00

Sometimes I don't see alternative ways of writing expressions until after the fact. So this will just be a brief modification of a previous post: Relating ROE with ROA and Leverage. The Previous Derivation The previous derivation rested on the following assumptions/definitions: \[\begin{align} ROE &= \frac{EBIT - I}{E} \\ ROA &= \frac{EBIT}{A} \\ A &= D + E \end{align}\] In

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-16576621889791011762014-11-17T04:00:00.000-05:002014-11-26T12:54:49.264-05:00

Previously, I looked at what we'd expect call and put options would be if we assumed that stock returns follow a normal distribution (see the Expected Return of a Call Option and Put Option). My findings indicated that the underlying assumptions of the Black-Scholes pricing model are inconsistent with the mean-variance view of risk. This was not an empirical result, mind you. Empirically, I've

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-8960322336097117882014-11-14T04:00:00.000-05:002014-11-14T04:00:09.671-05:00

For the first two parts in this series see: Exploring Operational Definitions: Part I Exploring Operational Definitions: Part II - Distance Perhaps the "simplest" procedure that most folks have learned is the technique(s) of counting. What I would like to explore is that there are a variety of techniques that we call counting. In some cases they build on one another. In other cases, they are

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-92226611763718269192014-11-10T04:00:00.000-05:002014-11-10T04:00:02.130-05:00

In statistics, there are a variety of calculations referred to as moments. We'll be discussing three types of moments: Raw Moments, Central Moments and Standardized Moments. Raw Moments Given a random variable, $X$, the $n$th raw moment is defined as the expected value of $X^n$ which looks like this for discrete and continuous random variables, respectively: \[\begin{align*} E[X^n] &= \

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-41477110469668308232014-11-03T04:00:00.000-05:002014-11-03T04:00:01.051-05:00

As I mentioned in my previous post - Inflation - Why the official numbers are wrong! - I pointed out that the general theory for which inflation is based upon implies that the "price level" is a vector but measures of inflation represent this as a scalar. Today I want to explore how that complicates the picture for the Quantity Theory of Money. The Equation of Exchange The Quantity Theory of

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-77627088310975789522014-10-31T04:00:00.000-04:002014-11-01T13:04:37.815-04:00

In statistics, a probability distribution is any function, $f(x)$ which is never negative (probability is either 0 or positive) and it sums up to 1 (100%). Mathematically we'd express this as: \[\begin{align*} \forall x f(x)\ge 0 \\ \sum_x f(x) = 1 \end{align*}\] In the case of a continuous random variable, the second formula would be expressed as an integral: $$\int_x f(x)dx = 1$$ There are

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-5293700278743696732014-10-28T05:00:00.000-04:002014-10-28T05:14:25.579-04:00

I'm going to begin a critique of the Efficient Markets Hypothesis (EMH). This is not the first nor will it be the last that have been presented. Most of these critiques accept the basic paradigm an attempt to empirically prove that one can "beat the market". For the practitioner, this can be quite appealing as it allows one to find some strategy that would allow one to earn "excess returns".

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-1053151301930615402014-10-20T05:00:00.000-04:002014-10-20T08:51:42.795-04:00

One of the most difficult things we face in the information age is the problem of too much information. It's everywhere around us. There's absolutely no way for us to get through all of that information much less be able to utilize it. There's even a good deal of research that indicates that, not only are we unable to handle extra information, that additional information may make us less

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-312810014179548602014-09-22T04:00:00.000-04:002014-09-22T16:15:01.666-04:00

In a previous post, CAPE - An Alternative Calculation, I discussed some problems with CAPE (cyclically adjusted price to earnings ratio) and offered a solution which addresses one of those problems which is the growth problem. Today I'll briefly illustrate the growth problem and then look at my solution from an historical perspective. CAPE and the Growth Problem The way Robert Shiller

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-20813051990056156382014-09-02T04:00:00.000-04:002014-09-02T04:00:08.132-04:00

So earlier, in Uncertainty of the Constant Growth Assumption, I discussed how even if we know with certainty (hah!) what rate of growth cash flows (in our example, dividends) will grow at, we may still end up getting the value incorrect. This is due to the fact that actual cash flows are lumpy and don't grow at a nice constant rate but vary quite a bit. The result is that the present value of the

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-15892305332620255392014-08-12T06:00:00.000-04:002014-08-12T06:56:07.501-04:00

So August 11 was a sad day apparently; I managed to misplace my keys. In other news, I found some of the movies you can find on Netflix and Amazon Prime starring a Mr. Robin Williams. There's actually less than I expected. I included the movie The Adventures of Baron Munchausen which I haven't seen but Williams appears to have a minor role. The movie is directed by none other than Terry

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-70155960533567487492014-08-11T04:00:00.000-04:002014-08-25T15:33:57.659-04:00

I'm certainly not the first to claim this and I won't be the last. But I think I'll say this differently than most who happen to say it. For starters, when I refer to inflation, I'm preferring to price inflation.  Some (particularly Austrians), by inflation, mean monetary inflation so I think it's important to be clear on what's being discussed. Many feel that the current inflation

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-5854374466327352682014-07-11T04:00:00.000-04:002014-07-11T04:00:00.123-04:00

Bruce Greenwald, in his book Value Investing: From Graham to Buffett and Beyond, devoted an entire chapter to Intel and its competitive advantages. Of particular note was its economies of scale which permitted it to spend less on research & development than AMD as a percentage of sales. That appears to still be true today but less so: I'm not sure how much one can infer from this. The

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-38441367490979664972014-07-04T04:00:00.000-04:002014-07-04T04:00:00.985-04:00

Every now and then I happen to catch some regular good 'ol fashion TV. Such events are not as common now as I typically stream content from the likes of Netflix and Amazon Prime if I'm going to sit myself down to be entertained. Anyway, I happened to catch a commercial for an upcoming movie called Lucy. Here's the trailer: In the trailer Morgan Freeman (or his character, rather), says the

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-60634563266636066842014-06-30T04:00:00.000-04:002014-06-30T04:00:00.788-04:00

In my previous post, I explored The Expected Return of a Call Option by assuming that stock price returns follow a normal distribution. I then looked at some attributes of the distribution of option returns under that assumption. Today I'll apply the same technique to put options. Put Option Returns I'll stick with the same assumptions I used in the call option example: The stock price

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-3343590783884463772014-06-26T04:00:00.000-04:002014-06-26T04:00:01.808-04:00

So I've made some changes recently. Here's a quick overview of some of the changes (feedback welcome). Look So I've changed the color scheme a bit. It looks different (better?) Take it for what it's worth (probably not much; I'm pretty lazy when it comes to aesthetics.) Share Buttons I've changed the share buttons a bit. If any of them don't work let me know. Reactions These are located

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-22094471675765986072014-06-23T04:00:00.000-04:002014-06-23T04:00:01.057-04:00

If I were to buy a call option, what return should I expect to get? Is it worth buying? Or is it a losing proposition? Today I hope to address this question from one angle. What does standard finance theory actually have to say about the matter? Now of course standard finance theory may very well be wrong. Some of the assumptions that will be used today are problematic. As it turns out, this

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-54656047675919861272014-06-15T04:00:00.000-04:002014-06-15T04:25:22.548-04:00

In my previous post, I discussed having a healthy dose of skepticism when one sees a correlation between two variables. The relationship may not hold very well out of sample (such as future performance). But I also discussed gold as an inflation hedge and I suggested that gold was a lousy inflation hedge in spite of what most people seem to believe. Today I want to discuss another asset class

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-59707913464701710672014-06-09T04:00:00.000-04:002014-06-09T04:00:00.768-04:00

Today I'm going to touch on a sort of theme I have here and that's regarding on how to assess correlated data. How much can we actually read into it? How do we determine that there's a fundamental relationship that, not only holds well in the past but will continue to do so in the future? To do that I'll be taking a quick look at gold and why I consider the "inflation hedge myth". In short, gold

Unknownnoreply@blogger.com1tag:blogger.com,1999:blog-7458035823787759885.post-23226491803250910342014-06-05T04:00:00.000-04:002014-06-06T19:15:41.444-04:00

This is motivated by a post from David Merkel of the Aleph Blog, called Buy Stocks When Credit Spreads are High, Sell When They are Low. Merkel suggests that "credit spreads and implied volatility are cousins. When there is complacency, both are low. When there is panic, both are high." I was curious about this relationship. The linear regression looks fairly ugly but grouping both implied

Unknownnoreply@blogger.com0tag:blogger.com,1999:blog-7458035823787759885.post-38674026944359806962014-06-02T04:00:00.000-04:002014-06-02T04:03:41.641-04:00

So in Part I, I began discussing operational definitions. In particular, I've been focusing on the concept of distance. I proposed that we might consider our intuitions regarding answering the question - what is distance? - by means of early experience of operational definitions of distance. The idea being that what we consider distance is going to be closely related to ways we were taught to

Unknownnoreply@blogger.com0