Financial Mathematics Text

Showing posts with label investing. Show all posts
Showing posts with label investing. Show all posts

Wednesday, December 17, 2014

Some Ambiguities Regarding the Cost of Capital

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.

Monday, November 17, 2014

Option Returns - Empirical Results

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 yet to find a single set of financial data that was normally distributed. It was a theoretical result; the theory is inconsistent with a mean-variance view of risk and return.

Today I'll be looking at some odd empirical results. I wanted to see what actual returns actually looked like. As it turns out, they're even worse than what the theory predicts.

Tuesday, October 28, 2014

The Efficient Markets Hypothesis is Meaningless

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".

My approach, which I've been toying with in my mind for the last year or so, is going to be a bit different. My contention is that the entire paradigm is questionable and perhaps "meaningless"1. At the very least, proponents of EMH have a a lot more work to do as there is a lot of ideological baggage and not much in the way of a legitimate scientific hypothesis.

Monday, October 20, 2014

How to Ignore the Noise in Financial News

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 accurate and more confident in our inaccurate predictions: The illusion of knowledge: When more information reduces accuracy and increases confidence.

Now it seems to me that there are at least three goals we need to focus on in order to handle all of this information:
  1. Focus on important information.
  2. Ignore the useless noise.
  3. Know what we do not know.
While I think this is important in general terms, there is the question of how to deal with financial news. 

Monday, September 22, 2014

Cape Alternative - Update

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.

Monday, January 20, 2014

CAPE - An Alternative Calculation

Today I want to look at an alternative way to calculating the Cyclically Adjusted Price to Earnings Ratio or CAPE for short. The standard approach to CAPE suffers from a few drawbacks and I think the calculation I'm proposing can address some of those drawbacks.

Friday, January 3, 2014

Interesting Approach to Predicting Future Stock Returns

So Jesse Livermore (the name on his twitter account, which comes from the trader who is known for his Reminiscences of a Stock Market Operator) has an interesting blog called Philosophical Economics. Under discussion today is an interesting approach to predicting future stock returns. The blog post under question is entitled The Single Greatest Predictor of Future Stock Returns.

In what follows I'll offer a brief summary of the post (he writes longer blog posts than I do!) and a few points of criticism as well. The criticisms offered, I think, will be in the spirit of Jesse Livermore's criticisms of other metrics which attempt to predict future returns (see here).

Friday, December 27, 2013

More on Benjamin Graham and Uncertainty

So in Uncertainty and the Margin of Safety, I suggested that an important concept in physics ought to be applied to investment analysis (and economics for that matter). Furthermore, I suggested that Benjamin Graham's concept of "margin of safety" was linked with this idea of uncertainty.

Today I want to take a closer look at the sorts of uncertainties faced in investment analysis and how Benjamin Graham recommend one face those uncertainties.

Thursday, December 19, 2013

Stock Valuation and Anchoring: AF2P Contest Results

Thanks to everyone that participated in my little study. I'm going to outline what questions I wanted to answer with this study. Hopefully, you will find this information useful.

Introduction


As investors, we're trying to find good companies trading at a good price. But how do we assess what to pay? Obviously there is a good deal we don't know; we must make decisions under conditions of uncertainty.

Wednesday, November 27, 2013

Thoughts On Backtesting

So I have a few methodological thoughts on backtesting strategies. The lack of sound methods in studies is problematic in my opinion. If anyone has some insight into this I'd appreciate it.

I'm going to lay out what I consider three common problems in empirical research into backtesting investing strategies. Not all studies suffer from all three problems but I think a lot do. And I think attempting to address these is a good start.

Thursday, October 24, 2013

Thoughts on the Sharpe Ratio

So this is going to be just a few musings on the Sharpe Ratio. But before that, I want to do a comparison to a technique I utilized because it has similiarities to the Sharpe Ratio. This is also somewhat related to Cullen Roche's question and my response here.

In my blog post, Are Bond Yield Spreads Adequate?, and the subsequent follow-up, Junk Bonds: A Closer Look, I developed a simple model to analyze spreads to see if they were adequate. Today I'll give a more "intuitive" explanation of that model.

Saturday, October 19, 2013

Some Thoughts on Risk/Return Tradeoff and EMH

So this is partly a response to a question asked by Cullen Roche on Twitter:

Is the Stock Market a Ponzi Scheme?

Today I want to explore the question on whether or not the Stock Market is a Ponzi scheme. The reason why is that I think many people view it as such but may not even realize it. So the big question here is this: are they right?

Charles Ponzi's Scheme


Wednesday, October 9, 2013

Junk Bonds: A Closer Look

So one of the questions I asked in Are Bond Yield Spreads Adequate? is whether or not junk bond spreads are adequate. I presented a simple model. The model predicted that returns on junk bonds would be about 2.27% in excess of treasuries. But the uncertainty in the model had a standard deviation of 2.36%. So if we were off by just 1 standard deviation, we would underperform treasuries.

But a model can't be better than the assumptions that one puts into it. I'd like to take a review of the assumptions I used in the model and change a few things. 

Saturday, September 28, 2013

Are Bond Yield Spreads Adequate?

Suppose you have the choice between three classes of assets: treasury bonds, investment grade corporate bonds and speculative grade corporate bonds (junk bonds). Which one should you choose?

Many people wrongly just look at yields. If you look at yields, the answer is simple: choose junk bonds. Junk bonds offer a higher yield.

The problem is that doesn't account for the fact that some junk bonds default and the losses that result from that.

The second issue is the uncertainty in modeling losses. I'm going to be using some models that require assumptions. These assumptions are not perfectly known. So we need to build in a margin of safety to make sure that we outperform treasuries.

Sunday, September 1, 2013

Useless Stock Metrics


So today I'm going to discuss metrics used in stock analysis that I think are useless and largely uninformative. In spite of this, many of these are popular and I would like to suggest they shouldn't be popular. (Granted, I think "pop" music shouldn't be popular so what do I know?)

Some of this will be an extension of a conversation at OSV forum (Firm Versus Equity (apples with apples)) as well as a great blog post by Prof Damodaran on the same subject (A tangled web of values: Enterprise value, Firm Value and Market Cap ). 

So without further ado . . .

Sunday, August 25, 2013

Shareholder Yield (Quasi-Book Review)

Mebane Faber has a nice read entitled Shareholder Yield: A Better Approach to Dividend Investing. If you keep an eye out, you may be able to get it the kindle edition for free. Regardless, it's still less than $6 for either the Kindle or paperback edition. This will be a quasi review/discussion of the book.

To be successful, managers of a company need to be good at two things: operations and capital allocation. While Faber notes many books focus on operations, the focus of this book is devoted to (a subset of) capital allocation.

Capital allocation concerns itself with whether or not to obtain financing, what type of financing (debt, equity, preferred, etc), how and when it should be employed, and how and when it should be paid back. Faber's book is concerned with the latter aspect of paying back financing.

Friday, June 7, 2013

Uncertainty and Margin of Safety

A topic that comes up frequently, and one that I think is not well understood, is the concept of "margin of safety" in value investing. The idea goes back to Benjamin Graham. But before we do that I want to take a detour through the notion of uncertainty.

Uncertainty

There are a few different concepts associated with uncertainty and a few of them have investing applications. I'm going to focus on one which is how it's often used in physics which is measurement uncertainty

Friday, March 22, 2013

Competitive Advantage Types

Economic models often posit the existence of "perfect competition". But in the real world, companies are often able to establish a solid competitive advantage over other companies. This enables them to either be able to charge a higher price than competitors without significantly harming or sales, or it allows them to have lower costs thereby earning them higher profits by charging the same price (or a lower price to compete out competition).

In markets that exhibit "perfect competition", these advantages should be short lived. But in reality, many persist over long periods of time.

The key metrics to look at here are return on capital and cost of capital.  In perfectly competitive markets the two are equal. But sometimes a company can earn a higher return on capital than their cost. If this persists for a long time, it's an indication of a competitive advantage.

In Valuation: Measuring and Managing the Value of Companies, the authors (Koller, Goedhart and Wessels) list a large number of types of competitive advantages. I will reproduce the list here.

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).