Happenings – 2012 Dec 29

Christmas vacation continues.

I was away from home over Xmas, from the Saturday afternoon before until the Wednesday evening afterwards… I visited an old friend in Sedona AZ, driving there in two cars with two other friends, but returning alone. It amounted to 500 miles of my driving on Sunday, and 750 on Wednesday. Whew!

Thursday I got caught up on the Coursera class (“Introduction to Computational Finance and Financial Econometrics”) I’m currently taking. This week there was a mistake in a lecture example which was not corrected in the supporting slides. Tsk.

Yesterday I read a little about The Standard Model of elementary particles, but mostly I worked on my annual end-of-year letter. And in the evening I watched some Teaching Company lectures on modern European history (i.e. starting in 1715, with the death of Louis XIV; ending on the eve of World War I).

Today I’ll try to do a mixture of math and the annual letter, and perhaps some more European history in the evening. No, I do not expect a technical post to go out on this Monday, New Year’s Eve.

Happy New Year.

Happenings – 2012 Dec 22

I’ve been doing holiday stuff and work, of course, this past week… now I’m off until Jan. 2… but I have lots of holiday stuff to do.

Oh, so much for the Mayan apocalypse – but did you (a reader of a math blog) really expect the world to end yesterday?

I’ve started a computational finance course from the University of Washington, thru Coursera… one week in, it’s everything the previous course, from Georgia Tech, should have been but wasn’t; I certainly hope it maintains this level. It has lectures with clear examples… although there have been some mistakes in the lectures, they are corrected in the downloadable slides… plenty of background tutorial material in Excel and R for anyone who needs it. (And I can use some of the R training. A four-week class got me up and running in R, but I’m still an apprentice at it. I still want to see journeyman-level solutions.)

Well, I have to get back to holiday preparations. For those of you who celebrate Xmas, whether as a sacred event or secular, I wish you a happy holiday.

Control Theory – Example 2

Review

Let us recall Example 1. Carstens’ final solution was to take K =.032, so that the plant and the parameters were… and the open loop transfer function was:

The corner frequency (the breakpont) is still 4 rad/sec. Here’s the open-loop Bode plot.

Happenings – 2012 Dec 15

There’s not a lot to talk about today.

Most of my free time this week went toward the Coursera class on computational investing… as I said before, the instructor didn’t manage to deliver all that he had hoped… but it forced me to look elsewhere for the CAPM (Capital Asset Pricing Model), and it introduced me to the programming language Python… with which I’m struggling. Since I got two things out of the class, it was worth more than I paid for it (namely, nothing). On the other hand, I spent my time on it….

Since this class was supposed to end tomorrow, and a different but related class is starting Monday, I’m going to bail on this first one and start the new one.

In other news, I have finally stopped following the sic.math newsgroup; there just hasn’t been much at all worth reading. I should get back to looking at the stack exchange for non-research math.

I hope to put out a technical post this coming Monday, but I doubt very much that there will be posts the following two Mondays, which are Christmas Eve and New Year’s Eve respectively. There might not even be a technical post on the first Monday of 2013, because I might still be working on my annual letter which goes out this time of year.

Introduction to CAPM, the Capital Asset Pricing Model

introduction

It can be difficult to find a clear statement of what the Capital Asset Pricing Model (henceforth CAPM) is. I’m not trying to do much more than provide that. In particular, I did not find the wiki article to be useful, even after acquiring a couple of recent books on the subject.

I own six references:

• Sharpe, Wiliam F.; “Investments”, Prentice Hall, 1978; 0-13-504605-X.
• Reilly, Frank K.; “Investments”, CBS College Publishing (The Dryden Press), 1980; 0-03-056712-2.
• Gringold, Richard C and Kahn, Ronald N.; Active Portfolio Management, McGraw-Hil, 2000; 0-07-024882-6.
• Roman, Steven; Introduction to the Mathematics of Finance, Springer, 2004; 0-387-21364-3.
• Benninga, Simon; Financial Modeling, 3rd ed. MIT, 2008; 0-262-02628-7.
• Ruppert, David; Statistics and Data Analysis for Financial Engineering; Springer 2011; 978-1-4419-7786-1.

There is more than one version of the CAPM… Roman (p. 62) tells me that “The major factor that turns Markowitz portfolio theory into capital market theory is the inclusion of a riskfree asset in the model…. generally regarded as the contribution of William Sharpe, for which he won the Nobel Prize…. the theory is sometimes referred to as the Sharpe-Lintner-Mossin (SLM) capital asset pricing model.”

Then Benninga (p. 265) told me about “Black’s zero-beta CAPM… in which the role of the risk-free asset is played by a portfolio with a zero beta with respect to the particular envelope portfolio y.” (We’ll come back to this, briefly.)

Happenings – 2012 Dec 8

Let’s see.

My friend who was visiting last weekend has returned home safely. He left me with something I must have heard before, but I didn’t actually remember: “the plural of anecdote is not data.”

While he was here, we checked the appearance of this blog on Windows under Firefox and Internet Explorer… it looks fine in Internet Explorer, but some of my Mathematica command images are too wide in Firefox (as I said, under Windows). I’m looking at other templates to see if I can fix that. It has always looked fine to me in both Safari and Firefox on my laptop Macs.

Happenings – 2012 Dec 1

There will almost certainly be no technical post this coming Monday; I have a friend in town for the weekend, and I won’t get much if any math done. Friends are important. Oh, we will almost certainly talk about mathematics, and it’s even possible that a discussion will lead to a blog post – but any such post isn’t likely to happen this weekend.